Optimization of electro-mechanical smart structures

• Antragsteller: Professor Dr. Eberhard Bänsch; Professor Dr. Manfred Kaltenbacher, Ph.D.; Professor Dr. Günter Leugering
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2006 bis 2010
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 25166897

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.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1253: Optimierung mit partiellen Differentialgleichungen