تحليل ارتعاشات غيرخطي يك تير دوسرآزاد با استفاده از تيوري اغتشاشات

In this paper, the nonlinear bending vibration of a free-free beam is analyzed using the perturbation theory. The nonlinear part of the equation of motion is obtained using two separate approaches i.e. the invariant manifold approach, and the perturbation theory. By application of the multiple scale method, the nonlinear differential equation of motion with necessary boundary conditions is solved and the vibrational mode shapes are obtained. The advantage of using perturbation method with regard to the well known numerical approaches is the possibility of simulating analytically the effect of magnitude changes of nonlinear part in the final solution. The result shows that magnitude changes of nonlinear part causes noticeable changes in the vibrational mode shapes of the beam. Also, it is shown that in the higher modes, the effect of the nonlinear part will increase dramatically.