Free Vibration of a Tapered Beam by the Aboodh Transform-based Variational Iteration Method

Physical systems frequently exhibit nonlinear behavior that remains unresolved in the majority of cases. In this study, we employ the Aboodh transform-based variational iteration method (ATVIM) to resolve the nonlinear model of a tapered beam. In order to solve the governing equation, the periodic motion is sought, and the explicit relationship between frequency and amplitude is revealed. The outcomes of the ATVIM approach are compared with those of other prevalent techniques, and a satisfactory concordance is observed between them. This study also provides an analytical approximation of the tapered beam for a detailed understanding of the effects of factors on the nonlinear frequency, which can be beneficial to researchers and engineers working on the analysis and design of structural projects.

Keywords:

Aboodh transform , Tapered beam , Variational iteration method , amplitude-frequency relationship , nonlinear oscillator