Multilayer Higher Order Piezolaminated Smart Composite Shell Finite Element and its Application to Active Vibration Control

Abstract

This paper deals with the formulation of a higher order shear-flexible piezolaminated 8-node C1 continuous multilayer smart composite shell finite element with higher order modeling of electric potential. The potential induced due to bending deformation is more accurately modeled assuming quadratic variation of electric potential through the thickness of each piezoelectric layer. This is achieved by interpolating using nodal mid-plane electric potentials and one electric degree of freedom representing the potential difference between the top and bottom surfaces of the piezoelectric layer, resulting in nine electric degrees of freedom per piezoelectric layer in the element. The higher order shell theory used satisfies the stress and displacement continuity at the interface of the composite laminates and has zero shear stress on the top and bottom surfaces. The transverse shear deformation is of a higher order represented by the trigonometric functions, allowing us to avoid the shear correction factors. In order to maintain the field consistency, the inplane displacements, u and v, and rotations θx and θ y, are interpolated using quadratic interpolation functions while the transverse displacement w is interpolated using Hermite cubic interpolation function, resulting in 48 elastic degrees of freedom per element. The active vibration control performances of the piezolaminated smart composite plates/shells have been studied by modeling them with the above element and applying LQR optimal control.