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The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the suppression of vibrations and radiated sound of a ring-stiffened circular cylindrical shell in contact with unbounded external fluid by means of piezoelectric sensors and actuators. The dynamic model of a circular cylindrical shell based on the Sanders shell theory was considered together with a ring stiffener model. The mass and stiffness matrices for a ring stiffener were newly derived in this study and added to the mass and stiffness matrices of the cylindrical shell, respectively. The fluid-added mass matrix, which was derived by using the baffled shell theory, was also added to the mass matrix. Finally, the equations representing the piezoelectric sensor measurement and piezoelectric actuation complete the theoretical model for the addressed problem. The natural vibration characteristics of the ring-stiffened cylindrical shell both in air and in water were investigated both theoretically and experimentally. The theoretical predictions were in good agreement with the experimental results. An active vibration controller which can cope with a harmonic disturbance was designed by considering the modified higher harmonic control, which is, in fact, a band rejection filter. An active vibration control experiment on the submerged cylindrical shell was carried out in a water tank and the digital control system was used. The experimental results showed that both vibrations and radiation sound of the submerged cylindrical shell were suppressed by a pair of piezoelectric sensor and actuator. [Copyright &y& Elsevier]

In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L 2 ( Ω × ( 0 , T ) ) . The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks. [ABSTRACT FROM AUTHOR]