Interaction of a plane pressure wave with a spherical shell in an elastic medium

DOI: 10.34759/trd-2023-129-08

Аuthors

Thant Z. H.

Defense Services Technological Academy (DSTA), Mandalay-Lashio Highway, Mandalay Division, Pyin Oo Lwin, Myanmar

e-mail: thantzinhein3646@gmail.com

Abstract

This article considers the nonstationary problem of a plane pressure wave impact on a spherical shell in an elastic medium. Both desired and prescribed functions are represented in the form of series by the Lejandre and Hegenbauer polynomials to obtain the analytical solution of the non-stationary diffraction problem of the flat pressure wave on the spherical surface in an elastic medium supported by the thin shell. The solution method is based on the expansion into series on the system of eigenfunctions and application of the Laplace integral transformation in time. As the result, analytical expressions were obtained for all desired functions, which allows studying non-stationary strain-stress state and displacements both on the shell and at any point of the elastic medium.

The problems of elastic waves diffraction on various types of heterogeneities relate to the most difficult and up-to-date problems in the dynamics of deformable bodies. In the applied terms, it is explained by the circumstance that the information on the stress-strain state near these irregularities is of great interest for various purposes. Besides, the presence of heterogeneities (inclusions, cavities, notches, local changes in properties, etc.) is an indispensable condition arising in various fields of modern engineering. Such tasks include the following: creation of new structures, working at dynamic loads, development of new composite materials and their introduction at creation of engineering constructions, modern tasks of geophysics and seismology, and also a number of other tasks of scientific and technical character.

Keywords:

elastic wave diffraction problems, method for solving eigenfunctions, spherical shell in an elastic medium, dynamic stress-strain state

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