2017
7
1
13
0
Free convective heat and mass transfer of magnetic bioconvective flow caused by a rotating cone and plate in the presence of nonlinear thermal radiation and cross diffusion
2
2
This article explores the heat and mass transfer behaviour of magnetohydrodynamic free convective flow past a permeable vertical rotating cone and a plate filled with gyrotactic microorganisms in the presence of nonlinear thermal radiation, thermo diffusion and diffusion thermo effects. We presented dual solutions for the flow over a rotating cone and a rotating flat plate cases. Similarity variables are employed to convert the nonlinear partial differential equations into ordinary differential equations. Comparisons with previously published work are performed and results are found to be in excellent agreement. The resultant nondimensional governing equations along with associated boundary conditions are solved numerically using Runge–Kutta and Newton’s methods. The impact of pertinent parameters on velocity, temperature, concentration and density of the motile microorganisms along with the friction factor, local Nusselt, Sherwood numbers and the local density of the motile microorganisms was determined and analyzed with the help of graphs and tables. Results proved that there is a significant variation of heat and mass transfer in the flow over a rotating cone and a plate. It is also found that the heat and mass transfer performance of the flow over a rotating cone is significantly high when compared with the flow over a rotating plate.
1

1
21


M.
Gnaneswara Reddy
India
India
Iran
mgrmaths@gmail.com


Sandeep
N
VIT, Vellore
VIT, Vellore
Iran
nsreddy.dr@gmail.com
MHD
Nonlinear thermal radiation
Cross diffusion
Gyrotactic microorganisms
Rotating cone and plate, Free convection
[[1] M. AboeldahabEmad, “Radiation effect on heat transfer in electrically conducting fluid at a stretching surface with uniform free stream”, J. Phys D App. Phys., Vol. 33, No. 24, pp. 3180–3185, (2000). ##[2] M. Gnaneswara Reddy, “Influence of magnetohydrodynamic and thermal radiation boundary layer flow of a nanofluid past a stretching sheet”, Journal of Scientific Research, Vol. 6,No.2, pp. 257272 (2014). ##[3] E. M. AboEldahab, and M. S. Elgendy, “Radiation effect on convective heat transfer in an electrically conducting fluid at a stretching surface with variable viscosity and uniform free stream”, Physica Scripta, Vol. 62, No. , pp. 321325, (2000). ##[4] A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition”,Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, pp. 1064068, (2009). ##[5] R. Cortell, “Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition”, Applied Mathematics and Computation, Vol. 206, No.1, pp. 832840, (2008). ##[6] A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition”, Appl Math Comput, Vol. 217, No. 2, pp. 837842, (2010). ##[7] S. Yao, T. Fang and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions”, Comm Nonlinear SciNumSimul, Vol. 16, No. 2, pp. 752760, (2011). ##[8] A. Alsaedi, Z. Iqbal, M. Mustafa, T. Hayat, “Exact solutions for the magnetohydrodynamic flow of a Jeffrey fluid with convective boundary conditions and chemical reaction”, Z Naturforsch, Vol. 67a, No. 1, pp. 517 524, (2012). ##[9] O. D. Makinde, and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition”, Int. J. Therm Sci., Vol. 50, No.7, pp. 13261332, (2011). ##[10] M. Gnaneswara Reddy, “Thermal radiation and chemical reaction effects on MHD mixed convective boundary layer slip flow in a porous medium with heat source and Ohmic heating”,Eur. Phys. J. Plus, Vol. 129, No. 41, pp.117, (2014). ##[11] M. Gnaneswara Reddy, “Effects of Thermophoresis, viscous dissipation and Joule heating on steady MHD flow over an inclined radiative isothermal permeable surface with variable thermal conductivity”,Journal of Applied Fluid Mechanics, Vol. 7, No. 1, pp. 5161, (2014). ##[12] A. Bejan, Convection Heat Transfer, 3rd edn. Wiley, New York (2013) ##[13] A. Bejan, and R. K. Khair, “Heat and mass transfer by natural convection in a porous medium”, Int. J. Heat Mass Transfer, Vol. 28, pp. 909–918, (1985). ##[14] D. A. Nield, and A. Bejan, Convection in Porous Media, 4th edn. Springer, New York (2013) ##[15] I. Pop, and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford (2001) ##[16] D. B. Ingham, and I. Pop, Transport Phenomena in Porous Media II, Pergamon, Oxford (2002) ##[17] E.M. Sparrow, and J. L. Gregg, “Mass transfer, flow and heat transfer about a rotating disk”, Trans. Am. Sot. Mech. Eng. Ser. C J. Heat Transfer, Vol. 82, No. 4, pp. 294–302, (1960). ##[18] R. G. Hering, and R. J. Grosh, “Laminar free convection from a nonisothermal cone at low Prandtl number”, Int. J. Heat Mass Transfer, Vol. 8, No. 10, pp. 1333–1337, (1965). ##[19] F. Kreith, “Convective heat transfer in rotating systems “, In: Irvine, T.F., Hamett, J.P. (eds.) Advances in Heat Transfer, Vol. 5, pp. 129–251, (1968). ##[20] K. Himasekhar, P.K. Sarma, and K. Janardhan, “Laminar mixed convection from a vertical rotating cone”, Int. Commun. Heat Mass Transfer, Vol. 16, No. 1, pp. 99–106, (1989). ##[21] A.J. Chamkha, “Combined convection heat transfer from a rotating cone embedded in a powerlaw fluid saturated porous medium”, Fluid/Particle Separat. J., Vol. 13, No. 1, pp. 12–29, (2000). ##[22] H.S. Takhar, A.J. Chamkha, and G. Nath, “Unsteady mixed convection flow from a rotating vertical cone with a magnetic field”, Heat Mass Transfer, Vol. 39, No. 4, pp. 297–304, (2003) ##[23] S. Roy, and D. Anil kumar, “Unsteady mixed convection from a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion”, Int. J. Heat Mass Transfer, Vol. 47, No. 8, pp. 1673–1684, (2004). ##[24] M. Gnaneswara Reddy ,and N. Bhaskar Reddy, “Mass Transfer and heat generation effects on MHD free convection flow past an inclined vertical surface in a porous medium”, Journal of Applied Fluid Mechanics, Vol. 4, No. 2, pp. 711, ( 2011). ##[25] R. Bhuvanavijaya, and B. Mallikarjuna,” Effect of variable thermal conductivity on convective heat and mass transfer over a vertical plate in a rotating system with variable porosity regime”, J. Naval Architect. Mar. Eng., Vol. 11, pp. 83–92, (2014). ##[26] M. Gnaneswara Reddy, “Lie group analysis of heat and mass transfer effects on steady MHD free convection dissipative fluid flow past an inclined porous surface with heat generation”, Theoret. Appl. Mech., Vol. 39, No. 3, pp. 233–254, (2012). ##[27] B. Mallikarjuna, A. M. Rashad, Ali J. Chamkha, and S. Hariprasad Raju, “Chemical reaction effects on MHD convective heat and mass transfer flow past a rotating vertical cone embedded in a variable porosity regime”, AfrikaMathematika, Vol. 27, pp. 645665, (2016). ##[28] G. Awad, P. Sibanda, S.S. Mosta, and O.D. Makinde, “Convection from an inverted cone in a porous medium with crossdiffusion effects”, Comp. Maths. Apps. , Vol. 61, No. 5, pp. 1431–1441, (2011). ##[29] N. Sandeep, B. Rushi Kumar and M. S. Jagadeesh Kumar, “A comparative study on convective heat and mass transfer in nonNewtonian nano fluid flow past a permeable stretching sheet”, J. Mol. Liq. Vol. 212, pp. 585591, (2015). ##[30] C.S.K. Raju, and N. Sandeep, Heat and mass transfer in MHD nonNewtonian bioconvection flow over a rotating cone/plate with cross diffusion, Journal of Molecular Liquids, Vol. 215, pp. 115126, (2016). ##[31] M. Gnaneswara Reddy, and N. Sandeep, “Heat and mass transfer in radiative MHD Carreau fluid with cross diffusion”, Ain Shams Engineering Journal, )2016( (Article in Press). ##]
Optimizing control motion of a human arm With PSOPID controller
2
2
Functional electrical stimulation (FES) is the most commonly used system for restoring function after spinal cord injury (SCI). In this study, we used a model consists of a joint, two links with one degree of freedom, and two muscles as flexor and extensor of the joint, which simulated in MATLAB using SimMechanics and Simulink Toolboxes. The muscle model is based on Zajac musculotendon actuator and composed of a nonlinear recruitment curve, a nonlinear activationfrequency relationship, calcium dynamics, fatigue/recovery model, an additional constant time delay, forcelength and forcevelocity factors. In this study, we used a classic controller for regulating the elbow joint angle; a Proportional Integral Derivative controller. First, we tuned the PID coefficients with trial and error, and then a particle swarm optimization algorithm was used to optimize them. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. This PSO PID controller uses particle swarm optimization algorithm to get the required pulse width for stimulating the biceps to reach the elbow joint to the desired angle. The fitness function was defined as sum square of error. The results for PSO PID controller show faster response for reaching the range of the set point than the PID controller tuned by trial and error. However the PSO PID is much better in terms of the rise time and the settling time, the PID tuned by trial and error has no overshoot. The time to reach the zero steady state error is half in PSO PID in comparison to PID tuned by trial and error.
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23
34


