Active vibration control of a stiffened plate with a piezoelectric actuator

The main objective of this paper is to control the vibration of a cross-stiffened plate with a very small laminated piezoelectric actuator (LPA) under low voltage. Based on the ordinary Kirchhoff bending theory, the governing equation of flexural motion for a stiffened plated attached with a small LPA is derived by smearing the system to an equivalent plate. Analytical expression of the control force is obtained, based on the control force formula position of the LPA is optimized. For a simply supported rectangular cross-stiffened plate, Galerkin method is employed to calculate the response of the system uncontrolled and controlled as the velocity proportional feedback scheme is used. With a 4-layered LPA, only 1% area of the plate, the vibration during a wide frequency span is depressed significantly by voltage about 80V. Analytical and numerical results show that with a very small LPA on its optimal position, the vibrations of the stiffened plate during a wide frequency span can be attenuated with a rather low voltage.