压电智能桁架结构的建模与最优振动控制

为了实现桁架结构振动主动控制,建立了智能桁架结构动力学模型和最优振动控制模型,对动力学建模和最优控制建模方法进行了研究。首先根据有限元理论和Hamilton原理,建立了智能桁架结构的机电耦合动力学方程,方程中含有与作动电压有关的耦合刚度矩阵,采用缩聚变换对动力学方程进行了简化,该动力学方程可用于机械/电荷作用下结构的静动力分析和控制系统设计。然后将推导的动力学模型变换为状态空间方程的形式,根据线性二次型最优控制理论,推导了结构振动控制的数学模型,通过最小化性能泛函,求解黎卡提矩阵代数方程确定了最优控制输入。最后给出了平面桁架结构振动控制算例验证建模过程和算法。结果表明,通过最优振动控制可以使结构振动快速衰减,达到振动抑制的效果。

Dynamic Modeling and Optimal Vibration Control of Piezoelectric Intelligent Truss Structures

In order to realize active vibration control of truss structure, the dynamic model and optimal vibration control model of the intelligent truss structure are established in this paper, and the method of structural mechanics and optimal vibration modeling method are investigated. Firstly, the mech electric coupling dynamic formulate of piezoelectric intelligent truss structures is modeled based on the finite element method and Hamilton theory. The coupling stiffness matrix which is related to control voltage is composed in dynamic formulations. The dynamic formulations are simplified by Guyan transformation. This dynamic formulation can be applied to the static/dynamic response analysis subjected to both mechanical and electrical loading. Then, the state space expressions of the dynamic formulations is obtained, and the mathematic model of vibration control is derived according to linear quadratic optimal control theory, the optimal control inputs are obtained through minimizing cost function and solving the Ricattii matrix algebra equation. Finally, the numerical example of plane intelligent truss structure is given to demonstrate the modeling process and algorithm. Simulation results indicate that the vibration response can be attenuated quickly and the effectiveness of vibration suppression is obvious.