5Transfer Matrix Method for Multi‐rigid‐body Systems

5.1 Introduction

Multibody system dynamics methods (MSDMs) have developed rapidly in the last 50 years and provide powerful tools for studying the dynamics of various mechanical systems. Although the various classical MSDMs have different styles, at the same time almost all of them share the following characteristics: first, it is necessary to develop the global dynamics equations of the system, and they have to be deduced again if the system’s topological structure is changed; second, the order of the global dynamics equations is not less than the number of degrees of freedom of the system, which may become very high for complex systems resulting in a rather long computational time.

The approach proposed in this chapter is different from the above and has a different origin. In 1986, Kumar and Sankar developed a discrete time transfer matrix method (DTTMM) for the structural dynamics of time‐variant systems by combining the transfer matrix method with a numerical integration procedure. In 1989, Rui and others extended the transfer matrix method to multibody systems (MSTMM) for vibration analysis of linear multi‐rigid‐flexible‐body systems by developing new transfer matrices, where eigenvalues of linear multi‐rigid‐flexible‐body systems can be computed easily and with high precision. For general nonlinear multi‐rigid‐body and multi‐rigid‐flexible‐body systems, the discrete time transfer matrix method of multibody systems ...

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