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Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

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Abstract

The three-dimensional free vibration analysis of a multi-directional functionally graded piezoelectric (FGP) annular plate resting on two parameter (Pasternak) elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method (SSDQM) is used to provide an analytical solution along the thickness using the state space method (SSM) and an approximate solution along the radial direction using the one-dimensional differential quadrature method (DQM). The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.

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Abbreviations

a :

outer radius of anuular plate

b :

inner radius of anuular plate

h :

thickness of anuular plate

k w :

Winkler stiffness of elastic foundation

k g :

shear stiffness of elastic foundation

σ r , σ θ , σ z :

axial stress components

τ rθ , τ θz , τ rz :

shear stress components

u r , u θ , u z :

mechanical displacement components

D r , D θ , D z :

electrical displacement components

\(\tilde \rho\) :

material density

t :

time

ε r , ε θ , ε z :

strain components

γ θz , γ rθ , γ rz :

strain components

E r , E θ , E z :

electric field components

ψ :

electric potential

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Authors and Affiliations

  1. Department of Mechanical Engineering, Razi University, Kermanshah, 67346-67149, Iran

    M. H. Yas & N. Moloudi

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  1. M. H. Yas
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  2. N. Moloudi
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Correspondence to M. H. Yas.

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Yas, M.H., Moloudi, N. Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method. Appl. Math. Mech.-Engl. Ed. 36, 439–464 (2015). https://doi.org/10.1007/s10483-015-1923-9

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  • DOI: https://doi.org/10.1007/s10483-015-1923-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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