Modeling and analysis of cantilever beam with active-passive hybrid piezoelectric network

The active-passive hybrid piezoelectric network （APPN） is investigated to reduce the vibration of cantilever beam. Hamilton＇s principle with the Rayleigh-Ritz method is used to derive the equations of motion of the beam with the APPN. Only one pie- zoelectric actuator is bonded on the cantilever beam, so in the segment of the beam where the piezoelectric actuator is attached, the neutral axis is not the geometric center of the beam. This change on the neutral axis is considered in the process of deriving equations. Selecting RL circuit as passive shunt circuit, open-loop analysis is performed to gain insight into the passive damp- ing features. Velocity feedback control is then employed to analyze the characteristics of the closed-loop system. Numerical results show that the APPN has a significant effect on vibration suppression, especially at narrow frequency bands. On this ba- sis, variable RL circuit is proposed and analyzed for broadband vibration attenuation. Numerical simulations illustrate that this scheme is effective and feasible.