In the multibody system transfer matrix method (MSTMM), the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations. However, regarding the transfer matrices of hinge elements, typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t. various types of outboard body's output links. This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper. Systematic procedures for chain, tree, closed‐loop, and arbitrary general systems are defined, respectively, to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process. As a result, accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.

Computational speed and stability are two important aspects in the dynamics analysis of large-scale complex multibody systems. In order to improve both in the context of the multibody system transfer matrix method, a new version of the Riccati transfer matrix method is presented. Based on the new version of the general transfer matrix method for multibody system simulation, recursive formulae are developed which not only retain all advantages of the transfer matrix method, but also reduce the truncation error. As a result, the computational speed, accuracy and efficiency are improved. Numerical computation results obtained by the proposed method and an ordinary multibody system formulation show good agreement. The successful computation for a spatial branch system with more than 100000 degrees of freedom validates that the proposed method is also working for huge systems.

Transfer matrix method is a practical technology for vibration analysis of engineering mechanics. In this article, a new version of mixed differential quadrature discrete time transfer matrix method is presented for simulating vibrations. First, ordinary differential equations of the substructure or the element of a mechanical system are determined by classical mechanics rules or the finite element method. These ordinary differential equations can be transformed to a set of algebraic equations at some discrete time points by the application of a differential quadrature method. After extending the state vector of the transfer matrix method, new transfer equations and transfer matrices of the substructures (or elements) of a mechanical system are developed finally. Riccati transformation is used to improve the computational convergence of the method. Several numerical examples show that the proposed method can be regarded as an efficient tool for transient response analysis of vibration systems.