Active Control Of Cantilever Beam Vibrations Based On Piezoelectric Stacked Actuators

Vibrations from ship propellers shorten the life of the ship and the noise they cause is a serious health hazard for the crew.Vibration and noise reduction technologies can significantly reduce the vibration and noise of propellers.Compared to traditional passive control technology,active vibration control technology can react immediately according to the vibration characteristics of the structure and has the advantages of being highly adaptable and effective in control.Piezoelectric stacked actuators are widely used in the field of active vibration control due to their high output,fast response and small size.In this paper,a high-stiffness cantilever beam with similar dynamics to a real-size propeller is used as the control object,and a piezoelectric stack actuator is used as the actuator to study the active control of vibration of the high-stiffness cantilever beam.The main research elements of this paper are as follows.The force-electric coupling(input voltage,output force and output displacement)mechanism of the piezoelectric stack actuator.Based on the piezoelectric equation to derive the relationship equations of input voltage,output force and output displacement of the piezoelectric stack and the equivalent stiffness of the piezoelectric stack;the study of the vibration active control mechanism of the cantilever beam is completed.Based on the Euler beam theory,the free vibration response of the cantilever beam is analyzed,and the forced vibration of the cantilever beam under the disturbance and control forces is analyzed using modal analysis theory,and the modal equations and state-space equations for the forced vibration of the cantilever beam are obtained.Based on the controllability criterion and the modal force maximization criterion,the layout optimization design of the piezoelectric stack actuator is completed and the optimal control law for the first three orders of the cantilever beam modalities is obtained.The linear quadratic controller(LQR)is designed according to the state space equations of the forced vibration of the cantilever beam,and the simulation of the layout optimization design of single and multiple piezoelectric stack actuators is completed,which shows that the closer the control position of the piezoelectric stack actuators is to the root,the better the control effect is.The control effect is obvious as the suppression rate is 75.0%,95.8% and 72.7% respectively.A piezoelectric stack actuator force-electric coupling test platform was designed and the relationship between the input voltage,output force and input frequency of the piezoelectric stack actuator was experimentally tested to verify the force-electric coupling mechanism of the piezoelectric stack actuator.The test results show that the closer the control position is to the fixed end of the cantilever beam,the better the control effect is.Under different excitation and control frequencies,most of the cantilever beam’s low and medium frequency vibration suppression rate is above 30%,and the control effect is obvious.The research work in this paper provides a strong theoretical and experimental basis for the study of vibration suppression of high stiffness cantilever beams.