Vibration suppression of cantilevered piezoelectric laminated composite rectangular plate subjected to aerodynamic force in hygrothermal environment

In this paper, a robust control method is proposed for the vibration suppression of the piezoelectric laminated composite cantilever rectangular plate subjected to the aerodynamic force in the hygrothermal environment. The laminated composite cantilever rectangular plate is placed on the piezoelectric actuator and sensor for the upper and lower surfaces. The classical laminated composite plate theory and Hamilton's principle are applied to derive the dynamic equation of motion for the piezoelectric laminated composite cantilever rectangular plate under the aerodynamic force and hygrothermal loads. The structural damping is considered for the piezoelectric laminated composite cantilever rectangular plate. Galerkin method is used to obtain a two-degree-of-freedom discrete ordinary differential control equation of motion. For the active vibration suppression, a robust controller for the uncertain systems is designed through the obtained ordinary differential equation of motion. Moreover, the full-dimensional state observer is constructed to calculate the close-loop system. The influences of the moisture, temperature and geometric parameters on the dynamics behaviors of the piezoelectric laminated composite cantilever rectangular plate are investigated. The accuracy and effectiveness of the robust controller are verified in terms of the moisture concentration, temperature, aspect ratio, damping and parameter uncertainty by numerical simulations.