Nonlinear vibration of conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch

Abstract

In this study, nonlinear vibration of a conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch is evaluated. The strain displacement relation is considered to be nonlinear and based on that the equations of motion and piezoelectric sensor output signal are extracted. For the first time, nonlinear electromechanical equations of motion for the conical shell with a piezoelectric sensor layer and a piezoelectric actuator layer are extracted in detail and presented. The producer of extraction of conical shell electromechanical equations of motions is presented for further clarifications. The output signal of the piezoelectric sensor patch considering the nonlinear strain displacement equation of motion is derived. For controlling the vibration actively, a proportional controller is defined by which the applied actuator signal is determined. The nonlinear electromechanical equations of motion are expanded based on conical shell strains. By applying the Galerkin method, the nonlinear time-domain equations are extracted. The complicated attained equations are solved using the harmonic balance method. Conical shell nonlinear frequency response in uncontrolled condition and controlled condition is computed and compared with each other. The frequency response shows that the active vibration control of the conical shell increases the nonlinearity of the system and reduces the vibration amplitude. In addition, free nonlinear vibration of the proposed system is calculated and presented. The results show higher impacts of piezoelectric patches on the conical shell free vibration response and they can reduce the vibration amplitude dramatically.