论文标题
热弹性和普遍的热弹性被视为波层次结构
Thermoelasticity and Generalized Thermoelasticity Viewed as Wave Hierarchies
论文作者
论文摘要
可以看出，如何将四个部分微分方程的标准划形式写在各向异性热弹性的四个未知数中，作为一个变量，就等于等温和等粒子波算子而言。扩散类型的该方程是空间衍生物中的第八顺序，在时间衍生物中是第七阶，在特征上是抛物线的。在看到了如何将1D扩散方程施加到Whitham的波浪层次结构形式中后，人们可以看到如何以波层次结构形式重塑整个方程，以进行单向运动。高阶波是等温的，较低的波是等等的，是等等的或纯粹扩散的。然后使用波浪层次结构形式来得出初始值问题的解决方案的主要特征，从而绕开了对精确解决方案积分形式的渐近分析的需求。结果专门针对各向同性情况。广义热弹性的理论将放松时间与热通量矢量和结果方程系统相关联是双曲线的。还可以看到如何以波层次结构形式编写此系统，该系统再次用于得出初始值问题解决方案的主要特征。在各向同性情况下获得了更简单的结果。
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.
