Riccati Transfer Matrix Method for Linear Tree Multibody Systems

Abstract

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

Multibody system transfer matrix method: The past, the present, and the future

“…However, the accumulative error resulting from successive multiplication of a large number of transfer matrices in a long‐chain system or subsystem may lead to computational instability. To address this problem, Chen et al, 41 and Gu et al 28 developed Riccati linear MSTMM for linear multibody systems by applying similar Riccati transformation 42 to linear MSTMM. He et al 13 proposed the Riccati DT‐MSTMM for chain systems by introducing a similar Riccati transformation in DT‐MSTMM.…”

Dynamics modeling and control of active track tensioning system for tracked vehicle

“…Owing to the extreme low order of the system matrix, the calculation speed is extremely high. In Gu et al (2017) and Rui et al (2017, 2016, 2015), the comparisons of computational precision and speed between the MSTMM and other dynamics methods can be found.…”

“…The workload is heavy, and the low computational efficiency for complex systems is a serious problem. Rui et al proposed a transfer matrix method for multibody systems (MSTMM) (Gu et al, 2017; Rui et al, 2017, 2016, 2015), which has the advantages of high programming, low system matrix order and high computational efficiency. It provides an effective approach for modeling of tracked vehicles.…”

On modeling and dynamics of a multiple launch rocket system

“…In subsequent years, the MSTMM has been developed and perfected unceasingly. [32][33][34][35] The MSTMM has been successfully applied to the analysis and evaluation of vibration characteristics and dynamics response of various mechanical systems. [36][37][38] However, the involved MSTMMs for the above studies on the MLRS dynamics are linear with the hypothesis of local linearization, which require a small enough calculation step to ensure calculation accuracy and stability of the MLRS dynamics.…”