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Three dimensional transient Green's functions in a thermoelastic transversely isotropic half‐space
Author(s) -
EskandariGhadi M.,
RaoofianNaeeni M.,
Pak R. Y. S.,
Ardalan Alireza A.,
Morshedifard A.
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600106
Subject(s) - thermoelastic damping , heaviside step function , mathematical analysis , transverse isotropy , laplace transform , dirac delta function , partial differential equation , ordinary differential equation , half space , boundary value problem , heat flux , mathematics , cylindrical coordinate system , physics , isotropy , differential equation , mechanics , thermal , heat transfer , quantum mechanics , meteorology
Abstract A transversely isotropic thermoelastic half‐space in both mechanical and thermal points of view is considered as the domain of the initial boundary value problem involved in this paper. The governing partial differential equations of thermoelasticity in a cylindrical coordinate system are uncoupled with the aid of a complete set of displacement‐potential and temperature‐potential functions, which with the help of Fourier series decomposition and Hankel‐Laplace integral transforms, are reduced to ordinary differential equations in terms of depth. Then, the general solutions due to an arbitrary patch‐load and surface heat flux are investigated for the case of a point load varying with time as Heaviside step function and a point heat flux varying with time as Dirac delta function in order to compute the related Green's functions. The governing equations for the potential functions are in such a way that different longitudinal and transverse waves are recognized and the transport properties can be discovered from the governing equations. Some numerical illustrations are also presented to depict the dependency of response on the thermal properties as well as the anisotropy of the medium.