Nonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy

Subject Areas : Engineering

M Poorjamshidian ¹ (Department of Mechanical Engineering, Imam Hossein University)
J Sheikhi ² (Civil Engineering, Imam Hossein University)
S Mahjoub-Moghadas ³ (Department of Mechanical Engineering, Imam Hossein University)
M Nakhaie ⁴ (Department of Mechanical Engineering, Imam Hossein University)

Received: 2014-07-21 Accepted : 2014-09-24 Published : 2014-12-30

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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 Mechanic 2(1): 29-36.
[2] Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, First Ed, New York, Wiley.
[3] Shames I.H., Dym C.L., 1985, Energy and Finite Element Methods in Structural Mechanics, First Ed, New York, McGraw-Hill.
[4] Malatkar P., 2003, Nonlinear Vibrations of Cantilever Beams and Plates, Virginia, Virginia Polytechnic Institute.
[5] Pirbodaghi T., Ahmadian M.T., Fesanghary M., 2009, On the homotopy analysis method for non-linear vibration of beams, Mechanics Research Communications 36(2):143-148.
[6] Sedighi H. M., Shirazi K. H., Zare J., 2012, An analytic solution of transversal oscillation of quantic non-linear beam with homotopy analysis method, International Journal of Non-Linear Mechanics 47(1): 777-784.
[7] Foda M.A., 1998, Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned Ends, Journal Computers and Structures 71(20): 663-670.
[8] Rafiee R., 2012, Analysis of nonlinear vibrations of a carbon nanotube using perturbation technique, Journal of Mechanics Modares 12(1): 60-67.
[9] 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(2): 611-615.
[10] Sedighi H. M., Shirazi K. H., Zare J., 2012, Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He’s parameter expanding method, Latin Am Journal of Solids Structure 9(1): 130-138.
[11] Barari A., Kaliji H.D., Ghadami M., Domairry G., 2011, Non-linear vibration of Euler- Bernoulli beams, Latin Am Journal of Solids Structure 8(2): 139-148.
[12] Aghababaei O., Nahvi H., Ziaei-Rad S., 2009 , Dynamic bifurcation and sensitivity analysis on dynamic responses of geometrically imperfect base excited cantilevered beams, Journal of Vibro engineering 13(1): 52-65.
[13] Sarma B.S., Vardan T.K., Parathap H., 1988, On various formulation of large amplitude free vibration of beams, Journal of Computers and Structures 29(1): 959-966.
[14] Parnell L.A., Cobble M.H., 1976, Lateral displacement of a cantilever beam with a concentrated mass, Journal of Sound and Vibration 44(2): 499-510.
[15] Chin C.M., Nayfeh A.H., 1997, Three-to-one internal resonance in hinged-clamped beams, Journal of the Nonlinear Dynamics 12(1): 129-154.
[16] Pan L., 2007, Stability and local bifurcation in a simply-supported beam carrying a moving mass, Acta Mechanica Solida Sinica 20(2):123-129.
[17] Rafieipor H., Lotfavar A., Shalamzari S.H., 2012, Nonlinear vibration analysis of functionally graded beam on winkler-pasternak foundation under mechanical and thermal loading via homotopy analysis method, Journal of Mechanics Modares 12(5): 87-101.
[18] Beléndez A., 2009, Homotopy perturbation method for a conservative x1/3 force nonlinear oscillator, Journal of Computers and Mathematics with Applications 58(3): 2267-2273.
[19] Xu M.R., Xu S.P., Guo H.Y., 2010, Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method, Journal of Computers and Mathematics with Applications 60:520-527.