Analysis on jump and bifurcation phenomena in the forced vibration of nonlinear cantilever beam using HBM

In this paper, jump and bifurcation phenomena for geometrical nonlinear cantilever beam is investigated regarding forced vibration. The nonlinear ODE of system is obtained by using Galerkin method. To solve the nonlinear ODE, harmonic balance method (HBM) is used. Moreover, validation of results and analysis-verification are considered based on the numerical fourth-order Runge-Kutta method. Forced vibration in this research is distributed excitation. Therefore, new analysis is achieved in the field of jump and bifurcation phenomena for geometrical nonlinear cantilever beams. Using HBM led us to accomplish valuable and accurate research regarding bifurcation. Finally, the achieved results are demonstrated suitable and valuable not only regarding agreement of the precise results, but also studying many significant phenomena such as jump, bifurcation and beat in this field.