热释电材料的一般解

GENERAL SOLUTION FOR PIEZOTHERMOELASTIC MATERIALS

利用Ｓｔｒｏｈ公式，给出了热释电材料热弹性问题的一般解，此解适用于四对复共轭压电本征值和一对热本征值互不相等的情况。然后，讨论了压电本征值问题出现重根时退化热释电材料的通解，并给出相应通解的形式。当热本征值与一个或多个压电本征值相等时，给出了退化热释电材料热弹性问题特解的具体形式。最后，通过共线界面裂纹问题证明了退化热释电材料和非退化热释电材料一般解中的任意函数ｆα（ｚα）形式相同，只是其中的某些系数有所变化。

A general solution for piezothermoelastic materials is obtained by applying the extended version of Stroh’s formulation when all eigenvalues are distinct. When some piezoelectric eigenvalues are equal, the general solution for this degenerate case has also been given and discussed. Attention is also paid to the case where the heat eigenvalue pair becomes equal to one or more pairs of the piezoelectric eigenvalues and the particular solution for this degenerate piezothermoelastic problem is also given. Finally, it is shown that one can make the form of the arbitrary function f α(z α) for the degenerate piezothermoelastic solution the same as that for the undegenerate case except for some parameters included in the formulation.