关键词: 常微分方程, 多刚体系统, 符号建模, 矩阵, 振动分析

Abstract: A new symbolic formulation based on matrix transformation is presented for vibration analysis of rigid multibody systems. The basic elements such as mass and inertia of body, coefficients of spring and damper, joint and spatial motion status, are defined in form of matrix or vector so as to keep structural integrity and get clear notation. The small displacements of bodies under vibration status are linearized, and the relationship between displacements at different points with respect to different reference frames is formulated by linear transformation. Linearized ordinary differential equations for unconstrained and open-loop constrained rigid multibody systems are derived respectively by using Lagrangian method, and the resulting equations are suitable for control and vibration analysis. The relationship between the two sets of equations is revealed by systematic coordinates transformation matrix. The rule of formulating the systematic transformation matrix for an open-loop constrained system is finally presented. The correctness and effectiveness of the proposed algorithm are proved by the result of numerical simulation and experiment.

Key words: Matrix, Ordinary differential equations, Rigid multibody systems, Symbolic formulation, Vibration analysis