ABSTRACT
The paper addresses stationary sound wave transmission through a thin plate of infinite extent, supported from both sides by a system of absolutely rigid crossed ribs, and located between two rigid barriers. One of barriers forms an incident sound wave due to harmonic vibration with an assigned displacements amplitude, while the other barrier is fixed and has a deformable energy-absorbing coating made from a material with high damping properties. It is assumed that the joint of the plate with the ribs located along the axes of Cartesian coordinate system with uniform steps is carried out through the interlayers (foundations) without slipping. The acoustoelasticity problem is formulated for the cell of periodicity, which is cut from the plate. The probem describes the interaction of the plate with the surrounding acoustic media and on its contour with deformable interlayers that are classified as transversally soft. Dynamic deformation of the plate is described by the linearized equations of the classical Kirchhoff-Love’s plate theory; the deformation of interlayer by two-dimensional and one-dimensional relations based on the linear approximations of covering and interlayer displacements in the direction of the thickness and taking into account only the transverse compression and transverse shear deformations; and the motion of acoustic environments by well-known wave equations. The internal friction of the plate, the barrier covering and the contour interlayers is taken into account in the elasticity relations by Thomson Kelvin-Voigt hysteresis model. With the use of trigonometric basis functions, the exact analytical solution of the formulated problem is conducted. On the basis of the solution, the influence is studied of physical-mechanical and geometric parameters of the considered mechanical system and of incident sound wave frequency on the sound reduction index and on the parameters of stress-strain state of the plate.
