Modified Harmonic Balance Method for Solving Nonlinear Free Vibration Problem of Beam Resting on Nonlinear Elastic Foundation - Rahman, M. Saifur; Hossain, Ahmed (Journal of Vibration Testing and System Dynamics, 2026)
Free vibration of beam is an important issue in structural engineering because of its various physical applications in the real field. In this paper, the free vibration of a nonlinear beam rest on a nonlinear elastic foundation is studied. A mathematical modeling for the free vibration of beam rest on nonlinear elastic foundation is presented. A modified harmonic balance is used to investigate the nonlinear free vibration response of beam. The main advantage of the method is that the unknown coefficients are expressed in power series of a new parameter. However, in a classical harmonic balance method the values of the unknown coefficients are determined by solving a set of complicated algebraic equations truncating higher order nonlinear terms. The results obtained by the proposed method have been compared with corresponding numerical results to verify the accuracy of method. Besides, the effects of various elastic foundation coefficients have been examined.