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Steel and Composite Structures
  Volume 45, Number 4, November25 2022 , pages 535-546

Thermo-mechanical response of size-dependent piezoelectric materials in thermo-viscoelasticity theory
Magdy A. Ezzat and Zeid I.A. Al-Muhiameed

    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 semiinfinite 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.
Key Words
    dual-phase lag; laplace transform; memory-dependent derivative; size-dependent thermo-viscoelastic coupling; thermo-piezoelectricity
Magdy A. Ezzat:1)Department of Mathematics, College of Science and Arts, Qassim University, Al Bukairyah, Saudi Arabia
2)Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

Zeid I.A. Al-Muhiameed:Department of Mathematics, Faculty of Science, Qassim University, Buraydah 51452, Saudi Arabia

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