Electromechanical dynamics of a coupled piezoelectric/mechanical system applied to vibration control and distributed sensing

A finite element methodology is developed to simulate the dynamic characteristics of a flexible mechanical system which is composed of a conventional elastic body and a piezoelectric material. One group of piezoelectric polyvinylidene fluoride (PVDF) films is used as sensors attached according to direct piezoelectric effect to observe the vibration of the elastic body, and another group is used as active actuators by applying voltage with the appropriate sign and magnitude.; The vibration sensed by the sensors is used in a control system, the output of which is applied to the actuators to suppress the vibration. The controller differentiates the sensor signal and changes its sign to attain negative feedback. This control algorithm is based on the Lyapunov method and effectively reduces the vibration of a laminated plate.; The dynamic equation to mathematically model the transverse motion of the laminated plate, using Hamilton's principle, is derived. The sensor equation is also derived, which is used to a obtain proper displacement information of the plate.; The laminated plate is further discretized in a finite element model using the variational principle based on the linear piezoelectric equations. A non-conforming eight node hexahedron element is chosen to accommodate the thin plate studied and the multi-field-coupled electric and mechanical problem encountered.; Finally, a finite element computer program is written to model the dynamic behavior of the designed laminated plate. The program is also able to simulate the dynamic performance of piezoelectric materials. Both time and frequency domain analyses are available. According to the control algorithms derived, several control strategies are implemented to compare the control effect. The finite element model is verified either by available laboratory results or other numerical solutions available. The finite element solutions are presented both in table format and graphically to illustrate the control of the vibrating system.