Abstract
The problems of propagation of non-stationary waves in linear viscoelastic bodies on condition that the Poisson’s ratio of the material does not change through the time are considered. The issues of finding of the solutions of such problems by the method of Laplace transform in time are discussed. Some properties of the solution in Laplace transforms, which relate to their singular points and simplify finding the originals, have also been considered. The case when a hereditary kernel is an exponential two-parametrical one is considered. We have demonstrated that in such case the singular points of the Laplace transforms are connected by a simple relation with the singular points of the Laplace transforms for the corresponding elastic body. The conditions under which the poles of the solution in transforms have the first order have been established. As an example, the solution of the problem of one-dimensional non-stationary wave propagation in a linear viscoelastic cylinder is presented.
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Acknowledgements
The reported study was funded by Russian Foundation for Basic Research, according to the research projects Nos. 18-08-00471 a, 19-38-70005 mol_a_mos.
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Igumnov, L., Korovaytseva, E.A., Pshenichnov, S.G. (2021). Construction of the Solutions of Non-stationary Dynamic Problems for Linear Viscoelastic Bodies with a Constant Poisson’s Ratio. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_6
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