MATHEMATICAL MODELING OF NON-STATIONARY ELASTIC WAVES STRESSES UNDER A CONCENTRATED VERTICAL EXPOSURE IN THE FORM OF DELTA FUNCTIONS ON THE SURFACE OF THE HALF-PLANE (LAMB PROBLEM)

Abstract

The problem of numerical simulation of longitudinal, transverse and surface waves on the free surface of an elastic half-plane is considered. The change of the elastic contour stress on the free surface of the half­plane is given. To solve the two-dimensional unsteady dynamic problem of the mathematical theory of elasticity with initial and boundary conditions, we use the finite element method in displacements. Using the finite element method in displacements, a linear problem with initial and boundary conditions resulted in a linear Cauchy prob­lem. Some information on the numerical simulation of elastic stress waves in an elastic half-plane under concen­trated wave action in the form of a Delta function is given. The amplitude of the surface Rayleigh waves is sig­nificantly greater than the amplitudes of longitudinal, transverse and other waves with concentrated vertical ac­tion in the form of a triangular pulse on the surface of the elastic half-plane. After the surface Rayleigh waves there is a dynamic process in the form of standing waves.

Keywords

• waves of stress, non-stationary process, computational mechanics, focused effects, a Delta function, leading edge of a disturbance, the falling edge of the perturbation, the direction of wave action, longitudinal wave, transverse wave, free surface, Rayleigh wave, surface wave, lamb problem, elastic half-plane, stress on the free surface