The solution of wave problems is usually connected with significant difficulties. One of the effective methods for solving these problems is the method of integral transformations. However, even if we use this method, then it is sometimes impossible to obtain a solution in the final form or at least in the form suitable for subsequent numerical calculations. By using an example of analysis of the process of propagation of waves in a plate from a spherical source, we propose a method for overcoming these difficulties. Simplification of the problem is realized by splitting the total wave into elementary components with respect to the wave numbers and complex frequencies. The solution is reduced to the possibility of numerical calculations on a computer. The practical application of these calculations can be useful, in particular, for the analysis of the data obtained by the acoustic-emission method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. McClintock and A. Argon, Deformation and Destruction of Materials, Mir, Moscow (1970).
C. L. Hom and R. M. McMeeking, “Three-dimensional void growth before blunting crack tip,” J. Mech. Phys. Solids, 37, No. 3, 395–416 (1989).
J. R. Rise and D. M. Tracey, “On the ductile enlargement of voids in triaxial stress fields,” J. Mech. Phys. Solids, 17, No. 3, 201–207 (1969).
S. Murakami, “Damage mechanics. Continuum mechanic approach to damage and fracture of materials,” J. Soc. Mat. Sci. Japan, 31, No. 340, 1–13 (1982).
V. Tvergard, “Influence of voids on shear band instability under plane strain conditions,” Int. J. Fracture, 17, No. 4, 389–407 (1981).
A. L. Gurson, “Continuum theory of ductile rupture by void nucleation and growth. Part 1. Yield criteria and flow rules for porous ductile material,” J. Eng. Mater. Technol., 99, No. 2 (1977).
D. Broek, “Some contributions of electron fractography to the theory of fracture,” Int. Metal. Rev., 19, 135–182 (1974).
B. Budiansky, J. W. Hutchinson, and S. Slutsky, “Voids growth and collapse in viscous solids,” in: Mechanics of Solids, Pergamon Press (1982), p. 13–46.
M. J. Worswick and R. J. Rick, “Void growth and constituting softening in a periodically voided solid,” J. Mech. Phys. Solids, 38, No. 5, 601–625 (1990).
G. P. Cherepanov, Mechanics of Brittle Fracture, Nauka, Moscow (1974).
S. A. Nedoseka and A. Ya. Nedoseka, “Comprehensive assessment of damage and residual life of metals with operating time,” Tech. Diagnost, Nondestruct, Testing, No. 1, 9–16 (2010).
S. A. Nedoseka, A. Ya. Nedoseka, et al., “Features of acoustic emission when assessing the material state,” Tech. Diagnost. Nondestruct. Testing, No. 2, 3–12 (2020).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Neliniini Kolyvannya, Vol. 25, No. 1, pp. 49–58, January–March, 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Nedoseka, S.A. Features of the Application of Integral Transformations to the Solution of Some Wave Problems. J Math Sci 274, 50–59 (2023). https://doi.org/10.1007/s10958-023-06570-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06570-3