Mohammad Hossein
Bayati Chaleshtari
Shahrood University of Technology
Shahrood University of Technology
Iran
mhbayati88@gmail.com


Elahe
Norouzi
MSc. Student, Amirkabir University of Technology, Biomedical Engineering Department, Tehran, Iran
MSc. Student, Amirkabir University of Technology,
Iran
eli.nrz@gmail.com


Habib
Ahmadi
Assistant Professor,Mechanical Engineering Department,Shahrood University of Technology,Shahrood, Iran
Assistant Professor,Mechanical Engineering
Iran
habibahmadif@shahroodut.ac.ir
Functional Electrical Stimulation (FES)
PID Controller
Particle Swarm Optimization Algorithm
Transverse Plane
[[1] C. C. L. Lynch, and M. R. Popovic, “ClosedLoop Control for FES: Past Work and Future Directions”, 10th Annual Conference of the International FES Society, Ottawa, Canada, pp. 5659, (2005). ##[2] S. Bin Mohamed Ibrahim, “The PID Controller Design Using Particle swarm optimization Algorithm”, PhD thesis, University of Southern Queensland, Toowoomba, Australia, pp.132137, (2005). ##[3] D. Blana, E.K. Chadwick, A. Bogert and R. F. Kirsch, “Feedback Control for a High Level Upper Extremity Neuroprosthesis”, ASB 29th Annual Meeting, Cleveland, Ohio, pp. 2833, (2005). ##[4] C. L. Lynch and M. R. Popovic, “Functional Electrical Stimulation”, IEEE Control Systems MaGAzine, Cleveland, Ohio, (2008). ##[5] D. Blana, R. F. Kirsch and E. K. Chadwick, “Combined Feed forward and Feedback Control of a Redundant, Nonlinear, Dynamic Musculoskeletal System”, International Federation for Medical and Biological Engineering, Vol. 47, No. 5, pp. 533542, (2009). ##[6] M. Ferrarin, F. Palazzo, R. Riener and J. Quintern, “ModelBased Control of FESInduced Single Joint Movements”, IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 9, No. 3. pp. 7888, (2001). ##[7] V. M. Zatsiorsky, “Kinetics of Human Motion”, Human Kinetics, New Zealand, pp. 265350, (2002). ##[8] D. Zhang, and W. T. Ang, “Tremor Suppression of Elbow Joint via Functional Electrical Stimulation: A Simulation Study”, Proceeding of the 2006 IEEE, International Conference on Automation Science and Engineering, Beijing, China, pp.7681 (2006). ##[9] A. Maleki and R. Shafaei, “Musculoskeletal Model of Arm for FES Research Studies”, 4th Cario International Biomedical Conference, University of Salford, Ireland UK, (2008). ##[10] Negin HesamShariati, “Control of Reanimation of Paralyzed Arm for Reaching Movement Using FES’’, M. Sc. Thesis, Bioelectrics, Amirkabir University of Technology, 183 pages, (2012). ##[11] K. Kurosawa, R. Futami, T. Watanabe and N. Hoshimiya, “Joint Angle Control by FES Using a Feedback Error Learning Controller”, IEEE Transactions on Neural Systems and Rehabilitation *Corresponding author email address: mhbayati88@gmail.com Engineering, Vol. 13, No. 3, pp. 6277, (2005). ##[12] M. O. Ali, S. P. Koh, K. H. Chong, S. K. Tiong and Z.A. Obaid, "Genetic Algorithm Tuning Based PID Controller for LiquidLevel Tank System", Proceedings of the International Conference on Man Machine Systems (ICoMMS), Kuala Lumpur, Malaysia, pp. 2933 (2009). ##[13] Eberhart R, and J. Kennedy, A New Optimizer Using Particle Swarm Theory. Proc of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan. IEEE Service Center Piscataway NJ, pp. 3943, (1995). ##[14] J. Kennedy, R. Eberhart, Particle Swarm Optimization. Proc of IEEE International Conference on Neural Network, Perth, Australia, IEEE Service Center Piscataway NJ, pp. 19421948, (1995). ##[15] M. Clerc, and J. Kennedy, The particle swarmexplosion stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, Vol. 6, No. 1, pp. 5873, (2002). ##[16] M. Dorigo, V. Maniezzo, and A. Colorni, Ant system: optimization by a colony of cooperationg agents. IEEE Transactions on Systems. Man, and CyberneticsPart B, Vol. 26, No. 1, pp. 2941, (1996). ##[17] Y. Shi, and R. C. Eberhart, A modified particle swam optimizer. IEEE Word Congress on Computational Intelligence, pp. 6973, (1998). ##[18] Zheng Jianchao, Jie Jing, and Cui Zhihua., Particle swam optimization. Science Publishing Company of Beijing. Vol. 22, No. 3, pp. 94112 (2004). ##[19] R. C. Eberhart, and Y. Shi, Comparison between genetic algorithms and Particle Swarm Optimization. Porto V W, Saravanan N, Waagen D, et al. Evolutionary Programming VII. [S.l.]: Springer, pp. 611616, (1998). ##[20] R. C. Eberhart, and Y. Shi, Comparing inertia weights and constriction factors in Particle Swarm Optimization. Proceedings of the Congress on Evolutionary Computation, pp. 8488, (2000). ##[21] N. Higashi, and H. Iba, Particle Swarm Optimization with Gaussian mutation. Proceedings of the 2003 Congress on Evolutionary Computation. Piscataway, NJ: IEEE Press, pp. 7279, (2003). ##[22] M. Clerc, The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. Proceedings of the Congress on Evolutionary Computation. Piscataway, NJ: IEEE Service Center, pp. 19511957, (1999). ##[23] A. Colorni, M. Dorigo, and V. Maniezzo, et al.; Distributed optimization by ant colonies. Proceedings of the 1st European Conference on Artificial Life, pp. 134 142, (1991). ##[24] P. J. Angeline, Using selection to improve Particle Swarm Optimization. Proceedings of the Congress on Evolutionary Computation. Piscataway. NJ: IEEE Press, pp. 8489, (1999). ##[25] Duan Haibin, Ant Colony Optimization theory and Application. Science Publishing Company of Beijing. Vol. 23, No. 1, pp. 8293 (2005). ##[26] Gao Ying, Xie Shengli, Particle swam optimization Algorithm based on simulated annealing (SA) approach .Computer Engineering and Application, Vol. 40, No. 1, pp. 4749, (2004). ##[27] Qinghai Bai, Analysis of Particle Swarm Optimization Algorithm ‘Journal of Computer and Information Science’, Vol. 3, No. 1, pp. 5771, (2010). ##[28] Chen Yonggang, Yang Fengjie, and Sun Jigui.; A new Particle swam optimization Algorithm. Journal of Jilin University, Vol. 24, No. 2, pp. 181185, (2006).##]
Unsteady MHD nonlinear radiative squeezing slipflow of Casson fluid between parallel disks
2
2
Effect of nonlinear thermal radiation on the unsteady magnetohydrodynamic slip flow of Casson fluid between parallel disks in the presence of thermophoresis and Brownian motion effects are investigated numerically. A similarity transformation is employed to reduce the governing partial differential equations into ordinary differential equations. Further, RungeKutta and Newton’s methods are adopted to solve the reduced ordinary differential equations. The effect of nondimensional governing parameters, namely magnetic field parameter, Casson parameter, thermophoresis parameter, Brownian motion parameter, thermal radiation parameter, unsteadiness parameter, velocity slip parameter and temperature slip parameter on velocity, temperature and concentration fields are discussed and presented through graphs. Reduced Nusselt and Sherwood numbers are computed and presented through a table. It is found that rising values of nonlinear thermal radiation parameter depreciate the reduced Nusselt and Sherwood numbers. Thermophoresis and Brownian motion parameters have tendency to regulate the thermal and concentration boundary layers. Rising values of Casson parameter enhances the heat and mass transfer rate.
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35
45


