敷设主动约束层阻尼圆锥壳的控制特性分析

Control characteristics of a conical shell covered with active constrained layer damping

基于压电材料的本构关系和内力位移方程,考虑压电材料的正、逆压电效应,求出了压电约束层的动力学控制方程和电学控制方程。根据圆锥壳的几何特性,将变量沿周向进行傅里叶展开,可将上述方程转化为沿母线方向的一阶常微分方程的形式。结合黏弹层的法向平衡方程和位移连续性条件,由主动约束层和基壳的力学方程导出层合结构的动力学方程,并将该方程与压电约束层的电学方程联立,建立了敷设主动约束层圆锥壳的机电耦合模型。然后,借助精细积分技术和叠加原理,采用速度反馈控制策略,提出了一种分析此类结构的半解析、半数值方法,并采用该方法分析了反馈系数、反馈点的布置等参数对敷设主动约束层阻尼圆锥壳振动特性和控制特性的影响。

Based on the constitutive relation and internal force-displacement equation of piezoelectric materials, dynamic and electrical control equations of piezoelectric constrained layer were derived considering positive and inverse piezoelectric effects.According the geometric properties of a conical shell covered with active constrained layer damping, the variables were expanded along circumferential direction with Fourier series,and the equations mentioned above were converted as a first-order differential matrix equation along meridian direction.Combining normal equilibrium equations and displacement continuity conditions of visco-elastic layer,the dynamic equations of the laminated structure were derived with dynamic equations of the active constrained layer and the base shell.Combining these equations and the electrical control equations of the piezoelectric constrained layer,the electromechanical coupling model of the conical shell covered with active constrained layer damping was built.Then,applying the speed feedback control strategy,a semi-analytical and semi-numerical method was proposed with the precise integration technique and the superposition principle. Finally,the effects of parameters,such as,feedback coefficient,positions of feedback points on vibration and control characteristics of the conical shell covered with active constrained layer damping were analyzed with the proposed method.