Dynamic Equations Of Beam-Column Members With Piezoelectric Actuators And Their Applications In The Active Vibration Control Of Structures

The study of active vibration control with the application of intelligent structures is a hot topic in vibration control of structures that is one of the most promising disciplines in vibration and control engineering. Intelligent structures have the advantages of fast reaction, self-adapting, self-diagnosing and self-recovery, and especially piezoelectric intelligent structures have strong electromechanical coupling effect so that they find wide applications.A piezoelectric intelligent beam-column member consists of piezoelectric layers used for actuators which are non-continuously and pair-wise affixed to the surfaces of the beam-column member and strain gauges used for sensors. The dynamic equations of piezoelectric beam-column members or structures are derived with a semi-analytic method and a finite element method. The vibration control of the intelligent structures is realized following the linear quadratic regulation (LQR) control strategy. The main contents of this thesis are as follows.(1) The mechanics model of a piezoelectric beam-column member is presented, and the induced force and moment between the piezoelectric actuator and elastic backing are derived. Furthermore, the induced moment of the piezoelectric actuator is optimized, and the optimum thickness ratio between the piezoelectric layers and the backing is obtained.(2) The dynamic equation of the piezoelectric beam-column member, which is subjected to a constant axial force and a transverse distributed force, is derived with the semi-analytic method based on the Lagrange抯Principle. This method can take the P-△effect into account.(3) The dynamic equation of a beam-column element with continuous piezoelectric layers is derived with the finite element method based on the Hamilton抯Principle. This element is Subjected to a constant axial force and various transverse loads. This method can also take the P-△effect into account. Finally, the dynamic equations of a beam-column member with non-continuous piezoelectric layers as well as a structure containing piezoelectric beam-column members are derived through element assemblage.(4) The problem of the active vibration control of the intelligent structures is analyzed by the modem control theory with LQR control strategy. Numerical examples are simulated by Simulink toolbox of Matlab software package, the simulation results show that active vibration control can significantly improve structure抯tvibration performance.