The Transmission of an Acoustic Wave Through a Composite Plate with Energy Dissipation in a Material Taken into Account Based on Three-Dimensional Equations of Elasticity Theory

Abstract

The problem of a plane monoharmonic sound wave passage through a thin composite rectangular plate hinged in the opening of an absolutely stiff dividing wall has been considered on the basis of two-dimensional in spatial coordinates motion equations. These equations have been constructed by the reduction of three-dimensional equations on the basis of the discrete layered model of a multilayer plate deformation at small displacements and deformations with account of the internal damping of layers according to the Kelvin–Voight model. Behavior of acoustic media has been described by the classical wave equations based on the model of an ideal compressible fluid. The exact analytical solutions of the formulated problem have been constructed. The dependence of sound insulation properties and parameters of the stress-strain state of a composite plate reinforced with carbon fiber textile on the incident sound wave frequency was studied. It is shown that under high-frequency acoustic impact, the deformation mechanics of the structures made of fiber reinforced composite must be described by refined equations of motion as they have a high degree of accuracy and intensionality since the formation of the stress-strain state in them is almost three-dimensional with components of the same order.