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Thermo-mechanical response of size-dependent piezoelectric materials in thermo-viscoelasticity theory

  • Ezzat, Magdy A. (Department of Mathematics, College of Science and Arts, Qassim University) ;
  • Al-Muhiameed, Zeid I.A. (Department of Mathematics, Faculty of Science, Qassim University)
  • Received : 2021.07.23
  • Accepted : 2022.11.14
  • Published : 2022.11.25
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Abstract

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

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References

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