Abstract
The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain and tree multibody systems with the transfer matrix method for multibody systems. However, for linear multibody systems with closed loops, the recursive relations of the Riccati transfer matrices are yet to be established. Therefore, it is difficult to compute linear multibody systems with closed loops using the RTMM. In this paper, a new Riccati transformation for such systems is established by transforming the system into a derived tree system by cutting the closed loops. An RTMM formalism for general linear multibody systems with closed loops is then formulated based on the chain and tree multibody systems. The steady-state response under harmonic excitation is taken as an example to validate the proposed method.
Highlights
The transfer matrix method for multibody systems (MSTMM) has been used widely in the analysis and design of complex multibody systems.1–5 For linear multibody systems, the MSTMM is concerned mainly with vibration characteristics such as eigenvalues and steady-state response
The Riccati transformation proposed by Horner and Pilkey8 combined with a transfer matrix, known as the Riccati transfer matrix method (RTMM), is an efficient way to improve the numerical stability
The order of the matrices involved in the RTMM is only half of those in the classical MSTMM, leading to less computational time and storage space
Summary
The transfer matrix method for multibody systems (MSTMM) has been used widely in the analysis and design of complex multibody systems. For linear multibody systems, the MSTMM is concerned mainly with vibration characteristics such as eigenvalues and steady-state response. The order of the matrices involved in the RTMM is only half of those in the classical MSTMM, leading to less computational time and storage space Using such an approach, Xue studied nonlinear eigenvalue problems and transient structural response problems, and Stephen performed elastostatic analysis of a repeated structure. A pair of new boundary points with unknown quantities is formed at each cutting point, and half of these unknowns are denoted as a column matrix λ and introduced into the Riccati transformation to establish a new one that is suitable for systems with CLs. The recursive relations of Riccati transfer matrices expressed in the new form are investigated according to the recursive relations of chain and tree systems. The RTMM can be used to solve linear multibody systems with arbitrary topology, thereby removing the obstacles to using the RTMM in the dynamic computation of large complex multibody systems
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