New finite element method techniques in modeling smart structures for vibration control applications

Piezoceramic wafer (patch) actuators have been used for the excitation and control of vibrations of beam and plate-like structures. Precise constitutive modeling of the system is important for accurate computer simulation and in some control applications. In this dissertation, novel 1-D beam and 2-D linear and non-linear plate elements are developed for multilayered electromechanically coupled structures. The effects of shear deformation in structures and resultant energy dissipation because of mechanical means as well as dissipation due to the nonlinearity of the electrical domain are considered for the developed models. The mechanical modeling of the linear beam and linear plate elements adapt Timoshenko beam and Mindlin plate theory that were originally developed for single layered structures and expands them to multilayered structures where the same strain equations are also used for deriving electromechanical coupling equations. The nonlinearity of the transducers is incorporated using a special case of the Preisach Nonlinear Model, which is called the Ishlinskii hysteresis model. Numerical results obtained by linear beam and plate models, as well as the nonlinear model, are compared with experimental and theoretical results, and it is observed that each element presents a good potential for simulating thick multilayered smart structures, both with linear and nonlinear electrical properties. The developed finite element model is used for control optimization problems where active, passive and hybrid control algorithms are developed. Passive control, based on shunting a piezoceramic patch with an inductor-resistor (LR) circuit, is combined with a linear quadratic regulator (LQR) added to the shunt to enable active control. An optimization study for hybrid control is presented where all of the control parameters, including active feedback gain, passive shunt inductance and resistance, are optimized numerically; the response of the structure to an impulse disturbance is simulated for both controlled and uncontrolled cases.