Semi-Analytical Modeling and Vibration Control of a Geometrically Nonlinear Plate

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.