Forced vibration analysis of a nonlinear structure connected in series: (Stability analysis based on the argument principle)

It is a very difficult problem to determine the stability of the periodic steady-state vibrations generated in a large-sized nonlinear system with multi-degree-of-freedom. In order to overcome such difficulty, a new practical method to accurately analyze the stability of the periodic solutions obtained from the method of harmonic balance is developed for a nonlinear structure connected in series. The present method is mainly based on the argument principle and is applicable to the stability analysis of any multi-degree-of-freedom system excited parametrically. By introducing the same treatment as that of the incremental transfer influence coefficient method into the computation process of the present method, the computation speed is improved and the memory size required in the computation is considerably reduced. The validity of the present method is confirmed by the results of numerical computation for some examples.