Some results on eigenvalue problems in the theory of piezoelectric porous dipolar bodies. (English) Zbl 1523.74003
Summary: In our study we construct a boundary value problem in elasticity of porous piezoelectric bodies with a dipolar structure To construct an eigenvalue problem in this context, we consider two operators defined on adequate Hilbert spaces. We prove that the two operators are positive and self adjoint, which allowed us to show that any eigenvalue is a real number and two eigenfunctions which correspond to two distinct eigenvalues are orthogonal. With the help of a Rayleigh quotient type functional, a variational formulation for the eigenvalue problem is given. Finally, we consider a disturbation analysis in a particular case. It must be emphasized that the porous piezoelectric bodies with dipolar structure addressed in this study are considered in their general form, i.e.,inhomogeneous and anisotropic.
MSC:
| 74A35 | Polar materials |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74F15 | Electromagnetic effects in solid mechanics |
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
Keywords:
piezoelectricity; boundary value problem; eigenvalue problem; Rayleigh quotient; variational approach; disturbation analysisReferences:
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