Transient Wave Propagation in Functionally Graded Viscoelastic Structures

Pshenichnov, S.; Ivanov, R.; Datcheva, M.

Авторы: Pshenichnov S., Ivanov R., Datcheva M.
Журнал: Mathematics
Том: 10
Год издания: 2022
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Номер статьи: 4505
DOI: 10.3390/math10234505
Аннотация: Transient wave processes in viscoelastic structures built from functionally graded material(FGM) still remain almost unexplored. In this article, the problem of the propagation of nonstationarylongitudinal waves in an infinite viscoelastic layer of a FGM with plane–parallel boundariesis considered. The physical and mechanical parameters of the FGM depend continuously on thetransverse coordinate, while the wave process propagates along the same coordinate. The viscoelasticproperties of the material are taken into account employing the linear integral Boltzmann–Volterrarelations. The viscoelastic layer of the FGM is replaced by a piecewise-homogeneous layer consistingof a large number of sub-layers (a package of homogeneous layers), thus approximatingthe continuous inhomogeneity of the FGM. A solution of a non-stationary dynamic problem for apiecewise-homogeneous layer is constructed and, using a specific example, the convergence of theresults with an increase in the number of sub-layers in the approximating piecewise-homogeneouslayer is shown. Furthermore, the problem of the propagation of nonstationary longitudinal waves inthe cross section of an infinitely long viscoelastic hollow FGM cylinder, whose material propertiescontinuously change along the radius, is also considered. The cylinder composed of the FGM isreplaced by a piecewise-homogeneous one, consisting of a large number of coaxial layers, for whichthe solution of the non-stationary dynamic problem is constructed. For both the layer and the cylindercomposed of a viscoelastic FGM, the results of calculating the characteristic parameters of the waveprocesses for the various initial data are presented. The influence of the viscosity and inhomogeneityof the material on the dynamic processes is demonstrated
Добавил в систему: Пшеничнов Сергей Геннадиевич

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Transient Wave Propagation in Functionally Graded Viscoelastic Structuresстатья

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