Stresses in Viscoelastic Half Space at Given on the Boundary Non-stationary Normal Displacement

Аннотация

Within the framework of linear model with coinciding volume and shear relaxation kernels non-stationary problem for viscoelastic half space with normal displacements given on its boundary is considered. Solution representation in the form of generalized convolution of corresponding plane elasticity theory problem solution and one-dimensional viscoelasticity theory problem solution is used. These solutions are written down as convolution of boundary conditions with the kernels - surface Green functions. Time Laplace transform is used for kernels constructing. Its inversion is carried out exactly using either analytical representations of the transforms (for plane problem of elasticity theory) or asymptotic method (for one-dimensional problem of viscoelasticity). Explicit formulas for normal and shear stresses on the boundary of viscoelastic half space are obtained using the structure of Green functions. Examples of calculation show that contrary to elastic medium discontinuities of the first kind don’t exist on the wave front.