A mixed model for composite beams with piezoelectric actuators and sensors

A theoretical formulation to model composite smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented here. The mathematical model is based on a high order displacement field coupled with a layerwise linear electric potential. This model is developed for a composite beam structure using Hamilton's variational principle and is facilitated by the finite element (FE) formulation. The generic element implemented in the FE analysis is a two-noded Hermitian - 2(n+1) layerwise noded element for an n-layered beam. The variational principle led to a derivation that could include dynamic analysis but the present work will only focus on the static beam structure. This formulation in general will enable the modeling of vibration and shape control applications. Comparison of numerical results from this formulation with previous works, including three configurations - non-piezoelectric, actuator and sensor configurations, showed a high to a reasonable degree of correlation. The effects of varying actuator locations and orientations on the deflection and curvature of the beam were also studied.