多孔压电线性理论中的唯一性定理、互易定理和特征值问题

假定弹性场和电场为正定，在多孔压电线性理论中建立起唯一性定理和互易定理．在准静态电场近似下，证明多孔压电材料线性理论中的一般性定理．利用弹性场的正定性，唯一性定理得到证明．在与多孔压电体自由振动相联系的特征值问题的研究中，给出了简明的公式．文中还研究了有关算子的某些特性．以简明公式为基础，利用变分法和算子法，研究了由于小扰动产生的频移问题．还给出了特殊情况下的扰动分析．

Uniqueness Theorem,Theorem of Reciprocity and Eigen Value Problems in the Linear Theory of Porous Piezoelectricity

The uniqueness theorem and theorem of reciprocity in the linearized theory of porous piezoelectricity were established with the assumption of positive definiteness of elastic and electric field.General theorems in the linear theory of porous piezoelectric materials were proved for the quasi-static electric field approximation.The uniqueness theorem was also proved without using positive definiteness of elastic field.An eigen value problem,associated with free vibrations of porous piezoelectric body,was stud...