Bending Vibration and Power Flow Analysis of Plate Assemblies in the Symplectic Space

The free wave propagation and forced vibration of thin rectangular plate assemblies were investigated with the symplectic method based on wave propagation theory. The governing equations of bending vibration of the thin plates were introduced into the symplectic duality system firstly, then the wave propagation parameters and wave shapes were determined as analytical solution to the symplectic eigenvalue problem. And responses of the thin plates described in physical domain were transformed into wave coordinates. The amplitudes associated with the mode shapes were obtained through solving of the equations involving excitation, scattering and propagation. Superimposition of the wave amplitudes gave the physical responses. Expressions were derived for the mean power flow through the system and mean energy in the plate components. Compared with the traditional wave methods, the provided method is applicable for any combination of classical boundary conditions. The method was applied to the forced vibration of a built-up structure of 3 directly connected thin plates and the results were compared with those from the ABAQUS finite element software. A significant improvement on accuracy and computational efficiency is achieved. As the derivation of the formulae is rigorously rational, the provided method is also applicable for the dynamic analysis of plate assemblies composed of any other types of plates (such as moderately thick plates, and layered plates, etc.).