Problem of Dynamics of an Elastic Rod with Decreasing Function of Elastic-Plastic External Resistance

The wave problem of propagation of shock perturbation in a semi-infinite elastic rod interacting with the medium is investigated using the model of elastic-plastic resistance with decreasing relation between shear stress and jump of displacement on the lateral surface. An exact solution of the initial-boundary problem is obtained using the Laplace transforms. A wave pattern of perturbation including the prefront zone of rest, the area of motion and the domain of stationary residual stresses has been built. The three-dimensional diagrams for nonstationary fields of displacement, velocity and stresses have been constructed too.