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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (10): 1315-1332.doi: https://doi.org/10.1007/s10483-011-1502-6

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Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

 M. ISLAM1, S. H. MALLIK2, M. KANORIA3   

  1. 1. Department of Mathematics, St. Xavier’s College (Evening), Kolkata 700016, India;
    2. Department of Mathematics, Aliah University, Kolkata 700091, India;
    3. Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India
  • 收稿日期:2011-01-29 修回日期:2011-05-04 出版日期:2011-10-09 发布日期:2011-10-09

Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

 M. ISLAM1, S. H. MALLIK2, M. KANORIA3   

  1. 1. Department of Mathematics, St. Xavier’s College (Evening), Kolkata 700016, India;
    2. Department of Mathematics, Aliah University, Kolkata 700091, India;
    3. Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India
  • Received:2011-01-29 Revised:2011-05-04 Online:2011-10-09 Published:2011-10-09

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651

被引次数

10

摘要：

This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the 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 generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material (Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg). The effect of the body forces is also studied.

Abstract:

This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the 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 generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material (Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg). The effect of the body forces is also studied.

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