Abstract: In order to improve the efficiency and stability of the active constrained layered damping beam, the dynamic model of a constrained damping piezoelectric beam is established based on the energy method and the finite element method. The reduced system model is achieved by use of the Ritz method. According to the characteristics of the model, an acceleration feedback is applied to suppress the vibration in a second order pattern and the Lyapunov equation of control system is proved to be stable. Based on these, a kind of piecewise linear quadratic programming (PLQR) adaptive control method is put forward. By analyzing transient response and frequency response of simply supported beam and the control voltage in different control ways and with various initial frequencies, it is shown that the control gain and compensation frequency directly influence the stability and convergence speed of the vibration control. PLQR adaptive control can attenuate the system vibration faster than the linear quadratic programming (LQR) and the control of constant gain and frequency. Compared with passive constrained damping treatment, the adaptive transformation of the midpoint amplitude and control voltage is most obvious near the natural frequency and makes damping effect better.

Key words: active constrained layered damping, piezoelectricity, self-adaptive, stability, vibration reduction