Free vibration and wave power reflection in Mindlin rectangular plates via exact wave propagation approach

TL;DR

This paper employs an exact wave propagation approach to analyze free vibrations and wave power reflection in thick rectangular plates based on shear deformation theory, providing validated frequency results and detailed boundary condition effects.

Contribution

It introduces an exact wave propagation method for analyzing resonant frequencies and wave reflections in thick plates, considering various boundary conditions, which enhances understanding of wave behavior in structural design.

Findings

Wave power reflection in thick plates is complex and boundary-dependent.

Validated frequency results align with existing literature.

Reflected wave power is independent of system parameters for simply supported boundaries.

Abstract

Reflection, propagation and energy analysis are crucially important in designing structures, especially plates. A thick plate is considered based on first order shear deformation theory. Wave Propagation Method (WPM) is employed to exactly derive resonant frequencies and wave power reflection from different classical boundary conditions. Firstly, the frequency results are compared with other literature to validate the exact proposed wave solution in the present work. Then, wave analysis and benchmark results for natural frequencies are presented for six different combinations of boundary conditions. The results indicate that the wave power reflection of thick rectangular plates is quite complicated and an incident wave of a specific type gives rise to other types of waves except for simply supported boundary conditions where the reflected wave power does not depend on the system parameters.