Abstract
Thin two-dimensional plates have been widely used in mechanical structures and systems, and their natural vibration characteristics play an important role in structural design and optimization. In this paper, we develop a novel modelling method for the vibration characteristic analyses of a system having two-dimensional structure components using the Reduced Transfer Matrix Method for Multibody System (MSRTMM). In the proposed modeling method, the Transfer Matrix Method for Multibody System (MSTMM) and the Riccati transformation are integrated to achieve high computational efficiency and stability for the vibration analyses of a system with two-dimensional structures. The principle and procedures of the modeling and vibration analysis method are presented with detailed theoretical derivations. To verify the proposed modeling and vibration analysis method, numerical simulations are performed with three case studies: a rectangular thin plate vibrating in the plane, a parallelogram thin plate vibrating in the plane, and a multi-body system with two-dimensional structure elements vibrating in the plane. The simulation results by MSRTMM well agree with the counterparts by Finite Element Method (FEM). Compared with the existing methods, MSRTMM not only avoids the global dynamics equation, but also has the advantages of high computational speed, highly formalized programmability, and high numerical stability.
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