主动约束层阻尼薄板有限元建模及振动控制

Finite element modeling and vibration control of an active confinement layer damping thin plate

为了解决薄板结构在应用于各个工程领域所产生的振动过大问题,以主动约束层阻尼(active constrained layer damping, ACLD)薄板结构作为研究对象,进行振动控制研究。首先,构造4节点28自由度单元对该结构进行离散,其中黏弹性层采用复常数剪切模量本构模型,引入等效Rayleigh阻尼表示基层的阻尼,通过Hamilton原理推出了ACLD薄板结构的动力学模型;其次,针对建立的动力学模型自由度过大的问题,采用物理空间下动力缩聚和状态空间内平衡联合降阶保证模型具有良好可控性和可观性;最后使用最优二次型LQR(linear quadratic regulator)控制对系统进行振动控制。研究结果表明,该文建立的有限元模型在不同边界条件、覆盖方式不同情况下仍然具有有效性,使用联合降阶法后模型依旧能够准确、可靠的表述原系统动态特性。在脉冲激励和带限白噪声下依旧能够抑制系统振动。

In order to solve the problem of excessive vibration caused by thin plate structures applied in various engineering fields,vibration control of an active constrained layer damping(ACLD)thin plate structure was carried out in this paper.The structure was divide into 4-node,28-DOF elements by a finite element modeling method.Equivalent Rayleigh damping was introduced to represent the damping of the base layer.The dynamic model of ACLD thin plate structures was derived by the Hamilton principle.The established dynamic model has too many degrees of freedom.The dynamic model obtained by using dynamic iteration in physical space and equilibrium in state space combined reduction method has good control effect.The optimal quadratic(LQR)control was used to control the vibration of the system.Results show that the finite element model established in this paper is still effective under different boundary conditions and different coverage modes,and the model can accurately and reliably describe the dynamic characteristics of the original system after using the joint reduced order method.Finally,the vibration of the structure can be suppressed by using LQR control under pulse excitation.