Precise Hsu’s method for analyzing the stability of periodic solutions of multi-degrees-of-freedom systems with cubic nonlinearity

This paper presents a new precise Hsu’s method for investigating the stability regions of the periodic motions of an undamped two-degrees-of-freedom system with cubic nonlinearity. Firstly, the incremental harmonic balance (IHB) method is used to obtain the solution of nonlinear vibration differential equations. Hsu’s method is then adopted for computing the transition matrix at the end of one period, and the precise time integration algorithm is adjusted to improve the computational precision. The stability regions of the system obtained from the precise Hsu’s, Hsu’s and improved numerical integration methods are compared and discussed.