Acoustic wave propagation through a plate fixed in a rigid frame using elastic interlayers and located between two barriers

The problem of the propagation of a stationary acoustic wave through an infinite thin plate stiffened on two sides by a system of absolutely rigid, crossed ribs and between two absolutely rigid barriers. It is assumed that the plate and the ribs evenly distributed along rectangular Cartesian axes are connected through elastic interlayers (foundations) without sliding. The dynamic deformation of the plate is described by the linearized Kirchhoff–Love equations of the classical theory of plates, the dynamic deformation of the interlayers is described by two-dimensional and one-dimensional relations based on linear approximations of displacements of points of the coating and interlayers along the thickness and taking into account only transverse compression and transverse shear, and the motion of acoustic media by the well-known wave equations. The solution of the problem is obtained using the Ritz method. The constructed solution was used to investigate how the physico-mechanical and geometric parameters of the mechanical system and the frequency of an acoustic wave incident on the plate influence the sound insulation parameters and the stress-strain state of the plate.