A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory

Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of thick plate, as it directly related mechanical characteristics an engineering structure or device, elastic wave scattering and stress concentration, motion stability control distributed parameter system. In this paper, based on partial differential operator theory, exact elasto-dynamics theory without assumptions for bending vibrations presented by using formal solution proposed Boussinesq–Galerkin, its equations obtained under appropriate gauge conditions. The plate then compared with other theories plates. Since derivation equation conducted any prior assumption, plates more can be wider frequency range greater thickness.