Asymptotic Model of Non-Stationary Processes in Shells of Revolution under the Action of End Impact Loads of Bending Type

Abstract

The present study deals with the construction of an asymptotic model of propagation of non-stationary waves in thin shells of revolution under the action of end impact loads of the bending type. The developed asymptotic methods for solving boundary value problems for the components of the stress-strain state that are the main ones for the considered type of waves, namely the bending component according to the Kirchhoff-Love theory and the hyperbolic boundary layer, are described. The asymptotic methods are based on various types of expansions in power series in a small parameter of thinness of the wall depending on the values of the indices of variability and dynamicity. In this case, integral Laplace transforms in time and Fourier transforms in the spatial coordinate, methods of frontal asymptotics, expansions in special functions are used. Calculations performed on the example of a spherical shell have shown the efficiency of the developed methods.