Calculation of nonstationary elastic waves in an isotropic layer

Abstract

A plane problem of nonstationary waves in an infinite isotropic layer is considered. A normal force begins to act on the boundary of the layer at the instant t=0. The opposite side of the layer is free from stresses. Using integral transformations, the solution of the problem is obtained in terms of transforms. Expanding the transform solution in a series of exponential powers and inverting each term of the resulting series, the exact solution of the problem is analytically determined. The fields of stresses and velocities in the layer are calculated. The use of analytical relationships for the calculation, in contrast to the calculation with finite-difference methods, allows us to fairly accurately determine the wave pattern and to eliminate the specific effects inherent in the difference equations. The calculation algorithm used in this work allows us to calculate the solutions of the problem at any point of the layer. The results presented give an idea about the distribution of stresses and velocities of particles across the thickness and in the longitudinal direction. The calculation of nonstationary problems by summing over waves, as is done in the present work, side by side with the methods presented in [1, 2], allows transient wave processes in the layer to be represented in a more complete manner.