A semi-analytical solution for free vibration analysis of a step beam with multiple concentrated masses using variational iteration method

Abstract

Vibrational characteristic in structures that can be modeled as several concentrated masses on the beam are of great interest. In this article, variational iteration method (VIM) is used to find a semi-analytical solution for the transverse vibration of an Euler–Bernoulli beam carrying concentrated masses and also to close the condition of the problem into real boundary conditions wherein the cross-sectional changes are applied at points where there is concentrated mass. In order to achieve the Lagrange multiplier, in addition to using variational theory and stationary conditions, a simple polynomial is considered for the initial approximation. © 2021 Taylor & Francis Group, LLC.