Stationary Dynamic Acoustoelasticity Problems of a Thin Plate in a Perfect Compressible Fluid, Taking into Account the Dissipation of Energy in the Plate and Liquid

We propose the refined equations of motion of the plate and the fluid with additional accounting of the energy dissipation in the material of the plate and fluid based on the Thompson–Kelvin–Voight hysteresis model. These equations are used for the formulation of stationary dynamic problems in the field of acoustoelasticity of thin plates surrounded on both sides by acoustic media, which is represented as a perfect compressible fluid. Refinement of fluid behavior is based on the assumption that the pressure increment in fluid is proportional not only to volumetric deformation, but also to its velocity. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing into consideration the complex velocity of sound according to the representation of Skudrzyk to account for energy dissipation. The equations of the plate motion are based on the classical Kirchhoff-Love model.