This paper addresses the design problem of piezoelectric actuators for multimodal active vibration control. The design process is carried out by a topology optimization procedure which aims at maximizing a control performance index written in terms of the controllability Gramian, which is a measure that describes the ability of the actuator to move the structure from an initial condition to a desired final state in a finite time interval. The main work contribution is that independent sets of design variables are associated with each modal controllability index, then the multi-objective problem can be split into independent single-objective problems. Thus, no weighting factors are required to be tuned to give each vibration mode a suitable relevance in the optimization problem. A material interpolation scheme based on the Solid Isotropic Material with Penalization (SIMP) and the Piezoelectric Material with Penalization (PEMAP) models is employed to consider the different sets of design variables and the sensitivity analysis is carried out analytically. Numerical examples are presented by considering the design and vibration control for a cantilever beam and a beam fixed at both ends to show the efficacy of the proposed formulation. The control performance of the optimized actuators is analyzed using a Linear-Quadratic Regulator (LQR) simulation.

中文翻译：

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考虑多模态振动控制的压电执行器设计的基于可控性的 TO 方法

本文解决了用于多模态主动振动控制的压电执行器的设计问题。设计过程由拓扑优化程序执行，该程序旨在最大化根据可控性 Gramian 编写的控制性能指标，这是描述执行器将结构从初始状态移动到所需最终状态的能力的度量在有限的时间间隔内的状态。主要工作贡献是独立的设计变量集与每个模态可控性指标相关联，然后可以将多目标问题分解为独立的单目标问题。因此，不需要调整加权因子以使每个振动模式在优化问题中具有适当的相关性。采用基于带惩罚的固体各向同性材料 (SIMP) 和带惩罚的压电材料 (PEMAP) 模型的材料插值方案来考虑不同的设计变量集，并进行敏感性分析。通过考虑悬臂梁和两端固定梁的设计和振动控制，给出了数值示例，以显示所提出公式的有效性。使用线性二次调节器 (LQR) 仿真分析优化的执行器的控制性能。通过考虑悬臂梁和两端固定梁的设计和振动控制，给出了数值示例，以显示所提出公式的有效性。使用线性二次调节器 (LQR) 仿真分析优化的执行器的控制性能。通过考虑悬臂梁和两端固定梁的设计和振动控制，给出了数值示例，以显示所提出公式的有效性。使用线性二次调节器 (LQR) 仿真分析优化的执行器的控制性能。