Linear Analytical Study of Large Deflection of Piezoelectric Layered Plate Under Initial Tension

Abstract

AbstractThe linear problem of large deflection of a clamped and layered piezoelectric circular plate under initial tension due to lateral pressure is solved. Von Karman plate theory for large deflection is extended to a symmetrically laminated case including a piezoelectric layer. The thus derived nonlinear governing equations are simplified by neglecting the arising nonlinear terms, yielding a modified Bessel equation or a standard Bessel equation for the lateral slope. These equations are solved analytically by imposing boundary conditions for the clamped edge. For a 3-layered nearly monolithic plate with a low applied voltage upon the piezoelectric layer, the results are in a good agreement with those available in literature for a single-layered plate under pure mechanical loading, thus validates the present approach. Typical 3-layered piezoelectric plates are then implemented and the results show that, piezoelectric effect seems to be apparent only up to a moderate initial tension. For a relatively high pretension, the effect of initial tension appears to be dominant, yielding nearly the same results for the structural responses, regardless of the piezoelectric effect, i.e., the magnitude of voltage applied upon the piezo-electric layer.