Nonlinear Vibration Control of a Piezoelectric–Elastic–Piezoelectric Sandwich Beam

This work presents the active control of nonlinear vibrations of a piezoelectric-elastic-piezoelectric sandwich beam, subjected to transverse excitation while neglecting axial displacement effects. By using a structure with piezoelectric actuators and sensors, and taking into account geometric nonlinearities, a nonlinear vibration control model was obtained through a feedback control law. The dynamic equation of the structure is derived by applying the variational principle and Hamilton’s principle. This equation is solved under primary and secondary resonance by adopting the method of averaging as a perturbation scheme and Galerkin’s approximation. The simulation results of amplitude-frequency responses are presented and discussed for different values of control gains and for three boundary conditions. Our results are in good agreement with those obtained by other methods.