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

**Chuanping Zhou 1,2,3, Maofa Wang 1,\*, Xiao Han 3, Huanhuan Xue 1, Jing Ni <sup>1</sup> and Weihua Zhou <sup>4</sup>**


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

**Keywords:** exact plate theory; thick plate; bending vibration; partial differential operator theory; gauge condition
