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《Acta Mechanica Sinica》 2003-02
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ONE-DIMENSIONAL GENERALIZED THERMAL SHOCK PROBLEM FOR A SEMI-INFINITE PIEZOELECTRIC ROD

He Tianhu Tian Xiaogeng Shen Yapeng(Dept. of Engineering Mechanics, Xi'an Jiaotong University, Xi'an 710049, China)  
The theory of generalized thermoelasticity, based on the theory of Green and Lindsay with two relaxation times, is used to solve a boundary value problem of one-dimension semi-infinite piezoelectric rod with one end subjected to a sudden heat. Approximate small-time analytical solutions of displacement and temperature are obtained by means of the Laplace transform and inverse transform. It is found that there are two discontinuous points in both displacement and temperature solutions. Numerical calculation for temperature is carried out and displayed graphically. From the distribution of temperature, it can be found temperature is zero when any x is bigger than the position of the second discontinuous point. It indicates the wave type heat propagation along the piezoelectric rod. At the given instant, heat wavefront only reaches the position of the second discontinuous point. After the second discontinuous point position, temperature remains the initial value. The heat wavefront will move backward or forward along the piezoelectric rod with the chang of considered instant. 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.
【Fund】: 国家自然科学基金资助项目(10132010);; 高校博士点基金资助项目(20010698018).
【CateGory Index】: O343.6
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