静水压力下压电弹性圆柱振动的主动控制  

Active Control of the Piezoelastic Laminated Cylindrical Shell's Vibration Under Hydrostatic Pressure

作　　者：李红云[1] 林启荣[1] 刘正兴[1] 王超[1] 

机构地区：[1]上海交通大学工程力学系,上海200030

出　　处：《应用数学和力学》2003年第2期163-174,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10132010);船舶工业国防科技应用;基础研究基金资助项目(99J41.4.4)

摘　　要：　对静水压力下压电弹性层合壳的振动控制进行了研究·　首先利用Hamiltion原理推导出压电弹性层合壳的非线性动力基本方程,进一步得到了静水压力作用下封闭压电弹性层合壳的动力方程·　对两端简支条件下的压电弹性圆柱壳的振动问题进行了求解,并基于速度反馈控制法得到了带压电感测层/激励层的层合圆柱壳的主动控制模型·　相应的数值结果表明在静载的情况下,压电层上施加合适大小、方向的电压可以改变圆柱壳的静变形;对于系统的动力响应问题,速度反馈的增益越大,越能抑制系统在共振区的振动。The control of the piezoelastic laminated cylindrical shell's vibration under hydrostatic pressure was discussed. From Hamilton's principle nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived. Based on which,the dynamic equations of a closed piezoelastic cylindrical shell under hydrostatic pressure are obtained. An analytical solution was presented for the case of vibration of a simply supported piezoelastic laminated cylindrical shell under hydrostatic pressure. Using veloctity feedback control,a model for active vibration control of the laminated cylindrical shell with piezoelastic sensor/actuator is established. Numerical results show that, the static deflection of the cylindrical shell can be changed when voltages with suitable value and direction are applied on the piezoelectric layers. For the dynamic response problem of the system,the larger the gain is, the more the vibration of the system is suppressed in the vicinity of the resonant zone. This presents a potential way to actively reduce the harmful effect of the resonance on the system and verify the feasibility of the active vibration control model.

关 键 词：压电弹性 圆柱壳 振动控制 速度反馈 静水压力 感测层 激励层 

分 类 号：O343.1[理学—固体力学]