Transient Waves Due to Thermal Sources in a Generalized Piezothermoelastic Half-Space

Abstract

This paper is devoted to the study of disturbances due to impact and continuous strip thermal sources, tem- perature or temperature gradient input acting on the rigidly fixed and charge free(open circuit) surface of a homogeneous, transversely isotropic, thermally conducting, generalized piezothermoelastic half-space. The Laplace and Fourier transforms technique have been employed to solve the model consisting of partial dif- ferential equations and boundary conditions in the transformed domain. In order to obtain the results in the physical domain the quadratic complex polynomial characteristic equation corresponding to the associated system of coupled ordinary differential equations has been solved by using DesCartes’ algorithm with the help of irreducible Cardano’s method. The inverse transform integrals are evaluated by using numerical technique consisting of Fourier series approximation and Romberg integration. The temperature change, stresses and electric potential so obtained in the physical domain are computed numerically and presented graphically for cadmium selenide (CdSe) material. The study may find applications in smart structures, pie- zoelectric filters, resonators, transducers, sensing devices and vibration control.

This paper is devoted to the study of disturbances due to impact and continuous strip thermal sources, tem- perature or temperature gradient input acting on the rigidly fixed and charge free(open circuit) surface of a homogeneous, transversely isotropic, thermally conducting, generalized piezothermoelastic half-space. The Laplace and Fourier transforms technique have been employed to solve the model consisting of partial dif- ferential equations and boundary conditions in the transformed domain. In order to obtain the results in the physical domain the quadratic complex polynomial characteristic equation corresponding to the associated system of coupled ordinary differential equations has been solved by using DesCartes’ algorithm with the help of irreducible Cardano’s method. The inverse transform integrals are evaluated by using numerical technique consisting of Fourier series approximation and Romberg integration. The temperature change, stresses and electric potential so obtained in the physical domain are computed numerically and presented graphically for cadmium selenide (CdSe) material. The study may find applications in smart structures, pie- zoelectric filters, resonators, transducers, sensing devices and vibration control.

Keywords

Thermal Sources, Integral Transforms, Romberg Integration, Relaxation Time, DesCartes’ Algorithm

Thermal Sources, Integral Transforms, Romberg Integration, Relaxation Time, DesCartes’ Algorithm

Cite this paper

nullJ. Sharma, A. Thakur and Y. Sharma, "Transient Waves Due to Thermal Sources in a Generalized Piezothermoelastic Half-Space,"*Engineering*, Vol. 3 No. 3, 2011, pp. 248-259. doi: 10.4236/eng.2011.33029.

nullJ. Sharma, A. Thakur and Y. Sharma, "Transient Waves Due to Thermal Sources in a Generalized Piezothermoelastic Half-Space,"

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