H. Rafieipour - M.Sc. Student, Department of Mechanical and Aerospace Engineering Shiraz University of Technology
A. Lotfavar - Assistant Professor, Department of Mechanical and Aerospace Engineering and Marine System Research Center Shiraz University of Technology
S. Mehrdad Tabatabaei - ۳M.Sc. Student, Department of Mechanical and Aerospace Engineering
Mohammad Abbaspour - M.Sc. in Mechanical Engineering;

In this study, a new analytical method called Laplace iteration method (LIM) is used to investigate nonlinear vibration behavior of Euler-Bernoulli and Rayleigh beams with two different edge conditions subjected to axial load. Closed form solutions for natural frequencies, beam deflection, critical buckling and postbuckling loads are also presented. Furthermore, the effects of vibration amplitude, slenderness ratio and axial load on the nonlinear frequency and buckling load are discussed. Finally, the obtained results by the proposed method are compared with those available in literature. The results showed that LIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes meanwhile one or two iterations are enough for obtaining the results

Laplace Iteration Method (LIM), Nonlinear Vibration, Euler-Bernoulli Beam, Rayleigh Beam,Slenderness Ratio, Vibration Amplitude