Statics analysis based on the reduced multibody system transfer matrix method

The reduced multibody system transfer matrix method can efficiently solve the generalized accelerations of a system without establishing global dynamics equations with a system inertia matrix, given the generalized coordinates and generalized velocities of the system. The equilibrium position of a m...

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Bibliographic Details
Published in:Multibody system dynamics 2024, Vol.61 (1), p.77-101
Main Authors: Zhang, Xizhe, Rui, Xiaoting, Zhang, Jianshu, Gu, Junjie, Zhang, Lina
Format: Article
Language:English
Subjects:
Automotive Engineering
Control
Dynamical Systems
Electrical Engineering
Engineering
Equilibrium
Iterative methods
Jacobi matrix method
Jacobian matrix
Mechanical Engineering
Multibody systems
Nonlinear equations
Optimization
Relaxation method (mathematics)
Static equilibrium
Transfer matrices
Vibration
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Summary:The reduced multibody system transfer matrix method can efficiently solve the generalized accelerations of a system without establishing global dynamics equations with a system inertia matrix, given the generalized coordinates and generalized velocities of the system. The equilibrium position of a multibody system is significant in the dynamics analysis, which is difficult to obtain directly. In this paper, a statics analysis method is proposed based on the reduced multibody system transfer matrix method by applying the notion of direct differentiation. The partial derivatives of generalized accelerations with respect to generalized coordinates called Jacobian matrix can be obtained easily by differentiating the transfer equations in the reduced multibody system transfer matrix method. Let the generalized velocities be zero and solve the system of nonlinear equations with zero generalized accelerations to obtain the static equilibrium position of a multibody system. The formulation and solution procedure of the proposed method are presented. The numerical examples are compared with dynamic relaxation method and the iterative method based on the first kind of Lagrange’s equation, which demonstrates the proposed approach and show computational advantages. The proposed method is straightforward, highly programmable, universal and provides a powerful tool for solving static equilibrium positions of multibody systems while extending the application of the multibody system transfer matrix method.
ISSN:1384-5640
1573-272X
DOI:10.1007/s11044-023-09916-6