NDLI: On Rayleigh Expansions in Thermoelastic Scattering

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kostopoulos, Vassilis Dassios, George
Copyright Year	1990
Abstract	A general thermoelastic plane wave is incident on a smooth, bounded, connected, three-dimensional body. Four basic types of boundary conditions, corresponding to an elastically rigid surface, or a cavity, combined to a zero temperature condition, or a thermally insulated body, express the physical characteristics of the scatterer. Low-frequency expansions are introduced and a systematic procedure is provided that reduces the thermoelastic scattering problem to an iterative scheme for elastostatic problems in the presence of thermal stresses. Complete Rayleigh expansions for the elastic and the thermal fields, as well as for the corresponding scattering amplitudes, for each one of the four basic scattering problems are given. The boundary value problems that determine the corresponding Rayleigh coefficients are stated explicitly in terms of four kinds of surface integrals, involving low-frequency approximations of the displacement, traction, temperature, and heat flux, as the case may be. An analysis of the thermoelastic scattering cross sections is also included. It is proved that the zeroth-order coefficient of the thermal field vanishes for all four scattering problems. Furthermore, the zeroth-order approximation of the displacement fields are not affected by the thermal coupling that influences only the low-frequency coefficients of order greater than or equal to one. In particular, two of the thermoelastic problems have identical leading approximations with the rigid scatterer, whereas the other two behave exactly as the leading approximation of a cavity. This behaviour is reflected on the thermoelastic radiation patterns. In fact, the thermal amplitudes start out with the wavenumber power one order of magnitude higher than the corresponding elastic amplitudes. The boundary value problems for the first low-frequency coefficients for each one of the four basic scattering problems are provided explicitly. Enough terms are given so as to be able to recover the leading approximation of the corresponding elastic problems. As an illustration of the method, the problem of a general thermoelastic plane wave scattered by a rigid sphere at zero temperature, is solved and the leading low-frequency approximations of the six thermoelastic amplitudes are given explictly.
Starting Page	1300
Ending Page	1324
Page Count	25
File Format	PDF
ISSN	00361399
DOI	10.1137/0150078
e-ISSN	1095712X
Issue Number	5
Volume Number	50
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-10
Access Restriction	Subscribed
Subject Keyword	low frequency approximation Rayleigh expansions thermoelastic scattering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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