Active control of acoustic radiation from laminated cylindrical shells integrated with a piezoelectric layer

Active control of sound radiation from piezoelectric laminated cylindrical shells is theoretically investigated in the wavenumber domain. The governing equations of the smart cylindrical shells are derived by using first-order shear deformation theory. The smart layer is divided into lots of actuator patches, each of which is coated with two very thin electrodes at its inner and outer surfaces. Proportional derivative negative feedback control is applied to the actuator patches and the stiffness of the controlled layer is derived in the wavenumber domain. The equivalent driving forces and moments generated by the piezoelectric layer can produce distinct sound radiation. Large actuator patches cause strong wavenumber conversion and fluctuation of the far-field sound pressure, and do not make any contribution to sound reduction. Nevertheless, suitable small actuator patches induce weak wavenumber conversion and play an important role in the suppression of vibration and acoustic power. The derivative gain of the active control can effectively suppress sound radiation from smart cylindrical shells. The effects of small proportional gain on the sound field can be neglected, but large proportional gain has a great impact on the acoustic radiation of cylindrical shells. The influence of different piezoelectric materials on the acoustic power is described in the numerical results.