基于压电曲壳单元的结构振动最优控制

曲壳结构已广泛应用于航空航天、航海等领域,结构微小的振动会极大地影响部件性能,抑制曲壳结构的振动就很必要。提出了压电曲壳结构的振动最优控制模型,利用空间曲壳单元理论及多点约束方程实现曲壳基结构壳元和压电壳元的耦合,推导了压电曲壳结构动力学有限元方程,并结合线性二次型最优控制理论,实现了压电作动器对曲壳结构的振动最优控制。数值算例表明,对曲壳结构进行动力分析和振动控制时,在达到同样精度及控制效果的情况下,与平壳相比,曲壳单元及作动器所需数目要少得多。

Optimal control of structural vibration using piezoelectric curved shell elements

Curved shell structures have been widely used in aerospace,navigation and other fields,the tiny vibration of the structure will greatly affect the performance of components,it is necessary to control the vibration of curved shell structure.Optimal vibration control model of piezoelectric curved shell structure is presented,the base shell elements and the piezoelectric shell elements are coupled on the basis of the theory of spatial curved shell element and the multipoint constraint equations,and the dynamics finite element equation of piezoelectric curved shell structure is deduced.Optimal vibration control of piezoelectric curved shell structure is achieved by piezoelectric actuators according to the linear quadratic optimal control theory.Numerical examples are given to demonstrate that the required number of curved shell elements and actuators is much less than that of plat shell elements when they have the same precision and control effect at the same time in the dynamic analysis and vibration control of the curved shell structure.