Abstract
The problems of non-stationary waves propagation in linear viscoelastic bodies are considered. The issues related to the construction of the solutions of such problems by method of integral Laplace transform in time are discussed. The statements about the properties of the solution in the space of Laplace transforms, which simplify the process of finding the originals, are formulated. As an example, the solution of the problem of propagation of one-dimensional shear waves in a viscoelastic cylinder is obtained.
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