Optimization of electro-mechanical smart structures

在拟议的研究中，原则调查员（PIS）考虑电声换能器的基础上压电致动器贴片和电容微机械超声换能器（CMUT）。在这两种应用中，连续机械结构元件经历强迫振动并耦合到设备周围的声场。出于明显的原因，技术目标是在远场的指定邻域中并且可能在指定区域中实现最大声压或最大声能。为了实现这种最大化，电声材料的拓扑结构将与电极层的拓扑结构一起被优化。这两种应用的不同之处在于所涉及的材料，以及在压电声学装置中没有对系统施加主动控制的事实，而在第二种应用中，其本身又是非线性的，根据所施加的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-机械耦合和要执行的优化的拓扑方面。所提出的研究中追求的方法与形状和拓扑梯度以及相应的Armijo型梯度和全球化形状Hessian步骤有关。形状和拓扑的同时处理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着改进，该方案与优化步骤中的充分减少有内在联系。这些发现预计将对优先计划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.