Constructing the Frequency-Energy Plot of Nonlinear Vibratory Systems via the Modified Lindstedt-Poincaré Method
The frequency-energy plot(FEP) of nonlinear vibration systems is a powerful tool for investigating the energy transfer phenomena related wiht the internal resonances occured in multi-digreeof- freedom(Multi-DOF) nonlinear vibration systems. In this paper, the modified Lindstedt-Poincare method is employed for constructing the FEP of a two-DOF nonlinear vibrating systems. First, the original vibartion equations are modified for the application of the modified Linstedt-Poincaré method. Then, by using the modified Linstedt-Poincaé method, the nonlinear normal modes(NNMs) of the system are obtained. Finally, the frequency-energy plot of the system is constructed analytically. Numerical results show that the method adopted in this paper is effective and accurate.