15Transfer Matrix Library for Multibody Systems

15.1 Introdution

Applying transfer matrix method for multibody systems (MSTMM) to solve the eigenvalue problem of linear time‐invariant multibody systems, steady‐state response and the dynamics problem of general multibody systems requires the transfer matrices of elements to be gathered into the overall transfer matrix of the system. From the boundary conditions of the system, we can easily compute the dynamics of the system by solving the overall transfer equation and the transfer equation of each element. The transfer matrix of each element has an important feature, that is, the element has the same transfer matrix even in a different system if it has the same connection relationship and motion mode. This feature makes the solution process of multibody system dynamics very simple and convenient. Once the transfer matrix of a certain element has been derived, it can be used for the same kind of elements in different multibody systems.

The transfer matrices of various elements [279–452] are listed in this chapter so readers can check them when they are needed. If the transfer matrix of a new element is not found in this chapter, readers can derive the corresponding transfer matrix using the proposed methods in Chapters 5, 6, 7, 8 and 10, and add it to the transfer matrix library. The transfer matrix library can be used to solve the dynamics problems of various complex multibody systems, including chain multibody systems, branch ...

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