Topology Optimization for Passive and Active Damping Materials Using Homogenization

近年来，人们对不同的被动和主动阻尼层结构进行了大量的研究。一些混合结构已经显示出比纯主动或纯被动阻尼层产生更大阻尼水平的希望。然而，先前的研究（包括优化研究）已经假设了各种成分的特定拓扑结构。本研究将采用均质化方法来优化层压主动和被动阻尼处理的拓扑结构，从而产生各种阻尼组件的最佳配置。将研究五种情况，随着每一个连续的情况，问题的复杂性增加：1)一个普通的粘弹性阻尼处理；2)粘弹性和硬弹性处理，如约束阻尼层；3)普通压电处理；4)压电和粘弹性处理，如主动约束阻尼层；5)压电、粘弹性和硬弹性处理，如主动阻尼复合材料。将对结构进行优化，以最大限度地提高第一模态的阻尼特性（通过系统损耗因子和/或基础弹性结构中的峰值位移来测量）。对于案例3、4和5，还将检查几种不同的控制策略，并检查控制策略对结果拓扑和最优目标的影响。最后，对计算结果进行实验验证。这项研究将涉及研究生和本科生。预计教材的某些方面将整合到现有的研究生和本科课程中，使广大学生对该主题有所熟悉。将考虑从代表性不足的群体中招收学生，并让硕士水平的学生在区域和国际会议上展示研究成果。

In recent years, much research effort has gone into the development of different passive and active damping layer configurations. Some hybrid configurations have shown the promise of producing greater damping levels than is possible with purely active or purely passive damping layers. However, prior studies, (including optimization studies) have assumed a certain topology of the various constituents. The proposed research will use the homogenization method to optimize the topology of laminated active and passive damping treatments, producing the optimal configuration of the various damping components. Five cases will be examined, with the problem complexity increasing with each successive case:1) A plain viscoelastic damping treatment;2) A viscoelastic and stiff elastic treatment, such as a constrained damping layer;3) A plain piezoelectric treatment;4) A piezoelectric and viscoelastic treatment, such as an active constrained damping layer;5) A piezoelectric, viscoelastic, and stiff elastic treatment, such as an active damping composite. Structures will be optimized to maximize the damping properties (measured by the system loss factor and/or peak displacement in the base elastic structure) over the first mode. Several different control strategies will also be examined for Cases 3, 4, and 5, and the impact of the control strategy on the resulting topology and the optimum objective will be examined. Finally, the computational results will be confirmed experimentally. This research will involve both graduate and undergraduate students. It is expected that certain aspects of the material will be integrated into existing graduate and undergraduate courses, giving a wide range of students some familiarity with the topic. Concern will be taken to recruit students from underrepresented groups, and to involve Master's level students in presenting research results in regional and international conferences.