Vibration Analysis of a Nonlinear Beam Under Axial Force by Homotopy Analysis Method

Subject Areas : Engineering

A.A  Motallebi ¹ (Department of Mechanical Engineering, Imam Hossein University)
M  Poorjamshidian ² (Department of Mechanical Engineering, Imam Hossein University)
J  Sheikhi ³ (Civil Engineering, Imam Hossein University)

Received: 2014-04-10 Accepted : 2014-06-13 Published : 2014-09-30

Keywords:

References:

[1] Ahmadian M.T., Mojahedi M., 2009, Free vibration analysis of a nonlinear beam using homotopy and modified lindstedt-poincare methods, Journal of Solid Mechanics 2(1): 29-36.
[2] Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, New York, Wiley, First Edition.
[3] Shames I.H., Dym C.L., 1985, Energy and Finite Element Methods in Structural Mechanics, New York, McGraw-Hill, First Edition.
[4] Malatkar P., 2003, Nonlinear Vibrations of Cantilever Beams and Plates, Virginia, Virginia Polytechnic Institute , PhD thesis.
[5] Pillai S.R.R., Rao B.N., 1992, On nonlinear free vibrations of simply supported uniform beams, Sound and Vibration 159(3): 527-531.
[6] Foda M.A., 1999, Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned Ends, Computers and Structures 71(1): 663-670.
[7] Ramezani A., Alasty A., Akbari J., 2006, Effects of rotary inertia and shear deformation on nonlinear free vibration of microbeams, ASME Journal of Vibration and Acoustics 128(5): 611-615.
[8] Liao S.J., 1995, An approximate solution technique which does not depend upon small parameters: a special example, International Journal of Nonlinear Mechanics 30(1): 371-380.
[9] Sedighi.H.M., Shirazi.K.H., 2012, An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method, Non-Linear Mechanics 47: 777-784.
[10] Hoseinia S.H., Pirbodaghi T., 2008, Nonlinear free vibration of conservative oscillators with inertia and static type cubic nonlinearities using homotopy analysis method, Sound and Vibration 316: 263-273.
[11] Samir A., Emam A., 2002, Theoretical and Experimental Study of Nonlinear Dynamics of Buckled Beams, Virginia, Virginia Polytechnic Institute, PhD thesis.
[12] Liao S.J., 1992, On the Proposed Homotopy Analysis Techniques for Nonlinear Problems and its Application , Shanghai, Jiao Tong University, PhD thesis.
[13] He J.H., 2000, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics 35: 37-43.
[14] Saff E.B., Varga R.S., 1977, Pade´ and Rational Approximation, Academic Press, New York.
[15] Wuytack L., 1979, Pade´ Approximation and its Applications, Lecture Notes in Mathematics, Springer, Berlin.
[16] Liao S.J., Cheung K.F., 2003, Homotopy analysis of nonlinear progressive waves in deep water, Journal of Engineering Mathematics 45(1): 105-116.