The Vibration Characteristics And Active Vibration Control Of Piezoelectric Intelligent Beams Carrying Concentrated Masses And Springs

In order to study the vibration response and vibration noise reduction problems of the ship hull and marine structures, the masts, propeller shaft and offshore wind turbines with similar figures and typical characteristics are simplified into the mechanical model of elastic beams with lumped parameters (concentrated masses and springs). For this model, we first studied its free vibration characteristic, which provides some useful references for the anti-vibration design of actual structures. Secondly, in order to study the control of vibration response of the structure when subjected to the external excitation, the model of piezoelectric intelligent beam carrying concentrated masses and springs is obtained by using piezoelectric actuators and sensors. Then the Active Vibration Control (AVC) of the structure is further studied.Based on the Laplace transform method, the mode shape functions and the frequency equations of the beams carrying multiple lumped masses and elastic spring supports in the typical boundary conditions are derived. An experiment is carried out to verify the correctness of the analytical method. By comparing the analytical and experimental results, the influence of the concentrated parameters like the locations of the lumped elements, the stiffness of the springs and the weight of masses on natural frequencies are discussed.The analytical expressions of actuating equation and sensing equation of the piezoelectric mtelligent beam carrying concentrated masses and springs are obtained by transforming the force of the piezoelectric actuator into a centralized torque. Based on the classic Bernoulli-Euler beam theory and Hamilton’s principle, considering the effect of electromechanical coupling of piezoelectric material, a two nodes element of the piezoelectric laminated beam is derived and the actuating equation and sensing equation in finite element form are obtained. The LQR, LQG and independent modal space control algorithm are respectively used to design the controller. The vibration responses of the piezoelectric smart beam carrying lumped parameters are controlled by numerical simulation. The effects of the locations of concentrated mass and spring on the overall level of vibration response of the cantilever and the impact on the efficiency of the feedback control are discussed. This paper provides a theoretical foundation for the vibration control of similar structures in the ship hull.