Volume 2, Issue 2
Mathematical Modelling and Analysis of Lamb Waves in a Elastothermodiffusive Material Plates

J. N. Sharma & P. K. Sharma

Adv. Appl. Math. Mech., 2 (2010), pp. 238-258

Published online: 2010-02

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  • Abstract

The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic, thermodiffusive, elastic plate have been investigated in the context of linear theory of generalized thermodiffusion. After developing the formal solution of the mathematical model consisting of partial differential equations, the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms. The secular equations for long wavelength and short wavelength waves have also been deduced and discussed. The amplitudes of displacement components, temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained. The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations. The numerically simulated results in respect of phase velocity, attenuation coefficient, specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.

  • Keywords

Diffusion Cardano method relative frequency thermal relaxation iteration method

  • AMS Subject Headings

74G15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-2-238, author = {J. N. Sharma and P. K. Sharma}, title = {Mathematical Modelling and Analysis of Lamb Waves in a Elastothermodiffusive Material Plates}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {2}, pages = {238--258}, abstract = {The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic, thermodiffusive, elastic plate have been investigated in the context of linear theory of generalized thermodiffusion. After developing the formal solution of the mathematical model consisting of partial differential equations, the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms. The secular equations for long wavelength and short wavelength waves have also been deduced and discussed. The amplitudes of displacement components, temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained. The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations. The numerically simulated results in respect of phase velocity, attenuation coefficient, specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0945}, url = {http://global-sci.org/intro/article_detail/aamm/8330.html} }
TY - JOUR T1 - Mathematical Modelling and Analysis of Lamb Waves in a Elastothermodiffusive Material Plates AU - J. N. Sharma & P. K. Sharma JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 238 EP - 258 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0945 UR - https://global-sci.org/intro/article_detail/aamm/8330.html KW - Diffusion KW - Cardano method KW - relative frequency KW - thermal relaxation KW - iteration method AB - The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic, thermodiffusive, elastic plate have been investigated in the context of linear theory of generalized thermodiffusion. After developing the formal solution of the mathematical model consisting of partial differential equations, the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms. The secular equations for long wavelength and short wavelength waves have also been deduced and discussed. The amplitudes of displacement components, temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained. The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations. The numerically simulated results in respect of phase velocity, attenuation coefficient, specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.
J. N. Sharma & P. K. Sharma. (1970). Mathematical Modelling and Analysis of Lamb Waves in a Elastothermodiffusive Material Plates. Advances in Applied Mathematics and Mechanics. 2 (2). 238-258. doi:10.4208/aamm.09-m0945
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