Active vibration control of smart piezolaminated composite structures using nonlinearity in strong field actuation

Abstract

Increasing demand for the development of lightweight structures particularly in aerospace, automobile and space applications has brought active vibration control of structures into the focus of research in recent times. Piezoelectric materials are widely used as sensors and actuators for such applications. But, the studies on active vibration control of plate and shell type structures reported so far have considered only a linear behaviour of the piezoelectric materials. Experiments have, however, shown that piezoceramic materials exhibit constitutive nonlinearity, when the applied electric field exceeds the coercive limit. In this talk, we will discuss a theoretical framework for modeling active vibration control of smart multilayered plates and shallow shells integrated with piezoceramic sensors and actuators, considering their constitutive nonlinearity under strong electric field. An efficient layerwise theory, which is nearly as accurate as a three dimensional (3D) solution, but is as economical as an equivalent single-layer theory with only five displacement unknowns is employed for the laminate mechanics. For the linear transient analysis of a piezo-sandwich plate, the computational time for the finite element (FE) model based on this theory has been found to be nearly 1/300th of that required for 3D FE analysis using ABAQUS, yielding nearly the same accuracy. The nonlinearity is modeled using rotationally invariant second order nonlinear constitutive equations, with the assumption of large electric field and small strains. The nonlinear finite element model for dynamic response is developed consistently using the extended Hamilton’s principle. The nonlinear system is transformed to an equivalent linear system using the feedback linearization approach, through control input transformation. The linear quadratic Gaussian (LQG) controller is adopted for control of the equivalent system. The results predicted by the nonlinear model compare very well with the experimental data available in the literature for static response. The effect of the piezoelectric nonlinearity on the static response and active vibration control is studied for piezoelectric bimorph as well as hybrid laminated plates and shells with isotropic, composite and sandwich substrates. It is revealed that, using the piezoelectric nonlinearity, the vibration control can be achieved at a much lower actuation potential than predicted by the linear model. While in the linear model, control voltage is almost independent of the actuator thickness, its nonlinear prediction reduces significantly with the decrease in the actuator thickness.