Sathish Kumar
M
VIT University
VIT University
Iran
msathismani@gmail.com


Sandeep
N
VIT University
VIT University
Iran
dr.nsrh@gmail.com


Rushi Kumar
B
VIT University
VIT University
Iran
b.rushikumar@vit.ac.in
Squeezing flow
slip flow
MHD
nonlinear radiation
Casson fluid
[[1]. M. J. Stefan, “Versuch Uber die scheinbare adhesion, Sitzungsberichte der akademie der Wissenschaften in Wien”, Mathematik Naturwissen, Vol. 69, pp. 713721, (1874). ##[2]. J. D. Jackson, “A study of squeezing flow”, Applied Science Research A, Vol. 11, pp. 148152, (1962). ##[3]. S. Ishizawa, “The unsteady flow between two parallel discs with arbitrary varying gap width”, Bulletin of the Japan Society of Mathematical Engineers, Vol.9, pp. 533550, (1966). ##[4]. R. J. Grimm, “Squeezing flows of Newtonian liquid films an analysis include the fluid inertia”, Applied Scientific Research, Vol.32, pp. 149 166, (1976). ##[5]. M.H. Hamdan and R.M. Baron, “Analysis of squeezing flow of dusty fluids”,Applied Scientifc Research, Vol. 49, pp.345354, (1992). ##[6]. C.Y. Wang and R. Sridharan, “Arbitrary squeezing of a viscous fluid between elliptic plates”, Fluid Dynamics Research, Vol. 18, pp. 3551, (1996). ##[7]. H.M. Duwairi, B. Tashtoush and R.A. Damseh, “On heat transfer effects in a viscous fluid squeezed and extruded between two parallel plates”, Heat and Mass Transfer, Vol. 41, pp. 112117, (2004). ##[8]. Khan, Ahmed, Z.A. Zaidi, Mir Asadullah and Syed Tauseef MohyudDin, “MHD squeezing flow between two infinite plates”, Ain Shams Engineering Journals, Vol. 5, pp. 187 192, (2014). ##[9]. S.Nadeem, R.L. Haq, N.S. Akbar and Z.H. Khan, “MHD threedimensional Casson fluid flow past a porous linearly stretching sheet”, Alexandria. Engineering Journal., Vol. 52, pp. 577 582, (2013). ##[10]. S.K. Raju, N. Sandeep and M. Gnaneswara Reddy, “Effect of nonlinear thermal radiation on 3D Jeffrey fluid flow in the presence of homogeneousheterogeneous reaction”, International journal of Engineering Research in Africa, Vol. 21, pp.5268, (2015). ##[11]. M.Mustafa, T. Hayat and S. Obaidat, “On heat and mass transfer in the unsteady squeezing flow between parallel plates”, Meccanica, Vol. 47, pp. 15811589, (2012). ##[12]. S. Islam, Murad Ullaii, Gul Zaman and M. Idrees, “Approximate solution to MHD squeezing fluid flow”, Journal of Applied Mathematics & Informatics, Vol. 29, pp. 10811096, (2011). ##[13]. S.Nadeem, R.U. Haq and N.S. Akbar, “MHD three dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition”,IEEE Transactions on NanoTechnogy, Vol.13, pp.109115, (2014). ##[14]. M.Hatami, Dengwei jing, Dongxing song, M.Sheikholeslami and D.D. Ganji, “Heat transfer and flow analysis of nanofluid flow between parallel plates in the presence of variable magnetic field using HPM”, Journal of Magnetism and Magnetic, Vol. 396, pp. 275282, (2015). ##[15]. G.Domairry and A.Aziz, “Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method”, Mathematical Problems in Engineering., (2009). ##[16]. M. Mustafa, T. Hayat, I. Pop and A. Hendi, “Stagnationpoint flow and heat transfer of a Casson fluid towards a stretching sheet”, Zeitschrift fur Naturforschung A, Vol. 67, pp. 7076, (2012). ##[17]. Mohammad Mehdi Rashidi, Behnam Rostami, Navid Freidoonimehr and Saeid Abbasbandy, “Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects”, Ain Shams Engineering Journal, Vol. 2, pp. 901912, (2014). ##[18]. A.K. Abdul Hakeem, R. Kalaivanan, N. Vishnu Ganesh and B. Ganga, “Effect of partial slip on hydro magnetic flow over a porous stretching sheet with nonuniform heat source/sink, thermal radiation and wall mass transfer”, Ain Shams EngineeringJournal, Vol.5, pp. 913922, (2014). ##[19]. M. Sheikholeslami and D. D. Ganji, “Unsteady Nano fluid flow and heat transfer in presence of magnetic field considering thermal radiation”, Journal of the Brazilian Society of Mathematical Sciences and Engineering, Vol. 37, pp. 895902, (2014). ##[20]. C.Sulochana, M.K. Kishore Kumar, N. Sandeep, “Radiation and chemical reaction effects on MHD thermosolutal Nano fluid flow over a vertical plate in porous medium”, Chemical and Process Engineering Research, Vol.34, pp. 28 37, (2015). ##[21]. M. Sheikholeslami, M. Hatami and G. Domairry, “Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in the presence of time dependent magnetic field”, Journal of the Taiwan Institute of Chemical Engineers, Vol. 46, pp. 4350, (2015). ##[22]. M. Sathish Kumar, N.Sandeep and B. Rushi Kumar, “Effect of nonlinear thermal radiation on unsteady MHD flow between parallel plates”, Global Journal of Pure and Applied Mathematics, Vol. 12, pp. 6065, (2016). ##[23]. N.Sandeep, “Effect of Aligned Magnetic field on liquid thin film flow of magneticnanofluid embedded with graphene nanoparticles”, Advanced Powder Technology, Vol. 28, pp. 865– 875, (2017). ##[24]. M. JayachandraBabu, N.Sandeep, “UCM flow across a melting surface in the presence of double stratification and crossdiffusion effects”, Journal of Molecular Liquids, Vol. 232, pp. 2735, ( 2017). ##[25]. G.Kumaran, N.Sandeep, “Thermophoresis and Brownian moment effects on parabolic flow of MHD Casson and Williamson fluids with cross diffusion”, Journal of Molecular Liquids, Vol. 233, pp. 262 269, (2017). ##[26]. J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, “Effect of frictional heating on radiativeferrofluid flow over a slendering stretching sheet with aligned magnetic field”, Europen Physical Journal Plus, Vol. 132, PP. 7, (2017).##]
Investigation of fluid flow and heat transfer in tube hot metal gas forming process
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2
In this study, hot metal gas forming process of AA6063aluminumtubeis studied with a focus on heat transfer of both fluid and solid phases numerically. An experimental study is simultaneously conducted to validate the numerical method. Some of the most important outputs of the present study, are velocity distribution of fluid inside the tube as well as the fluid in the gap between tube and matrices. As a result of nonhomogenous distribution of temperature on tube surface, circulating flows are generated inside the tube which may have considerable effects on heat transfer phenomenon. It is seen that in 600 s after start, number of the circulating flows doubles. Analysis of temperature distribution reveals thatmiddle part of the tube reaches 500 ̊C after 600 s from process start and other parts have higher temperature. By applying an efficient control method for heater elements, temperature distribution of the tube reaches a homogenous form.
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47
56


Javad
Shahbazi Karami
Faculty of Mechanical Engineering, ShahidRajaee Teacher Training University, Tehran, Iran
Faculty of Mechanical Engineering, ShahidRajaee
Iran
shahbazi.mech@gmail.com


GH.
Payganeh
SRTTU
SRTTU
Iran
g.payganeh@srttu.edu
Hot metal gas forming
Aluminum alloy tube
Fluid flow
Heat transfer
Temperature distribution
Evaluation of combined hardening model in ratcheting behavior of pressurized piping elbows subjected to inplane moments
2
2
In this paper the ratcheting behavior of carbon steel(ASTM A106B) and stainless steel(304L) elbows is studied under steady internal pressure and inplane external moments at frequencies typical of seismic excitations. The finite element analysis with the nonlinear isotropic/kinematic (combined) hardening model has been used to evaluate ratcheting behavior of the elbows. Material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The rate of ratcheting depends significantly on the magnitudes of the internal pressure, dynamic bending moment and material constants for combined hardening model. The results show that the maximum ratcheting is occurred in the hoop direction at crown. Also, the results show that initially, the calculated rate of ratcheting is large and then decreases with the increasing of cycles. Also, the results obtained by using the Combined hardening model gives acceptable adaptation in comparison with the other hardening models(AF and Chaboche hardening models); however this model gives over estimated values comparing with the experimental data.
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57
71


Seyed javid
Zakavi
University of Mohagheh Ardabili
University of Mohagheh Ardabili
Iran
zakavi@uma.ac.ir


Behzad
Shiralivand
Un. of Mohaghegh Ardabili
Un. of Mohaghegh Ardabili
Iran
b.shiralivand@gmail.com


