ON THE PROPAGATION OF TORSIONAL WAVES IN LAYERED COMPOSITE MATERIALS WITH INITIAL STRESSES UNDER THE LAYERS’ SLIPPAGE

Abstract

The study of torsional waves plays an important role in various fields of science and technology, providing innovative approaches to solving complex problems and improving existing technologies. In particular, torsional waves are widely used in materials science, especially in the study and diagnosis of material properties. Within the framework of the linearised theory of elasticity for bodies with initial stresses, the formulation and method of solving problems on propagation of torsional waves in layered composite compressible prestressed materials at slipping of layers are considered. The paper deals with the propagation of torsional waves in the radial direction along layers in composite compressible materials with initial stresses. The problem is reduced to the construction of solutions of the equation with respect to the amplitude function under the conditions of continuity at the interfaces and periodicity conditions, according to the Floquet theory. Dispersion equations and their long-wave approximations are obtained for symmetric and antisymmetric torsional waves. The dispersion equations are solved analytically. In the case of slip, there is no interaction between the composite material layers. The propagation velocities of symmetric and antisymmetric torsional waves in each layer depend on the mechanical parameters of the layer material, layer thickness and initial stresses. In the long-wave approximation, the propagation velocities of symmetric and antisymmetric torsional waves for each layer are equal to the propagation velocities of transverse waves in a homogeneous material with initial stresses in the first and second layers, respectively.