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Memory response in a two‐dimensional transversely isotropic thick plate with varying heat source
Author(s) -
Islam Mohsin,
Mondal Sudip
Publication year - 2021
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.202000236
Subject(s) - laplace transform , transverse isotropy , fourier transform , integral transform , thermoelastic damping , mathematical analysis , isotropy , mathematics , geometry , materials science , mechanics , physics , thermal , optics , thermodynamics
This present survey deals with a novel mathematical model of generalized thermoelasticity which investigates the transient phenomena in a two‐dimensional problem for a transversely isotropic thick plate having a heat source. The upper surface of the plate is stress‐free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the three‐phase‐lag thermoelastic model. The governing equations for displacement and temperature fields are obtained in the Laplace‐Fourier transform domain by applying the Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of the Laplace transform is done by using a method based on the Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the memory‐dependent derivative on the solutions has been studied.