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

A·K·瓦西世; V·古泊塔

doi:10.3879/j.issn.1000-0887.2011.04.008

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

doi: 10.3879/j.issn.1000-0887.2011.04.008

古鲁格舍德拉大学数学系,古鲁格舍德拉136119,印度

基金项目: 印度大学教育资助委员会资助项目(No.f.No.8(42)/2010(MRP/NRCB))

详细信息

中图分类号: O343.7
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出版历程
- 收稿日期: 2010-09-20
- 修回日期: 2011-01-19
- 刊出日期: 2011-04-15

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

Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India

摘要

摘要: 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．
- 特征值问题 /
- 压电性 /
- 多孔性 /
- 唯一性定理 /
- 互易定理
Abstract: 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 studied employing abstract formulation.Some properties of involved operators were also studied.The problem of frequency shift due to small disturbances,based on an abstract formulation,was studied using variational and operator approach.A perturbation analysis of a special case is also given.
- eigen value problem /
- piezoelectric /
- porous /
- uniqueness theorem /
- reciprocal theorem

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参考文献(32)

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