Nonlinear vibration analysis of a Timoshenko beam with concentrated mass using variational iteration method

Abstract

Complicated structures used in a wide variety of engineering fields consist of simple structural elements like beams which in some cases include one discontinuity such as a crack or mass and are more likely to vibrate with larger amplitude. In this article, considering shear deformation and rotatory inertia, transverse vibration of nonlinear Timoshenko beam carrying a concentrated mass oscillating with large amplitude is investigated using VIM. This method is a very powerful method with suitable convergence speed in which by choosing the proper Lagrange’s multiplier and Initial Function, the convergence speed could increase even more. This method would be able to present analytical solutions for linear equations and semi-analytical solutions for non-linear ones. One of the greatest advantages of this method is that its calculations are not dependent on the number of masses located on the beam. In this paper, along with presenting the suitable trend for determining the Lagrange’s multiplier, the effects of concentrated mass on natural frequencies in linear and non-linear states are taken into account. The obtained results, moreover, are compared with the results gained through other procedures and the accuracy and speed convergence are studied as well.