基于振动变换约束建模的空间机械系统动力学分析

novel symbolic-numeric formulation with high efficiency is presented for linear vibration analysis of spatial mechanism systems with holonomic constraints, using systematic topology transformation instead of solving constraint equations. Based on uniform transformation of vibrational displacements, formulation of minimal set of second-order linear ordinary differential equations (ODEs) can be easily completed in three steps. Firstly, a set of linearized ODEs are formulated in terms of absolute coordinates without considering any constraint in the system. Secondly, an open-loop constraint matrix is generated to formulate ODEs for an open-loop mechanism system which is obtained by ignoring all cut-joints in the original system. Finally, a cut-joint constraint matrix is generated to formulate a minimal set of ODEs for the original closed-loop mechanism system. Since there is no need for derivation of matrices and linearization of equations, computational efficiency can be significantly improved by using the proposed method as compared with traditional approaches. The correctness and efficiency of the proposed method are then verified by numerical experiments on mechanism systems with different kinds of constraint topologies. The presented algorithm is particular effective for sensitivity analysis and optimization of large-scale mechanism systems.