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Free vibration of a functionally graded annular sector plate integrated with piezoelectric layers

Shahdadi, A ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.apm.2019.10.039
  3. Publisher: Elsevier Inc , 2020
  4. Abstract:
  5. Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then employed to present analytical solutions for free vibration of smart FG annular sector plates with simply supported radial edges and arbitrarily supported circular edges. The results, which can be used as a benchmark and suitable for design purposes, are verified with those reported in the literature. Finally, by presenting extensive ranges of frequencies, the effects of geometric parameters, power law index, FG and piezoelectric materials, electrical and mechanical boundary conditions as well as the piezoelectric layer thickness on vibration response of smart annular sector plates are discussed in detail. © 2019
  6. Keywords:
  7. Analytical solution ; First order shear deformation theory ; Functionally graded material ; Piezoelectric layer ; Beams and girders ; Boundary conditions ; Electric potential ; Equations of motion ; Fourier series ; Functionally graded materials ; Piezoelectricity ; Plates (structural components) ; Shear deformation ; Annular sector plate ; Coupled partial differential equations ; Electrical boundary conditions ; First-order shear deformation theory ; Fourier series method ; Fourth-order equations ; Free vibration behavior ; Piezoelectric layers ; Vibration analysis
  8. Source: Applied Mathematical Modelling ; Volume 79 , 2020 , Pages 341-361
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0307904X19306274