The Vibration Suppression Of The Piezoelectric Composite Laminated Cantilever Plate In Hygrothermal Environment

As a new type of smart material,piezoelectric materials are most commonly used in electromechanical and vibration control system due to the excellent mechanical and electrical coupling properties,which are usually embedded in engineering structures as the actuators and sensors,respectively.The piezoelectric laminated composite plate are the important part of the wing panel,therefore,researches on vibration control of piezoelectric composite cantilever laminated plate in a hygrothermal environment are essential.This paper proposes the study of the active vibration suppression of cantilevered piezoelectric laminated composite rectangular plate subjected to the hygrothermal loads and aerodynamic force.The main researches are as follows:Firstly,the dynamic modeling of the piezoelectric laminated composite rectangular plate in the hygrothermal environment is studied.The mechanical model is proposed by using the piezoelectric patches,which are attached to the upper and lower surfaces of the plate as the actuators and sensors,respectively.Through the classical laminated composite plate theory,the small deformation hypothesis,the constructive equation of the laminated plate under the hygrothermal environment,the linear constructive equation of the piezoelectric patches,the aerodynamic forces using first-order piston theory and the action of piezoelectric loadings,this study derives the dynamic equation of motion for the plate using the Hamilton’s principle.According to the boundary conditions of the cantilevered piezoelectric laminated composite rectangular plate,the two-order mode displacement function is given.The partial differential equations of the piezoelectric laminated composite plate are discretized to be a two-degree-of-freedom control equation by using Galerkin method.The electromechanical model of the piezoelectric sensors is proposed by using the positive piezoelectric effect of the piezoelectric martial.Secondly,the controller of the piezoelectric laminated composite rectangular plate is designed.The closed-loop dynamic control system is established through the obtained ordinary differential equation of motion and the electromechanical coupling equation of the piezoelectric sensor.Moreover,the state feedback controller and the full-dimensional state observer under the parameter uncertain system are designed to calculate the close-loop system.Using the Lyapunov Matrix Inequality(LMI)method and Lyapunov Stability Theory,the feedback gain matrix and observation gain matrix for the system are designed to make the closed-loop system asymptotically stable.Finally,the effect of the hygrothermal environment on the natural property of the the piezoelectric laminated composite rectangular plate and the accuracy and effectiveness of the controller are verified by numerical simulation,which are given by the Matlab programming.The influences of the moisture,temperature and geometric parameters on the dynamics behavior of the cantilevered piezoelectric laminated composite rectangular plate are investigated.The first-two order time history curves of the piezoelectric composite cantilever plate under the case of controlled and uncontrolled are given to verify the effectiveness of the current designed controller.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.