Multibody System Dynamics

, Volume 19, Issue 3, pp 179–207

# Transfer matrix method for linear multibody system

• Xiaoting Rui
• Guoping Wang
• Yuqi Lu
• Laifeng Yun
Article

## Abstract

A new method for linear hybrid multibody system dynamics is proposed in this paper. This method, named as transfer matrix method of linear multibody system (MSTMM), expands the advantages of the traditional transfer matrix method (TMM). The concepts of augmented eigenvector and equation of motion of linear hybrid multibody system are presented at first to find the orthogonality and to analyze the responses of the hybrid multibody system using modal method. If using this method, the global dynamics equation is not needed in the study of linear hybrid multibody system dynamics. The MSTMM has a small size of matrix and higher computational speed, and can be applied to linear multi-rigid-body system dynamics, linear multi-flexible-body system dynamics and linear hybrid multibody system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study on linear hybrid multibody system dynamics. This method can be used in the following: (1) Solve the eigenvalue problem of linear hybrid multibody systems. (2) Obtain the orthogonality of eigenvectors of linear hybrid multibody systems. (3) Realize the accurate analysis of the dynamics response of linear hybrid multibody systems. (4) Find the connected parameters between bodies used in the computation of linear hybrid multibody systems. A practical engineering system is taken as an example of linear multi-rigid-flexible-body system, the dynamics model, the transfer equations and transfer matrices of various bodies and hinges; the overall transfer equation and overall transfer matrix of the system are developed. Numerical example shows that the results of the vibration characteristics and the response of the hybrid multibody system received by MSTMM and by experiment have good agreements. These validate the proposed method.

## Keywords

Linear hybrid multibody system Transfer matrix method Eigenfrequency Augmented eigenvector Orthogonality

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## Authors and Affiliations

• Xiaoting Rui
• 1
• Guoping Wang
• 1
• Yuqi Lu
• 1
• Laifeng Yun
• 1
1. 1.Institute of Power EngineeringNanjing University of Science & TechnologyNanjingChina