Actuation Equations and Dimensionless Analysis of Piezoelectric Actuators Under Strong Electric Fields

The application of piezoelectric actuators in structural vibration control has become quite mature, but it still faces the challenge of high voltage loading requirements. For membrane structures, the actuation force of the piezoelectric actuator must not only consider the generated bending moment but also take into account the effect of axial force. To address this, we adopt the nonlinear constitutive equations of electromechanical materials and derive the actuation equation of the actuator. To verify its effectiveness, the derived actuation axial force and bending moment are compared through simulations in COMSOL software. Furthermore, the actuation equation has been simplified through the analysis of Poisson’s ratio effect. A dimensionless analysis is then performed to propose optimization strategies for the actuation equations.