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Some results on eigenvalue problems in the theory of piezoelectric porous dipolar bodies

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093, Brasov, Romania

    Marin Marin

  2. Faculty of Mechanical and Systems Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    Andreas Öchsner

  3. Department of Mechanical Engineering, Transilvania University of Brasov, 500036, Brasov, Romania

    Sorin Vlase

  4. Romanian Academy Technical Sciences, 030167, Bucharest, Romania

    Sorin Vlase

  5. Faculty of Medicine, Transilvania University of Brasov, 500036, Brasov, Romania

    Dan O. Grigorescu

  6. Department of Civil Engineering, Transilvania University of Brasov, 500036, Brasov, Romania

    Ioan Tuns

Authors
  1. Marin Marin
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  2. Andreas Öchsner
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  3. Sorin Vlase
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  4. Dan O. Grigorescu
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  5. Ioan Tuns
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Correspondence to Marin Marin.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by Andreas Öchsner.

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Marin, M., Öchsner, A., Vlase, S. et al. Some results on eigenvalue problems in the theory of piezoelectric porous dipolar bodies. Continuum Mech. Thermodyn. 35, 1969–1979 (2023). https://doi.org/10.1007/s00161-023-01220-0

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  • DOI: https://doi.org/10.1007/s00161-023-01220-0

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