Huang Zhicheng, Peng Huanyou, Wang Xingguo, Chu Fulei
College of Mechanical and Electrical Engineering, Jingdezhen Ceramic University, Jingdezhen 333001, China.
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China.
Materials (Basel). 2023 Jan 17;16(3):896. doi: 10.3390/ma16030896.
A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton's principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.
基于经典层合板理论和哈密顿原理，建立了夹层复合板的有限元动力学模型。构建了一个4节点、7自由度的三层板单元，以模拟基板、粘弹性阻尼层和压电材料层之间的相互作用。其中，粘弹性层采用复常数剪切模量模型，并引入等效瑞利阻尼来表示基板的阻尼。所建立的动力学模型自由度过多，采用物理空间动态凝聚和状态空间平衡的联合降阶方法后，得到的动力学模型具有良好的可控性和可观性。针对夹层板的主动控制设计了最优二次（LQR）控制器，并通过仿真分析对控制器参数、粘弹性层厚度以及夹层板的最优覆盖位置进行了优化。结果表明，本文建立的有限元模型在不同边界条件和不同覆盖方式下仍然有效，采用联合降阶方法后该模型仍能准确可靠地反映原系统的动态特性。在不同激励信号和不同边界条件下，LQR控制能有效抑制夹层板的振动。夹层板的最优覆盖位置靠近固定支撑端，远离自由端。分别从多个角度对控制器参数和粘弹性层厚度的参数进行了优化，可根据实际需求选择合理的优化方案。
