Forced Vibration Analysis of a Nonlinear Structure Connected in Series: (1st Report, Suggesting the Incremental Transfer Influence Coefficient Method)

The incremental transfer influence coefficient method is developed in order to analyze the periodic steady-state vibrations of a nonlinear system with a multi-degree-of-freedom system on a personal computer, combining the concepts of both the method of harmonic balance and the transfer influence coefficient method through the incremental method. The present method has some merits, that is, high computation speed, high numerical computational accuracy, applicability to the various types of nonlinearity and so on. For the stability problem, general and simplified methods are suggested in order to determine the stability of the periodic solutions from the behavior of the solutions of the corresponding variational equation, which is described as a multi-degree-of-freedom system with parametric excitations. The former is applicable to the variational equation in general and with high accuracy. The latter gives the sufficient condition for certain main unstable regions of the variational equation.