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

Anil K. Vashishth; Vishakha Gupta

doi:10.3879/j.issn.1000-0887.2011.04.008

Volume 32 Issue 4

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Anil K. Vashishth, Vishakha Gupta. Uniqueness Theorem,Theorem of Reciprocity and Eigen Value Problems in the Linear Theory of Porous Piezoelectricity[J]. Applied Mathematics and Mechanics, 2011, 32(4): 455-469. doi: 10.3879/j.issn.1000-0887.2011.04.008

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

doi: 10.3879/j.issn.1000-0887.2011.04.008

Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India

Received Date: 2010-09-20
Rev Recd Date: 2011-01-19
Publish Date: 2011-04-15

Abstract

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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References(32)

References

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