Nonlinear analysis of two-degree of freedom system with nonlinear springs

In this paper, an analytic solving procedure for a two degree of freedom oscillatory system (2DOF) is considered. Vibration of the two-mass system is mathematically modeled with two coupled second-order equations. The system is assumed to be strongly nonlinear, and a high order Homotopy Perturbation Method (HPM) for solving the system is developed. The frequency of vibration is obtained in the second approximation. To validate the method, two examples are considered. The solutions of the HPM are compared with those of Newton-harmonic balance (NHB) and numerical approaches. It has been demonstrated that HPM leads to a highly accurate solution even with the first iteration of the solution and is valid for a wide range of vibration amplitudes, showing promise as a means to provide an exact or closed-form solution of nonlinear dynamical systems, as indicated in the following examples.

Automated summary

This paper investigates the analytic solving procedure for a two degree of freedom oscillatory system using a high order Homotopy Perturbation Method (HPM). The method is shown to provide highly accurate solutions and is applicable to a wide range of vibration amplitudes, as demonstrated by comparison with other methods.