An Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motion of Nonlinear Systems With Cubic Nonlinearity

Abstract A new incremental harmonic balance (IHB) method with two time scales procedure is used to analyze quasi-periodic motion of multiple degrees of freedom systems with cubic nonlinearity. An amplitude increment algorithm is adapted to deal with cases where the two frequencies are unknown a priori, in order to automatically trace frequency response of quasi-periodic motion of the system and accurately calculate all frequency components and their corresponding amplitudes. Results of application of the present IHB method to quasi-periodic free vibration of the nonlinear system are shown and compared with previously published results with Lau method and those from numerical integration. While differences are noted between results predicted by the present IHB method and Lau method, excellent agreement is achieved between results from the present IHB method and numerical integration even in cases of strongly nonlinear vibration.