一维半无限压电杆的广义的热冲击问题

采用具有两个热松驰时间的G－L广义热弹性理论，研究了一维无限无限长杆在其端部受到热冲击时的边值问题，借助于拉普拉斯正、反变换技术，在所考虑时间非常短的情况下，对问题进行了求解。得到了位移及温度分布的近似妥析角，发现位移及温度分布中分别存在两上阶跃点，并通过数值计算，把温度的分布规律用图形反映了出来，从温度的分布图上可以看出，当任何x的值大于第二个阶跃点的位置值时，温度值都是零，也即在当前所绘定的时刻，热以波的形式沿压电杆仅传播到第二阶跃点的位置，而在第二个阶跃点之后，压电杆上的温度分布保持初始温度；定不同时刻，热波波前的位置也将相应的在压电杆上移动，也即热波波前在压电杆上的位置随考虑时刻不同而不同，这与经典的热传导是完全不同的，它说明热是以波的形式以有限的速度，而不是以无限的速度在介质中进行传播的。

ONE-DIMENSIONAL GENERALIZED THERMAL SHOCK PROBLEM FOR A SEMI-INFINITE PIEZOELECTRIC ROD

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.