Optimization of electro-mechanical smart structures

在提出的研究中，主要研究者（Pis）考虑了基于压电致动器贴片的电声换能器和电容式微机械超声换能器（CMUTs）。在这两种应用中，连续机械结构元件承受强制振动，并与设备周围的声场耦合。由于显而易见的原因，技术目标是在指定邻域和可能的远场指定区域内实现最大声压或最大声能。为了达到这样的最大化，需要对电声材料的拓扑结构和电极层的拓扑结构进行优化。这两种应用的不同之处在于所涉及的材料，以及在压电声学设备中没有主动控制强加于系统的事实，而在第二个应用中，反过来，本质上是非线性的，根据施加电压的主动控制是至关重要的。然而，这两个应用程序共享声学-机械耦合和拓扑优化方面要执行。所提出的研究方法涉及形状和拓扑梯度以及相应的armijo型梯度和全球化形状- hessian步骤。同时处理形状和拓扑是方法部分的最终目标。Pis期望通过自适应数值方案在处理水平集方法方面有显著的改进，该方案与优化步骤的充分减少有着内在的联系。研究结果预计将对优先项目中调查的其他应用产生影响。

In the proposed research the principle investigators (Pis) consider electro-acoustic transducers based on piezo-electric actuator-patches and capacitative micro-machined ultrasound transducers (CMUTs). In both applications continuum-mechanical structural elements undergoing forced vibrations and are coupled to the acoustic field around the device. For obvious reasons, the technological goal is to achieve a maximal acoustic pressure, or a maximal acoustic energy in a specified neighborhood and possibly in specified regions of the far-field. In order to achieve such a maximization, the topology of the electro-acoustic material is to be optimized together with topology of the electrode-layers. The two applications differ in the material involved and in the fact that in piezo-electric-acoustic devices no active controls are imposed on the system, while in the second application which, in turn, is inherently nonlinear, active controls in terms of applied voltages are crucial. The two applications, however, share the acoustic-mechanical coupling and the topological aspect of the optimization to be performed. The method pursued in the proposed research is related to shape- and topology-gradients and corresponding Armijo-type gradient and globalized shape-Hessian steps. The simultaneous handling of both the shape and the topology is an ultimate goal of the methodological part. The Pis expect a significant improvement in handling the level-set approach by an adaptive numerical scheme that is intrinsically linked to the sufficient decrease in the optimization steps. The findings are expected to have impact on other applications investigated in the priority program.