A spectral relation for Chebyshev-Laguerre polynomials and its application to dynamic problems of fracture mechanics |
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| Affiliation: | 1. Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street s/n, Salinópolis, PA 68721-000, Brazil;2. Department of Energy Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Muegyetem rkp. 3., Budapest H-1111, Hungary;3. Department of Theoretical Physics, Wigner Research Centre for Physics, Budapest, Hungary;4. Ph.D. Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, Belém, PA 66075-110, Brazil |
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| Abstract: | A new spectral relation for Chebyshev-Laguerre polynomials is derived and its use to construct an exact solution of the antiplane problem of the theory of elasticity on the diffraction of a shock SH-wave by a semi-infinite crack is described, when this wave is incident on the crack at an arbitrary angle. The problem is reduced to an integro-differential equation by the method of discontinuous solutions. An exact solution of this equation using the spectral relation obtained is given. A formula is obtained for the scattered wave and for the stress intensity factor. |
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