Mohammad
nourbakhsh
Un. of Mohaghegh Ardabili
Un. of Mohaghegh Ardabili
Iran
moh.nourbakhsh65@gmail.com
Ratcheting
Pressurized elbow pipe
inplane bending moment
Strain hardening
Finite element
[[1] J. L. Chaboche, “Timeindependent constitutive theories for cyclic plasticity”, Int. J. of Plasticity, Vol. 2, No. 2, pp.149188, (1986). ##[2] J. L. Chaboche, “On some modifications of kinematic hardening to improve the description of ratcheting effects”. International Journal of Plasticity, Vol. 7, No. 7, pp. 661–678, (1991). ##[3] J. L. Chaboche, “Modeling of ratcheting: evaluation of various approaches”. European Journal of Mechanics, A/Solids, Vol. 13, No. 13, pp. 501–518, (1994). ##[4] J. L. Chaboche , “A review of some plasticity and viscoplasticity constitutive theories”, Int. J. of Plasticity, Vol. 24, No. 10, pp. 1642–1963, (2008). ##[5] N. Ohno, and J. D. Wang, “Kinematic hardening rules with critical state of dynamic recovery, part I: formulations and basic features for ratcheting behavior”. International Journal of Plasticity, Vol. 9, No. 3, pp. 375–390, (1993a). ##[6] N. Ohno, and J. D. Wang , “Kinematic hardening rules with critical state of dynamic recovery, Part II: application to experiments of ratcheting behavior”. International Journal of Plasticity, Vol. 9, No. 3, pp. 391–403, (1993b). ##[7] N. Ohno, “Constitutive modeling of cyclic plasticity with emphasis on ratcheting”. International Journal of Mechanics and Sciences, Vol. 40, No. 23, pp. 251–261, (1998). ##[8] T. Hassan, and S. Kyriakides, “Ratcheting in cyclic plasticity, part I: uniaxial behavior”, International Journal of Plasticity, Vol. 8, No. 1, pp. 91–116, (1992). ##[9] T. Hassan, E. Corona, and S. Kyriakides, “Ratcheting in cyclic plasticity, Part II: multiaxial behavior”, International Journal of Plasticity, Vol. 8, No. 2, pp. 117146, (1992). ##[10] T. Hassan, and S. Kyriakides, “Ratcheting of cyclically hardening and softening materials, Part I: uniaxial behavior”, International Journal of Plasticity, Vol. 10, No. 2, pp. 149–184, (1994a). ##[11] T. Hassan, and S. Kyriakides, “Ratcheting of cyclically hardening and softening materials, Part II: multiaxial behavior”. International Journal of Plasticity, Vol. 10, No. 2, pp. 185212, (1994b). ##[12] M. Abdel Karim, and N. Ohno, “Kinematic hardening model suitable for ratcheting with steadystate”, International Journal of Plasticity, Vol. 16, No. 3, pp. 225240, (2000). ##[13] S. Bari, and T. Hassan, “Anatomy of coupled constitutive model for ratcheting simulation”, International Journal of Plasticity, Vol. 16, No. 34, pp. 381409, (2000). ##[14] S. Bari, and T. Hassan, “Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation”, International Journal of Plasticity, Vol. 17, No. 7, pp. 885905, (2001). ##[15] S. Bari, and T. Hassan, “An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation”, International Journal of Plasticity, Vol. 18, No. 7, pp. 873–894, (2002). ##[16] X. Chen, B. Gao, and G. Chen, “Multiaxial ratcheting of pressurized elbows subjected to reversed inplane bending”, J. Pres. Eq. Syst., Vol. 3, No. 3, pp. 3844, (2005). ##[17] X. Chen, B. Gao, and G. Chen, “Ratcheting study of pressurized elbows subjected to reversed inplane bending”, J. of Pressure Vessel Technology, Vol. 128, No. 4, pp. 525532, (2006). ##[18] X. Chen, R. Jiao, and K. S. Kim, “Simulation of ratcheting strain to a high number of cycles under multiaxial loading”, International Journal of Solids and Structures, Vol. 40, No. 26, pp. 74497461, (2003). ##[19] X. Chen, and R. Jiao, “Modified kinematic hardening rule for multiaxial ratcheting prediction”, International Journal of Plasticity, Vol. 20, No. 45, pp. 871898, (2004). ##[20] X. Chen, R. Jiao, and S.K. Kwang, “On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel”, Int. J. of Plasticity, Vol. 21, No. 1, pp. 161184, (2005). ##[21] X. Chen, Xu. Chen, D. Yu, and B. Gao, “Recent progresses in experimental investigation and finite element analysis of ratcheting in pressurized piping”, Int. J. of Pressure Vessels and Piping , Vol. 101, No. 1, pp. 113–142, (2013). ##[22] W. F. English, “Piping and fitting dynamic reliability programfourth semiannual progress report” Nov. 1986 Apr.1987,GE Nuclear Energy, NEDC 31542, (1988). ##[23] S. Ranganath, H. Hwang, and S. W. Tagart, “Piping and fitting dynamic reliability program”. EPRI Nuclear Power Division, (1989). ##[24] K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Techniques for the investigation of the ratcheting behavior of piping components under internal pressure and simulated seismic loading”, BSSM J. strain, Vol. 28, No. 2, pp. 5390, (1992). ##[25] K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Single frequency seismic loading tests on pressurized branch pipe intersections machined from solid”, J. of strain Analysis, Vol. 28, No. 3, pp. 197207, (1993). ##[26] K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Stress Limits for Pressurized Piping Branch Junctions Under InPlane Run pipe Simulated Seismic Loadings”. ASME J. Pressure Vessel Tec, Vol. 116, No. 2, pp. 150–160, (1994). ##[27] K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Cumulative damage assessment at pressurized piping branch junctions under in plane run pipe simulated seismic bending”, Int. J. pres. ves. piping, Vol. 63, No. 2, pp. 119–128, (1995). ##[28] K. Yahiaoui, D. G. Moffat, and D. N. Moreton, “Response and cyclic strain accumulation of pressurized piping elbows under dynamic in plane bending”, J. of strain analysis, Vol. 31, No. 2, pp. 135–151, (1996). ##[29] K. Yahiaoui, D. N. Moreton, and D. G. Moffat, “Response and cyclic strain accumulation of pressurized piping elbows under dynamic outof plane bending”, J. of strain analysis, Vol. 311, No. 2, pp. 153–166, (1996). ##[30] T. Hassan, T. Lakhdar, and K. Shree, “Influence of nonproportional loading on ratcheting responses and simulations by two recent cyclic plasticity models”, Int. J. of Plasticity, Vol. 24, No. 10, pp. 18631889, (2008). ##[31] T. Igaria, M. Kobayashi, F. Yoshida, and S. Imatani, Inoue, T., “Inelastic analysis of new thermal ratcheting due to a moving temperature front”, International Journal of Plasticity, Vol. 18, No. 9, pp. 11911217, (2002). ##[32] X. Feaugas, and C. Gaudin, “Ratcheting ## process in the stainless steel AISI 316L at 300 K: An experimental investigation”. International Journal of Plasticity, Vol. 20, No. 4, pp. 643662, (2004). ##[33] P. J. Armstrong, and C. O. Frederick, “A mathematical representation of the multi axial Bauschinger effect”. CEGB Report RD/B/N 731, Central Electricity Generating Board. The report is reproduced as a paper: 2007, Materials at High Temperatures, Vol. 24, No. 1, pp. 126, (1966). ##[34] J. L. Chaboche, “Constitutive equations for cyclic plasticity and cyclic viscoplasticity”. Int. J. of Plasticity, Vol. 5, No. 3, pp. 247302, (1989). ##[35] S. J. Zakavi, M. Zehsaz, and M. R. Eslami, “The ratcheting behavior of pressurized plain pipework subjected to cyclic bending moment with the combined hardening model”, Nuclear Engineering and Design, Vol. 240, No. 4, pp. 726737, (2010). ##]
An Experimental Study on the process parameters of Incremental Forming of ExplosivelyWelded Al/Cu Bimetal
2
2
Single point incremental sheet metal forming is a sheet metal forming process that forms products without the complex dies and tools with low cost. In this study, the incremental sheet metal forming process has been experimentally investigated on the explosivelywelded Al/Cu bimetal sheets. Also, the effects of process parameters, such as arrangement of layer`s bimetal, tool diameter and tool path were investigated on the forming force, thickness distribution, formability and roughness. At first, the bimetals were produced by explosive welding process. Then, two tool diameters, step and spiral tool paths and layer arrangement were chosen as input parameters. The results showed that the forming force increases with increasing the tool diameter and using aluminum as a top layer (contact with tool). Also, using spiral tool path increases the average forming force and decreases the maximum thickness changing. The formability increases with increasing the tool diameter and using the copper as top layer with spiral tool path.
1

73
83


Mohammad
Honarpisheh
university of kashan
university of kashan
Iran
honarpishe@kashanu.ac.ir


