3-D free vibration analysis of piezoelectric coupled circular/annular thick plates via Chebyshev-Ritz method

This paper provides natural frequencies of thick circular and annular plates, both upper and lower surfaces of which are in contact with a piezoelectric layer, on the basis of three-dimensional (3-D) small-strain, linear elasticity theory. Three displacement components along with electrical potential field of the piezoelectric coupled circular/annular plate are expressed in the Ritz method by adopting a set of Chebyshev polynomials multiplied by geometric boundary functions in a cylindrical coordinate system. Various combinations of free, soft simply supported, hard simply supported and clamped boundary conditions are considered at the inner and outer edges of the plate. A new strategy is introduced to reduce computational cost significantly through decreasing the number of integration for the potential and kinetic energy functions and eliminatingdifferentiation with respect to unknown coefficients while minimizing the energy functional. Convergence studies are carried out for the iezoelectric coupled annular plate with different boundary conditions to demonstrate high numerical stability of the present method. A comparison of the present non-dimensional vibration frequencies of piezoelectric coupled annular plates is made with previously published results obtained by the Mindlin plate theory, Reddy plate theory and 3-D modified finite element method. The effects of plate parameters such as thickness to radius ratios, inner to outer radius ratios and piezo to host thickness ratios on the natural frequencies of coupled piezoelectric circular/annular plates are investigated for ifferent combinations of boundary conditions. All mode shapes, including flexural and torsional modes, are illustrated in the present analysis.

Keywords:

Free vibration , laminated plate , 3-D elasticity theory , piezoelectric , Ritz method