Waves in inhomogeneous viscoelastic materials

The work is devoted to the improvement of one of the methods for constructing solutions to problems of transient wave processes in viscoelastic inhomogeneous bodies. Piecewise homogeneous and functionally graded materials are considered. The disturbances propagations domain is considered limited. The hereditary properties of materials are characterized by linear Boltzmann–Volterra relations with hereditary kernels of various types. The integral Laplace transform in time and the operation of its reversal are used. New forms of representation of solutions to nonstationary viscoelasticity problems in originals are obtained for both regular and singular relaxation kernels. The solutions contain series expansions as well as integrals. Their advantage is the absence of rapidly oscillating functions under the signs of improper integrals. They are convenient for numerical implementation for any point in time. The proposed approach is demonstrated on examples. The results of studies of nonstationary processes in inhomogeneous viscoelastic bodies under specific initial data are presented.
The research was supported by the Russian Science Foundation, grant No 24-29-00164, https://rscf.ru/en/project/24-29-00164/.