Ahmad
Gheysarian
University of Kashan
University of Kashan
Iran
ahmad.gheysarian@gmail.com
Incremental forming
Explosivelywelded Al/Cu
Layer Arrangement
Forming force
Thickness distribution
Formability
[[1] Cristino, V. A. M., L. Montanari, M. B. Silva, and P. A. F. Martins. "Towards square holeflanging produced by single point incremental forming." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications Vol. 229, No. 5, pp. 380388, (2015). ##[2] J. E. Jeswiet, Hagan, and A. Szekeres. "Forming parameters for incremental forming of aluminium alloy sheet metal." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture Vol. 216, No. 10, pp. 13671371, (2002). ##[3] M. B. Silva, Pedro Teixeira, Ana Reis, and P. A. F. Martins. "On the formability of holeflanging by incremental sheet forming." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications (2013): 1464420712474210. ##[4] L. V. Montanari, A. Cristino, M. B. Silva, and P. A. F. Martins. "On the relative performance of holeflanging by incremental sheet forming and conventional pressworking." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications Vol. 228, No. 4, pp. 312322, (2014). ##[5] G. Ambrogio, L. Filice, and G. L. Manco. "Warm incremental forming of magnesium alloy AZ31." CIRP AnnalsManufacturing Technology Vol. 57, No. 1, pp. 257260, (2008). ##[6] G. L. Manco, and G. Ambrogio. "Influence of thickness on formability in 6082T6." International Journal of Material Forming Vol. 3, No. 1, pp. 983 986, (2010). ##[7] M. J. Mirnia, B. Mollaei Dariani, H. Vanhove, and J. R. Duflou, "An investigation into thickness distribution in single point incremental forming using sequential limit analysis." International Journal of Material Forming Vol. 7, No. 4, pp. 469477, (2014). ##[8] E. Hagan, and J. Jeswiet. "Analysis of surface roughness for parts formed by computer numerical controlled incremental forming." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture Vol. 218, No. 10, pp. 1307 1312, (2004). ##[9] L. Fratini, G. Ambrogio, R. Di Lorenzo, L. Filice, and F. Micari, "Influence of mechanical properties of the sheet material on formability in single point incremental forming." CIRP AnnalsManufacturing Technology Vol. 53, No. 1. pp. 207210, (2004). ##[10] Iseki Hideo, "An approximate deformation analysis and FEM analysis for the incremental bulging of sheet metal using a spherical roller." Journal of Materials Processing Technology Vol. 111, No. 1, pp. 150154, (2001). ##[11] Iseki Hideo, and Takashi Naganawa, "Vertical wall surface forming of rectangular shell using multistage incremental forming with spherical and cylindrical rollers." Journal of materials processing technology, Vol. 130, pp. 675 679, (2002). ##[12] L. Filice, L. Fratini, and F. Micari. "Analysis of material formability in incremental forming." CIRP annalsManufacturing technology Vol. 51, No. 1, pp. 199202, (2002). ##[13] A. Attanasio, E. Ceretti, and C. Giardini, "Optimization of tool path in two points incremental forming." Journal of Materials Processing Technology Vol. 177, No. 1, pp. 409412, (2006). ##[14] D. Young, and J. Jeswiet. "Wall thickness variations in singlepoint incremental forming." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture Vol. 218, No. 11, pp. 14531459, (2004). ##[15] G. Hussain, L. Gao, and Z. Y. Zhang. "Formability evaluation of a pure titanium sheet in the cold incremental forming process." The International Journal of Advanced Manufacturing Technology, Vol. 37, No. 910, pp. 920926, (2008). ##[16] K. Hamilton, and J. Jeswiet. "Single point incremental forming at high feed rates and rotational speeds: Surface and structural consequences." CIRP AnnalsManufacturing Technology, Vol. 59, No. 1, pp. 311314, (2010). ##[17] AlGhamdi, K. A., and G. Hussain. "SPIF of Cu/steel clad sheet: annealing effect on bond force and formability." Materials and Manufacturing Processes Vol. 31, No. 6, pp. 758763, (2016). ##[18] M. Honarpisheh, M. J. Abdolhoseini, and S. Amini, "Experimental and numerical investigation of the hot incremental forming of Ti6Al4V sheet using electrical current." The International Journal of Advanced Manufacturing Technology Vol. 83, No. 912, pp. 20272037, (2016). ##[19] Honarpisheh, M., Niksokhan, J., and F. Nazari. "Investigation of the effects of cold rolling on the mechanical properties of explosivelywelded Al/St/Al multilayer sheet." Metallurgical Research & Technology Vol. 113, No. 1 p. 105, (2016). [20] Sedighi, M., and M. Honarpisheh, "Investigation of cold rolling influence on near surface residual stress distribution in explosive welded multilayer." ##[20] Sedighi, M., and M. Honarpisheh, "Investigation of cold rolling influence on near surface residual stress distribution in explosive welded multilayer." Strength of Materials Vol. 44, No. 6, pp. 693698, (2012). [21] Honarpisheh, M., M. J. Abdolhoseini, and S. Amini. "Experimental and numerical investigation of the hot incremental forming of ##[21] Honarpisheh, M., M. J. Abdolhoseini, and S. Amini. "Experimental and numerical investigation of the hot incremental forming of Ti6Al4V sheet using electrical current." The International Journal of Advanced Manufacturing Technology Vol. 83, No. 912, pp. 2027 2037, (2016).##]
LQG vibration control of sandwich beams with transversely flexible core equipped with piezoelectric patches
2
2
The purpose of this paper is control of simply supported flexible core sandwich beam's linear vibration equipped with piezoelectric patches under different loads. The effects of external forces imposed on sandwich beam can be reached to a minimum value by designing an appropriate controller and control the beam's vibration. Threelayer sandwich beam theory is used for analytical modeling of sandwich beam vibration. EulerBernoulli beam theory and linear displacement field are used for the facesheets and the soft core, respectively. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. Governing equations of motion are obtained using Hamilton’s principle. The state space equations of system are derived from governing equations of motion, by defining suitable state variables and using Galerkin’s method. The controller is designed using linear quadratic Gaussian (LQG) technique and Kalman filter is used to estimate the state of the system. The numerical results are compared with those available in the literature. The obtained results show that the controller can play a big role toward damping out the vibration of the sandwich beam. It also shows the difference between the vibration of top face sheets and bottom face sheets because of the flexibility of the core and the situations of sensor and actuator on the top or bottom face sheets have an important role on the dynamic response of sandwich beam.
1

85
97


Nima
Nadirian
University of Tabriz
University of Tabriz
Iran
nimanadirian@gmial.com


Hasan
Biglari
Tabriz of University
Tabriz of University
Iran
hbiglari@tabrizu.ac.ir


Mohammad
Hamed
University of Tabriz
University of Tabriz
Iran
ma.hamed@tabrizu.ac.ir
Three layered sandwich theory
Flexible core
Active damping
Linear quadratic regulator
[[1] L. Librescu, and T. Hause, “Recent developments in the modeling and behavior of advanced sandwich constructions: a survey,” Composite Structures, Vol. 48, pp. 117, (2000). ##[2] H. Biglari,and A. Jafari, “Static and free vibration analyses of doubly curved composite sandwich panels with soft core based on a new threelayered mixed theory,” Composite Structures, Vol. 92, pp. 2684 2694, (2010). ##[3] M. Ganapathi, B.P. Patel, and D.P. Makhecha, “Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higherorder theory,” Composites Part B: Engineering, Vol. 35, No. 4, pp. 345355, (2004). ##[4] J. L. Mantari, and C. Guedes Soares, “Generalized layerwise HSDT and finite element formulation for symmetric laminated and sandwich composite plates,” Composite Structures, Vol. 105, pp. 319 331, (2013). ##[5] H. Abramovich, and B. Pletner, “Actuation and sensing of piezolaminated sandwich type structures,” Composite Structure, Vol. 38, No.1–4, 1727, (1997). ##[6] W. C. H. C. Chang, and S. S. Gai, “Forced vibration of composite sandwich beams with piezoelectric sensors and actuators,” 4th Pacific International Conference on Aerospace Science and Technology, Kaohsiung, Taiwan, 2123, (2001). ##[7] S. Kapuria, A. Ahmed, and P. C. Dumir, ”An efficient coupled zigzag theory for dynamic analysis of piezoelectric composite and sandwich beams with damping,” Journal of Sound and Vibration, Vol. 279, No. 1–2, pp. 345 371, (2005). ##[8] L. Azrar, S. Belouettar, and J. Wauer, “Nonlinear vibration analysis of actively loaded sandwich piezoelectric beams with geometric imperfection,” Computers and structures, Vol. 86, No. 2, pp. 2191182, (2008). ##[9] K. Ramesh Kumar, and S. Narayanan, “Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs,” Smart Materials and Structures, Vol. 17, No. 5, pp. 115, (2008). ##[10] P. Dash, and B. N. Singh, “Nonlinear free vibration of piezoelectric laminated composite plate,” Finite Elements in Analysis and Design, Vol. 45, No. 10, pp. 686694, (2009). ##[11] M. Azadi, E. Azadi, and M. Roopaei, “Adaptive inverse dynamics control for vibration suppression,” World Applied Sciences Journal, Vol. 12, No. 12, pp. 23432351, (2011). ##[12] D. Chhabra, P. Chandna, and G. Bhushan, “Design and analysis of smart structures for active vibration control using piezocrystals,” International Journal of Engineering and Technology, Vol. 1, No. 3, pp. 153162 , (2011). ##[13] A. Moutsopoulou, G. Stavroulakis, and T. Pouliezos. “Simulation and modelling of smart beams with robust control subjected to wind induced vibration," Open Journal of Civil Engineering, Vol. 2, No. 3, pp. 106114, (2011). ##[14] E. Hamed, and O. Rabinovitch, “Modeling and dynamics of sandwich beams with a viscoelastic soft core,” AIAA Journal, Vol. 47, No. 9, pp. 21942211, (2009). ##[15] J. N. Reddy, “On laminated composite plates with integrated sensors and actuators,” Engineering Structures, Vol. 21, No. 7, pp. 568593, (1999). ##[16] E. Padoin, O. Menuzzi, E. A. Perondi, and J. Ono Fonseca, ”Modeling and LQR/LQG control of a cantilever beam using piezoelectric material”, 22nd International congress of mechanical engineeringCOBEM 2013, Ribeirão Preto, SP, Brazil. November 37, (2013). ##[17] Y. M. Huang, and T. J. Chen,” Passive piezoelectric absorbers on supperessing vibration of a rotating beam”, Twelfth International Congress on Sound and Vibration, (2005). ##[18] B. D. O. Anderson, and J. B. Moore, "Optimal Control, Linear Quadratic Methods," PrenticeHall Inc., New Jersey, (1989). ##[19] A. R. Damanpack, M. Bodaghi, M. M. Aghdam, and M. Shakeri, ”Active control of geometrically nonlinear transient response of sandwich beams with a flexible core using piezoelectric patches", Composite Structures, Vol. 100, pp. 517– 531, (2013).##]
On the flexural properties of multiscale nanosilica/Eglass/epoxy anisogridstiffened composite panels
2
2
In the present study, multiscale nanosilica/Eglass/epoxy anisogrid composite panels were investigated for flexural properties as a function of nanosilica loading in the matrix (0, 1, 3 and 5 wt.%). The surface of the silica nanoparticles was firstly modified with 3glycidoxypropyltrimethoxysilane (3GPTS). The fourier transform infrared (FTIR) spectroscopy revealed that the organic functional groups of the silane were successfully grafted on the surface of the nanoparticles. It was illustrated that flexural properties of the composite panel loaded from the skin side can be significantly enhanced by incorporating silica nanoparticles. The use of 3 wt.% nanosilica was the most effective in increasing the load bearing capacity and energy absorption value, while the specimen containing 5 wt.% nanosilica demonstrated the highest flexural stiffness. From the results obtained for the anisogrid panels loaded from the skin side, it was found that these structures displayed excellent damage resistance which is represented by their energy absorption capability. Moreover, a significant portion of energy absorbed after the primary failure at the peak load. Finally, the results correlated well with the observation of field emission scanning electron microscopy (FESEM) micrographs where the nanocomposite panels exhibited higher degree of fibermatrix interfacial strength and also enhanced matrix characteristics, imparted by the incorporation of surface modified silica nanoparticles.
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99
108


