热弹性力学和广义热弹性力学的波系
Thermoelasticity and Generalized Thermoelasticity Viewed as Wave Hierarchies
摘要：
它是看到如何写的四个偏微分方程的标准形式在四个未知数的各向异性热弹性作为一个单一的方程在一个变量，在等温和等熵波算子。该方程是扩散型的，空间导数为八阶，时间导数为七阶，因此是抛物型的。在看到如何将一维扩散方程转换为惠特姆的波层次形式之后，我们看到如何将单向运动的完整方程转换为波层次形式。高阶波是等温的，低阶波是等熵的或纯扩散的。波的层次形式，然后用来推导出的初始值问题的解决方案的主要特点，从而绕过了需要的渐近分析的积分形式的精确解。结果是专门的各向同性的情况下。广义热弹性理论将松弛时间与热流矢量联系起来，得到的方程组具有双曲性质。它也看到了如何写这个系统的波层次的形式，这是再次用来推导出的主要特点的解决方案的初始值问题。在各向同性的情况下，得到了更简单的结果。
英文摘要：
It is seen how to write the standardÊ form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This equation, of diffusive type, is of the eighth order in the space derivatives and seventh order in the time derivatives and so is parabolic in character. After having seen how to cast the 1D diffusion equation into Whitham's wave hierarchy form it is seen how to recast the full equation, for uni-directional motion, in wave hierarchy form. The higher order waves are isothermal and the lower order waves are isentropic or purely diffusive. The wave hierarchy form is then used to derive the main features of the solution of the initial value problem, thereby bypassing the need for an asymptotic analysis of the integral form of the exact solution. The results are specialized to the isotropic case. The theory of generalized thermoelasticity associates a relaxation time with the heat flux vector and the resulting system of equations is hyperbolic in character. It is seen also how to write this system in wave hierarchy form which is again used to derive the main features of the solution of the initial value problem. Simpler results are obtained in the isotropic case.
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