Eigenvalue analysis of planar linear multibody system under conservative force based on the transfer matrix method

Abstract

The linear multibody system transfer matrix method (LMSTMM) provides a powerful tool for analyzing the vibration characteristics of a mechanical system. However, the original LMSTMM cannot resolve the eigenvalues of the systems with ideal hinges (i.e., revolute hinge, sliding hinge, spherical hinge, cylindrical hinge, etc.) or bodies under conservative forces due to the lack of the corresponding transfer matrices.This paper enables the LMSTMM to solve the eigenvalues of the planar multibody systems with ideal hinges or rigid bodies under conservative forces. For a rigid body, the transfer matrix can now consider coupling terms between forces and kinematic state perturbations. Also, conservative forces that contribute to the eigenvalues can be considered. Meanwhile, ideal hinges are introduced to LMSTMM, which enables the treatment of eigenvalues of general multibody systems using LMSTMM. Finally, the comparative analysis with ADAMS software and analytical solutions verifies the effectiveness of the proposed approach in this paper.

Enabling the transfer matrix method to model serial–parallel compliant mechanisms including curved flexure beams

“…Exploration of methods for modeling kinetostatic and dynamic behaviors of compliant mechanisms and rigid‐body mechanical systems has been an interesting technological subject though software packages are commercially available 1–6 . A process‐efficient, result‐accurate, and parameter‐insightful modeling methodology is often desirable.…”