Reza
EslamiFarsani
Associate Prof., Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, Tehran, Iran
Associate Prof., Faculty of Materials Science
Iran
eslami@kntu.ac.ir


Hamed
Khosravi
Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, Tehran, Iran.
Faculty of Materials Science and Engineering,
Iran
hkhosravi@mail.kntu.ac.ir
Anisogridstiffened composite structures
Multiscale composites
Silica nanoparticles
Surface Modification
3point bending response
Energy absorption
[[1] V. V. Vasiliev, V. A. Barynin, and A. F. Razin, "Anisogrid composite lattice structuresDevelopment and aerospace applications", Composite Structures, Vol. 94, No. 3, pp. 11171127, (2012). ##[2] V. V. Vasiliev, and A. F. Razin, "Anisogrid composite lattice structures for spacecraft and aircraft applications", Composite Structures, Vol. 76, No. 12, pp. 182189, (2006). ##[3] V. V. Vasiliev, V. A. Barynin, A. F. Rasin, S. A. Petrokovskii, and V. I. Khalimanovich, "Anisogrid composite lattice structuresdevelopment and space applications", Composite structures, Vol. 3, pp. 3850, (2009). ##[4] H. Fan, F. Jin, and D. Fang, "Characterization of edge effects of composite lattice structures", Composites Science and Technology, Vol. 69, No. 1112, pp. 18961903, (2009). ##[5] W. Akl, A. ElSabbagh, and A. Baz, "Optimization of the static and dynamic characteristics of plates with isogrid stiffeners", Finite Elements in Analysis and Design, Vol. 44, No. 8,pp. 513523, (2008). ##[6] F. R. Gibson, "Energy absorption in composite grid structures", Advanced Composite Materials, Vol. 14, No. 2, pp. 113119, (2005). ##[7] T. D. Kim, "Fabrication and testing of thin composite isogrid stiffened panel", Composite Structures, Vol. 49, No. 1, pp. 2125, (2000). ##[8] P. Jadhav, and P. R. Mantena, "Parametric optimization of gridstiffened composite panels for maximizing their performance under transverse loading", Composite Structures, Vol. 77, No. 3, pp. 353363, (2007). ##[9] P. Jadhav, and P. R. Mantena, "Impact response and damage evaluation of grid stiffened composite panels", SEM Annual Conference and Exposition on Experimental and Applied Mechanics, USA, (2005). ##[10] E. Wodesenbet, S. Kidane, and S. S. Pang, "Optimization for buckling loads of grid stiffened composite panels", Composite Structures, Vol. 60, No. 2, pp. 159169, (2003). ##[11] H. Khosravi, and R. EslamiFarsani, "On the mechanical characterizations of unidirectional basalt fiber/epoxy laminated composites with 3glycidoxypropyltrimethoxysilane functionalized multiwalled carbon nanotubesenhanced matrix", Journal of Reinforced Plastics and Composites, Vol. 35, No. 5, pp. 421434, (2016). ##[12] M. M. Shokrieh, A. Saeedi, and M. Chitsazzadeh, "Evaluating the effects of multiwalled carbon nanotubes on the mechanical properties of chopped strand mat/polyester composites", Materials and Design, Vol. 56, pp. 274279, (2014). ##[13] M. F. Uddin, and C. T. Sun, "Strength of unidirectional glass/epoxy composite with silica nanoparticleenhanced matrix", Composites Science and Technology, Vol. 68, No. 78, pp. 16371643, (2008). ##[14] A. Chira, A. Kumar, T.V lach, L. Laiblova, A. S. Skapin, and P. Hajek, "Property improvements of alkali resistant glass fibers/epoxy composite with nanosilica for textile reinforced concrete applications", Materials and Design, Vol. 89, pp. 146155, (2016). ##[15] Y. Rostamiyana, A. Fereidoonb, M. Rezaeiashtiyanic, A. H. Mashhadzadeh, and A. Salmankhani, "Experimental and optimizing flexural strength of epoxybased nanocomposite: Effect of using nano silica and nano clay by using response surface design methodology", Materials and Design, Vol. 69, pp. 96104, (2015). ##[16] S. Jacob, K. K. Suma, J. M. Mendez, and K. E. George, "Reinforcing effect of nanosilica on polypropylenenylon fiber composite", Materials Science and Engineering: B, Vol. 168, No. 13, pp. 245249, (2010). ##[17] L. X. Gong, L. L. Hu, J. Zang, Y. B. Pei, L. Zhao, and L. C. Tang, "Improved interfacial properties between glass fibers and tetrafunctional epoxy resins modified with silica nanoparticles", Fibers and Polymers, Vol.16, No. 9,pp. 20562065, (2015). ##[18] P. Panse, A. Anand, V. Murkute, A. Ecka, R. Harshe, and M. Joshi, "Mechanical properties of hybrid structural composites reinforced with nanosilica", Polymer Composites, Vol. 37, No.4, pp. 12161222, (2016). ##[19] H. Khosravi, and R. EslamiFarsani, "An experimental investigation into the effect of surfacemodified silica nanoparticles on the mechanical behavior of Eglass/epoxy grid composite panels under transverse loading", Journal of Science and Technology of Composites, Vol. 3, No. 1, pp. 1120, 2016 (In Persian). ##[20] Y. YE, X. Zeng, H. Qiangli, P. Chen, and C. Ye, "Synthesis and characterization of nanosilica/ polyacrylate composite emulsions by solgel method and insitu emulsion polymerization", Journal of Macromolecular Science Part A, Vol. 48, No. 1, pp. 4246, (2011). ##[21] D. K. Shukla, S. V. Kasisomayajula, and V. Parameswaran, "Epoxy composites using functionalized alumina platelets as reinforcements", Composite Science and Technology, Vol. 68, No. 14, pp. 30553063, (2008). ##[22] N. A. Siddiqui, S. U. Khan and J. K. Kim, "Experimental torsional shear properties of carbon fiber reinforced epoxy composites containing carbon nanotubes", Composite Structures, Vol. 104,pp. 230238, (2013). ##[23] S. Houshyar, A. Shanks, and A. Hodzic, "Modelling of polypropylene fibermatrix composites using finite element analysis", eXPRESS Polymer Letters, Vol. 3, No. 1, pp. 212, (2009). ##[24] A. Mirzapour, M. H. Asadollahi, S. Baghshaei, and M. Akbari, "Effect of nanosilica on the microstructure, thermal properties and bending strength of nanosilica modified carbon fiber/phenolic nanocomposite", Composites: Part A, Vol. 63, pp. 159167, (2014). ##[25] R. EslamiFarsani, S. M. R. Khalili, Z. Hedayatnasab, and N. Soleimani, "Influence of thermal conditions on the tensile properties of basalt fiber reinforced polypropyleneclay nanocomposites", Materials and Design, Vol. 53, pp. 540549, (2014). ##[26] D. R. Bortz, C. Merino, and I. MartinGullon,"Mechanical characterization of hierarchical carbon fiber/nanofibercomposite laminates", Composites: Part A, Vol. 42, No. 11, pp. 15841591, (2011).##]
The effect of small scale and intermolecular forces on the nonlinear Pullin instability behavior of nanoswitches using differential quadrature method
2
2
Using differential quadrature method (DQM), this study investigated pullin instability of beamtype nanoswitches under the effects of smallscale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nanoswitches, electrostatic forces served as the driving force, and vonKarman type nonlinear strain was used to examine nonlinear geometric effects. To derive nonlinear governing equations as well as the related boundary conditions for the nanobeam, variation method was used. Besides, to study the influence of size effect, the nonlocal elasticity theory was employed and the resulting governing equations were solved using DQM. Finally, the pullin parameters were studied using the nonlocal theory and the results were compared with the numerical results of the classical continuum theory as well as experimental results contained in the references. Results demonstrated that taking into consideration the vonKarman type nonlinear strain increases the beam stiffness and hence, the pullin voltage. Besides, use of the small scale, compared with the classical theory of elasticity, yields results much closer to experimental results.
1

109
125


Yaghoub
Tadi Beni
Shahrekord University
Shahrekord University
Iran
tadi@eng.sku.ac.ir


