Analysis of nonlinear vibrations of two-degree-of-freedom systems

Abstract

In this paper, the motions of two-mass systems with two-degree-of-freedom are investigated by using an analytical approach. The masses are connected by linear and nonlinear springs. The motions of systems are described by systems of two coupled strong nonlinear differential equations. Nonlinear differential equations are transferred into a single equation by using some intermediate variables. An analytical method, the equivalent linearization method, is employed to analyze the free nonlinear vibration of systems. The oscillation systems with different values of the parameters are investigated in this paper. In order to verify the accuracy of the obtained results, the present solutions are compared with those achieved by the Hamiltonian approach and the exact solutions. The comparison results show that the obtained solutions are more accurate than those obtained by the Hamiltonian approach.