Active Passive Integrated Vibration Control Of Piezoelectric Intelligent Structures Based On Pole Placement Method

Frequency and mode shape reflect the inherent dynamic characteristics of structure.From the view of frequency domain,the local resonance metamaterial uses the oscillator resonance to generate the band gap to complete the passive vibration control of the structure.Due to their excellent low-frequency vibration isolation performance,local resonance metamaterial has become commonly in the field of passive vibration control.However,local resonance metamaterials also have some unavoidable limitations as passive vibration control method,such as the vibration isolation range could not be changed according to the operating conditions,and the vibration isolation effect is determined by the mass of the oscillators.Compared to passive control,the advantage of active control lies in the presence of feedback,which mean that the frequency range and the effect of vibration control can be changed in real time according to operating conditions.Therefore,starting from the localization phenomenon of structural vibration,this paper studies the influence of oscillators on structural vibration in the frequency domain.By combining active and passive control,a vibration control method using piezoelectric material to achieve the integration of active and passive structure is designed.Specific work is as follows:Firstly,the mechanism of band gap generation in localized resonances periodic metamaterials is studied.The Hamilton’s principle is used to form the motion equation of the structure,and the FEM(finite element method)is used to form the electromechanical coupling matrix of piezoelectric material.Exploring the influence of variable stiffness oscillators on structural band gaps by changing the elastic coefficient of the spring in the oscillator.On this basis,the design of a local resonance type closed-loop piezoelectric metamaterial structure is further completed.The metamaterial structure is based on active control of the oscillators to achieve the purpose of intelligent band gap control.Secondly,the pole placement method is applied to the vibration control of active-passive integrated metamaterial structures,and the control law based on out-put feedback in state space is derived to solve the gain value under different conditions.By using a cantilever beam structure with MFC piezoelectric fibers bonded on the top and bottom surfaces,closed-loop control experiments were designed to verify the control effects of piezoelectric closed-loop and pole placement,respectively.Aiming at the problem of structural instability caused by residual high order modes after control,a modes decoupling method is proposed to achieve mutual independence between pole to be control and other poles,thereby compensating for the limitations of traditional pole placement methodsFinally,taking segmented cantilever beams with significant differences in material properties as the research object,a structural model was established using a three-node beam element to study the localized vibration phenomenon of the structure.By dividing substructure,the application of the concept of substructure in pole placement method is studied,and the ultimate goal of controlling "the whole" from "the local" is achieved through the pole placement of substructure with obvious mode localization phenomenon.Based on the concept of substructure,the dynamic condensation method is further studied to maintain the calculation accuracy while greatly reducing the DOFs(degrees of freedom)of the structure to reduce the calculation cost.