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Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent. (English) Zbl 1211.74083
Summary: The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to deal with a thermoelastic-piezoelectric coupled two-dimensional thermal shock problem of a thick piezoelectric plate of infinite extent by means of the hybrid Laplace transform-finite element method. The generalized thermoelastic-piezoelectric coupled finite element equations are formulated. By using Laplace transform the equations are solved and the solutions of the temperature, displacement and electric potential are obtained in the Laplace transform domain. Then the numerical inversion is carried out to obtain the temperature, displacement and electric potential distributions in the physical domain. The distributions are represented graphically. From the distributions, it can be found the wave type heat propagation in the piezoelectric plate. The heat wavefront moves forward with a finite speed in the piezoelectric plate with the passage of time. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in media.

MSC:
74F05 Thermal effects in solid mechanics
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