Influence of piezoelectric nonlinearity on active vibration suppression of smart laminated shells using strong field actuation

In this work, we study the effect of piezoelectric nonlinearity on shape and active vibration control of smart piezolaminated composite and sandwich shallow shells under strong field actuation. An efficient finite element model with advanced laminate kinematics and full electromechanical coupling is developed for this purpose. The nonlinearity is modeled using a rotationally invariant quadratic constitutive relationship for the piezoelectric material. For the laminate kinematics, a recently developed efficient layerwise theory, which is computationally as efficient as an equivalent single-layer theory, and has been shown to yield very accurate results in comparison with three-dimensional piezoelasticity based solutions for linear electromechanical response of hybrid laminated shells, has been employed. The nonlinear static response for shape control is obtained using the direct iteration method, and the active vibration control response with linear quadratic Gaussian controller is obtained by using the feedback linearization approach through control input transformation. It is shown that the linear model significantly overestimates the voltage required for shape or vibration control, when the applied electric field is beyond the threshold limit of the actuator. Thus, the use of the nonlinear model is essential for designing the control system utilizing the full actuation authority of the actuators. The effects of actuator thickness, radius of curvature to span ratio and applied loading on the relative difference between linear and nonlinear predictions are illustrated for shape and vibration control of smart cylindrical and spherical shells.