Seyyed Mohammad
Fatemi
Shahrekord University
Shahrekord University
Iran
ytadibeni@yahoo.com
Nanoswitches
NEMS
Nonlocal theory
Pullin instability
DQM
Nonlinear geometry
[[1] L. Zhang, S. V. Golod, E. Deckardt, V. Prinz and D. Grutzmacher, “Freestanding Si/SiGe micro and nanoobjects”, Physica E, Vol. 23, No. 34, pp. 280–284, (2004). ##[2] C. H. Ke and H. D. Espinosa, “Nanoelectromechanical systems (NEMS) and modeling, in: M. Rieth, W. Schommers”, P. D. Gennes (Eds.), Handbook of Theoretical and Computational Nanotechnology, American Scientific Publishers, Valencia, CA, (Chapter 121), (2006). ##[3] Hamid M. Sedighi1, Nazanin Farjam, “A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tipcharge concentration and Casimir attraction”,Microsyst. Technol., DOI: 10.1007/s0054201629566, (2016). ##[4] A. Darvishian, H. Moeenfard, M. T. Ahmadian and H. Zohoor, “A coupled two degree of freedom pullin model for micromirrors under capillary force”, Acta Mech.,Vol. 223, No. 2, pp. 387–394, (2012). ##[5] J. Zhang. Y. Fu, “Pullin analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory”, Meccanica, Vol. 47, No. 7, pp. 16491658, (2012). ##[6] Y. TadiBeni, A. Koochi and M. Abadyan, “Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pullin instability of beamtype NEMS”, Physica E, Vol. 43, No. 4, pp. 979988, (2011). ##[7] H. Sadeghian and G. Rezazadeh, “Comparison of generalized differential quadrature and Galerkin methods for the analysis of microelectromechanical coupled systems”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, pp. 28072816, (2009). ##[8] W. H. Lin and Y. P. Zhao, “Casimir effect on the pullin parameters of nanometer switches”, Microsystem Technologies, Vol. 11, No. 2, pp. 80–85, (2005). ##[9] Y. Ga Hu, K. M. Liew, Q. Wang, X. Q. He and B. I. Yakobson, “Nonlocal shell model for elastic wave propagation in single and doublewalled carbon nanotubes”, Journal of the Mechanics and Physics ofSolids, Vol. 56, No. 12, pp. 3475–3485, (2008). ##[10] M. Danesh, A. Farajpour and M. Mohammadi, “Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method”, Mechanics Research Communications, Vol. 39, No. 1, pp. 23–27, (2012). ##[11] C. W. Lim, C. Li and J. L. Yu, “Free torsional vibration of nanotubes based on nonlocal stress theory”, Journal of Sound and Vibration, Vol. 331, No. 12, pp. 2798–2808, (2012). ##[12] H. Zeighampour and Y. TadiBeni, “Cylindrical thinshell model based on modified strain gradient theory”, International Journal of Engineering Science, Vol. 78, pp. 27–47, (2014). ##[13] M. KarimiZeverdejani and Y. TadiBeni, “The nano scale vibration of protein microtubules based on modified strain gradient theory”, Current. Applled Physics, Vol. 13, No. 8, pp. 1566–1576, (2013). ##[14] S. L. Kong, S. J. Zhou, Z. F. Nie and K. Wang, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science, Vol. 47, pp. 487498, (2009). ##[15] Y. TadiBeni and M. Abadyan, “Sizedependent pullin instability of torsional nanoactuator”, Physica Scripta, Vol. 88, No. 5, pp. 055801, (2013). ##[16] A. C. M. Chong and D. C. C. Lam, “Strain gradient plasticity effect in indentation hardness of polymers”, Journal of Materials Research, Vol. 14, No. 10, pp. 4103–4110, (1999). ##[17] P. Mohammadi Dashtaki and Y. TadiBeni, “Effects of Casimir force and thermal stresses on the buckling of electrostatic nanobridges based on couple stress theory”, Arabian Journal for Science and Engineering, Vol. 39, No. 7, pp. 5753–5763, (2014). ##[18] Y. TadiBeni, A. Koochi and M. Abadyan, “Using modified couple stress theory for modeling the size dependent pullin instability of torsional nanomirror under Casimir force”, International Journal of Optomechatronics, Vol. 8, No. 1, pp. 47–71, (2014). ##[19] H. Zeighampour and Y. TadiBeni, “Sizedependent vibration of fluidconveying doublewalled carbon nanotubes using couple stress shell theory”, Physica E, Vol. 61, pp. 28–39, (2014). ##[20] S. Kong, S. Zhou, Z. Nie and K. Wang, “The sizedependent natural frequency of Bernoulli–Euler microbeams”, International Journal of Engineering Science, Vol. 46, pp. 427–437, (2008). ##[21] H. Zeighampour and Y. Tadi Beni, “Analysis of conical shells in the framework of coupled stresses theory”, International Journal of Engineering Science, Vol. 81, pp. 107–122, (2014). ##[22] J. Yang, X. L. Jia and S. Kitipornchai, “Pullin instability of nanoswitches using nonlocal elasticity theory”, Journal of Physics D: Applied Physics, Vol. 41, No. 3, pp. 035103, (2008). ##[23] J. Abdi, Y. Tadi, A. Noghrehabadi, A. Koochi, A. S. Kazemi, A. Yekrangi, M. “Abadyan and M. Noghrehabadi, Analytical Approach to compute the Internal stress field of NEMS Considering Casimir Forces”, Procedia Engineering,Vol. 10, pp. 3757–3763, (2011). ##[24] Y. TadiBeni, M. R. Abadyan and A. Noghrehabadi, “Investigation of Size Effect on the Pullin Instability of Beamtype NEMS under van der Waals Attraction”, Procedia Engineering, Vol. 10, pp. 1718–1723, (2011). ##[25] X. L. Jia, J. Yang and S. Kitipornchai, “Pullin instability of geometrically nonlinear microswitches under electrostatic and Casimir forces”, Acta Mech., Vol. 218, No. 1, pp. 161–174, (2011). ##[26] J. G. Guo, Y. P. Zhao, “Influence of van der Waals and Casimir Forces on Electrostatic Torsional Actuators”, Journal of Micro electromechanical Systems, Vol. 13, No. 6, pp. 1027–1035, (2004). ##[27] A. Ramezani, A. Alasty and J. Akbari, “Influence of van der Waals force on the pullin parameters of cantilever type nanoscale electrostatic actuators”, Microsystem Technologies, Vol. 12, No. 12, pp. 1153–1161, (2006). ##[28] S. Malihi, Y. TadiBeni, H. Golestanian, “Analytical modeling of dynamic pullin instability behavior of torsional nano/micromirrors under the effect of Casimir force”, OptikInternational Journal for Light and Electron Optics, Vol. 127, No. 10, pp. 4426–4437, (2016). ##[29] A. C. Eringen, “Nonlocal polar elastic continua”, International Journal of Engineering Science, Vol. 10, pp. 116, (1972). ##[30] A. C. Eringen, Nonlocal Continuum Field Theories, SpringerVerlag, New York, USA (2002). ##[31] A. C. Eringen and D. G. B. Edelen, “On nonlocal elasticity, International Journal of Engineering Science, Vol. 10, pp. 233–248, (1972). ##[32] B. Fang, Y. X. Zhen, C. P. Zhang and Y. Tang, “Nonlinear vibration analysis of doublewalled carbon nanotubes based on nonlocal elasticity theory”, Applied Mathematical Modelling, Vol. 37, No. 3, pp. 10961107, (2013). ##[33] S. Malihi, Y. TadiBeni, H. Golestanian,“Size dependent pullin instability analysis of torsional nano/micromirrors in the presence of molecular force using 2D model”, OptikInternational Journal for Light and Electron Optics, Vol. 127, No. 19, pp. 7520–7536, (2016). ##[34] W. Chena, C. Shu, W. He and T. Zhong, “The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates”, Computers and Structures, Vol. 74, No. 1, pp. 6576, (2000). ##[35] J. Zhao, S. Zhou, B. Wang and X. Wang, “Nonlinear microbeam model based on strain gradient theory”, Applied Mathematical Modelling, Vol. 36, No. 6, pp. 26741107, (2012). ##[36] C. W. Bert and M. Malik, “Differential quadrature method in computational mechanics, a review”, Applied Mechanics Reviews, Vol. 49, No. 1, pp. 127, (1996). ##[37] C. Shu and H. Du, “A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates”, International Journal of Solids and Structures, Vol. 34, No. 4, pp. 837846, (1997). ##[38] G. L. Klimchitskaya and V. M. MohhideenUMostepanenko, “Casimir and van der waals Forces between Two Plates or a sphere (lens) above a Plate Made of Real Metals”, Physics Review A, Vol. 61, pp. 62107, (2000). ##[39] M. Bestrom and B. E. Sernelius, “Fractional Van Der Waals Interaction”, Physics Review B, Vol. 61, pp. 2204, (2000). ##[40] J. N. Israelachvili and D. Tabor, “Measurement of van Der Waals Dispersion Forces in the Range 1.5 to 130 nm”, Proceedings of the Royal society A, Vol. 331, pp. 1938, (1972). ##[41] P. M. Osterberg, Electrostatically actuated micromechanical test structure for material property measurement, Ph.D. Dissertation, Massachusetts Institute of Technology, (1995). ##[42] M. Ahmadi and W. C. Miller, “A closedform model for the pullin voltage of electrostatically actuated cantilever beam”, Journal of Micromechanics and Microengineering, Vol. 15, No. 4, pp.756763, (2005). ##[43] T. Mousavi, S. Bornassi and H. Haddadpour, “The effect of small scale on the pullin