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A model for bending and stretching of piezoelectric rods obtained by asymptotic analysis

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Abstract

The aim of this paper was to obtain a new model for the bending-stretching of an anisotropic heterogeneous linearly piezoelectric cantilever rod when the electric potential is applied on the both ends. The process is assumed to be static, and the piezoelectric material is monoclinic of class 2. To derive the model, we start with the corresponding three-dimensional problem, introduce a change of variable together with a scaling of the unknowns and then we use a passage to the limit procedure, based on arguments of asymptotic analysis taking the diameter of the cross-section as small parameter. Finally, we prove a result of strong convergence that justifies both the method and the one-dimensional model obtained. One of the most relevant features of this one-dimensional model is that the stretching is coupled with the electric potential, while the bendings are not.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Univ. de Santiago de Compostela, Santiago de Compostela, Spain

    J. M. Viaño

  2. Departamento de Matemática e Aplicações and Centro de Matemática, Univ. do Minho, Guimarães, Portugal

    J. Figueiredo & C. Ribeiro

  3. Departamento de Métodos Matemáticos e Representación, Univ. de A Coruña, A Coruña, Spain

    Á. Rodríguez-Arós

Authors
  1. J. M. Viaño
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  2. J. Figueiredo
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  3. C. Ribeiro
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  4. Á. Rodríguez-Arós
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Correspondence to Á. Rodríguez-Arós.

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Viaño, J.M., Figueiredo, J., Ribeiro, C. et al. A model for bending and stretching of piezoelectric rods obtained by asymptotic analysis. Z. Angew. Math. Phys. 66, 1207–1232 (2015). https://doi.org/10.1007/s00033-014-0438-1

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  • DOI: https://doi.org/10.1007/s00033-014-0438-1

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