The Mathematical Model of Transverse Vibrations of the Three-Layer Plate
Abstract
Abstract The article in a flat setting investigated the antisymmetric oscillations of a three-layer plate, which is infinite in plan. It is believed that the plate is not symmetrical in thickness. Based on the exact solutions of the equations of the linear theory of elasticity in transformations, a theory of unsteady transverse vibrations of a three-layer plate is developed. The oscillation equations are derived with respect to two auxiliary functions, which are the main parts of the longitudinal and transverse displacements of the points of some “intermediate” surface of the middle layer. The distance of this surface to the coordinate plane of the plate is arbitrary. All components of the stress tensors and displacement vectors at the points of the layers are expressed, like the vibration equations, through the introduced auxiliary functions. The problem of harmonic antisymmetric vibrations of an elastic three-layer plate is solved.