instability of nanoswitches using DQM”, International Journal of Solids and Structures, Vol. 50, No. 9, pp. 11921202. ##[44] H. Ataei, Y. TadiBeni, “SizeDependent PullIn Instability of Electrically Actuated Functionally Graded NanoBeams Under Intermolecular Forces”, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 40, No. 4, pp. 289301, (2016). ##[45] D. Son, J.h. Jeong, D. Kwon, “Filmthickness considerations in microcantileverbeam test in measuring mechanical properties of metal thin film”, Thin Solid Films, Vol. 437, No. 1 ##2, pp. 182187, (2003). ##[46] Y. Cao, D. Nankivil, S. Allameh, W. Soboyejo, “Mechanical properties of Au films on silicon substrates”, Materials and Manufacturing Processes, Vol. 22, No. 2, pp. 187194, (2007). ##[47] D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, “Experiments and theory in strain gradient elasticity”, Journal of the Mechanics and Physics of Solids, Vol. 51, No. 8, pp. 144771508, (2003). ##[48] Jamal Zare,“Pullin behavior analysis of vibrating functionally graded microcantilevers under suddenly DC voltage”, Journal of applied and computational mechanics, Vol. 1, No. 1, pp. 1725, (2015). ##[49] Morteza Karimi, Mohammad Hossein Shokrani, Ali Reza Shahidi, “Sizedependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method”, Journal of applied and computational mechanics, Vol. 1, No. 3, pp. 122133, (2015). ##[50] Hamid M. Sedighi,“The influence of small scale on the Pullin behavior of nonlocal nanoBridges considering surface effect, Casimir and van der Waals attractions”, International Journal of Applied Mechanics, Vol. 6, No. 3, pp. 1450030, (2014). ##[51] Hamid M. Sedighi, Farhang Daneshmand, Mohamadreza Abadyan, “Modeling the effects of material properties on the pullin instability of nonlocal functionally graded nanoactuators”, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 96, No. 3, pp. 385400, (2016). ##[52] R. Maranganti, P. Sharma, “A novel atomistic approach to determine straingradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies”, J. Mech. Phys. Solids, Vol. 55, No. 9, pp. 18231852, (2007).##]
An efficient analytical solution for nonlinear vibrations of a parametrically excited beam
2
2
An efficient and accurate analytical solution is provided using the homotopyPade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the EulerBernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordinary differential equation, which is then solved by the homotopy analysis method (HAM). An explicit expression is obtained for the nonlinear frequency amplitude relation. It is found that the proper value of the socalled auxiliary parameter for the HAM solution is dependent on the vibration amplitude, making it difficult to rapidly obtain accurate frequencyamplitude curves using a single value of the auxiliary parameter. The homotopyPade technique remedied this issue by leading to the approximation that is almost independent of the auxiliary parameter and is also more accurate than the conventional HAM. Highly accurate results are found with only third order approximation for a wide range of vibration amplitudes.
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saeed
mahmoudkhani
Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University, GC
Aerospace Engineering Department, Faculty
Iran
s_mahmoudkhani@sbu.ac.ir
Parametrically Excited Beam
Nonlinear Vibration
FrequencyAmplitude Relation, Homotopy Analysis Method (HAM)
HomotopyPade
[[1] M. N. Hamdan, A. A. AlQaisia, “B. O. AlBedoor, Comparison of analytical techniques for nonlinear vibrations of a parametrically excited cantilever”, International Journal of Mechanical Sciences, Vol. 43, No. 6, pp. 15211542, (2001). ##[2] E. C. Haight, W.W. King, “Stability of nonlinear oscillations of an elastic rod”, Journal of the Acoustical Society of America, Vol. 52, No. 3B, pp. 899911, (1971). ##[3] R. S. Haxton, A. D. S. Barr, “The autoparametric vibration absorber”, Transactions of the ASME, Journal of Engineering for Industry, Vol. 94, No. 1, pp. 11923, (1972). ##[4] K. Sato, H. Saito, K. Otomi, “The parametric response of a horizontal beam carrying a concentrated mass under gravity”, Transactions of the ASME Journal of Applied Mechanics, Vol. 44, No. 3, pp. 6438, (1978). ##[6] F.C. Moon, Experiments on chaotic motion of a forced nonlinear oscillator a strange attractors, Journal of Applied Mechanics, Vol. 47, No. 3, pp. 63944, (1980). ##[7] F. Pai, A.H. Nayfeh, “Nonlinear nonplanar oscillations of a cantilever beam under lateral base excitations”, Journal of Sound and Vibration, Vol. 25, No. 5, pp. 45574, (1990). ##[8] L. D. Zavodney, A. H. Nayfeh, “The nonlinear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment”, International Journal of Nonlinear Mechanics, Vol. 24, No. 2, pp. 10525, (1989). ##[9] T. D. Burton, M. Kolowith, “Nonlinear resonance and chaotic motion in a flexible parametrically excited beam”, Proceedings of the Second Conference on Nonlinear Vibrations, Stability and Dynamics of Structures and Mechanisms, Blacksburg, VA, (1988). ##[10] H. M. Sedighi, K. H. Shirazi and A. Noghrehabadi, “Application of recent powerful analytical approaches on the nonlinear vibration of cantilever beams”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 13, No. 7, pp. 487494, (2012). ##[11] H. M. Sedighi, K. H. Shirazi, “A new approach to analytical solution of cantilever beam vibration with nonlinear boundary condition”, Journal of Computational and Nonlinear Dynamics, Vol. 7, No. 3, pp. 14, (2012). ##[12] H. M. Sedighi, K. H. Shirazi, A. Reza and J. Zare, “Accurate modeling of preload discontinuity in the analytical approach of the nonlinear free vibration of beams”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 226, No. 10, pp. 24742484, (2012). ##[13] H. M. Sedighi, K. H. Shirazi, M. A. Attarzadeh, A study on the quantic nonlinear beam vibrations using asymptotic approximate approaches, Acta Astronautica, Vol. 91, pp. 245250, (2013). ##[14] H. M. Sedighi, A. Reza, “High precise analysis of lateral vibration of quintic nonlinear beam”, Latin American Journal of Solids and Structures, Vol. 10, No. 2, pp. 441 452, (2013). ##[15] H. M. Sedighi, F. Daneshmand, “Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term”, Journal of Applied and Computational Mechanics, Vol. 1, No. 1, pp. 19 , (2015). ##[16] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, (2003). ##[17] S. J. Liao, K. F. Cheung, “Homotopy analysis of nonlinear progressive waves in deep water”, Journal of Engineering Mathematics, Vol. 45, No. 2, pp. 105116, (2003). ##[18] S. J. Liao, A. Campo, Analytic solutions of the temperature distribution in Blasius viscous flow problems, Journal of Fluid Mechanics. Vol. 453, No. 1, pp. 411425, (2002). ##[19] T. Pirbodaghi, M. T. Ahmadian, M. Fesanghary, “On the homotopy analysis method for nonlinear vibration of beams”, Mechanics Research Communications, Vol. 36, No. 2, pp. 143148, (2009). ##[20] R. Wu, J. Wang, J. Du, Y. Hu, H. Hu, “Solutions of nonlinear thicknessshear vibrations of an infinite isotropic plate with the homotopy analysis method”, Numerical Algorithms, Vol. 59, No. 2, pp. 213226, (2012). ##[21] M. Poorjamshidian, J. Sheikhi, S. MahjoubMoghadas, M. Nakhaie, “Nonlinear vibration analysis of the beam carrying a moving mass using modified homotopy”, Journal of solid mechanics, Vol. 6, No. 4, pp. 389396, (2014). ##[22] H. M. Sedighi, K. H. Shirazi, J. Zare, “An analytic solution of transversal oscillation of quintic nonlinear beam with homotopy analysis method”, International Journal of NonLinear Mechanics, Vol. 47, No. 7, pp. 777784, (2012). ##[23] S. H. Hoseini, T. Pirbodaghi, M. T. Ahmadian, G.H. Farrahi, “On the large amplitude free vibrations of tapered beams: an analytical approach”, Mechanic Research Communication, Vol. 36, No. 8, pp. 892897, (2009). ##[24] M. R. M. Crespo da Silva, C. C. Glynn, ## “Nonlinear flexuralflexuraltorsional dynamics of inextensible beams, I: equations of motion”, Journal of Structural Mechanics, Vol. 6, No. 4, pp. 43748, (1978). ##[25] A. H. Nayfeh, P. F. Pai, Linear and Nonlinear Structural Mechanics, John Wiley & Sons, Weinheim, (2004). ##[26] E. B. Saff, R. S. Varga, Pade and Rational Approximation, Academic Press, New York, (1977). ##[27] J. Kallrath., On Rational Function Techniques and Pade Approximants. An Overview, Report, Ludwigshafen, Germany, (2002).##]