Design Optimization of Multi-Resonant Micro Systems

Some say, “the soul of beings is their scent“. While this statement is a controversial one, few would argue that the “soul” of every technical system indeed comes from their shape. As the shape of a violin define whether it is a Stradivarius or a plaything, the shape of a microsystem significantly influences its performance.

Many microsystems use resonance effects, for e.g. motion detection or energy harvesting. Some even include multiple subsystems operating at different resonant frequencies and are referred to as multi-resonant. Everyday-life examples are e.g. gyroscopes in smartphones, laser scanners in head-up displays or magnetic resonance detectors. Design of these devices aims at specific placing of system’s resonant frequencies. For some applications, the resonant frequencies need to be significantly different to minimize energy transfer between the subsystems, while for others, the coupling is an integral part for system’s functionality. In addition the respective eigenmodes have to be actual resonance modes, i.e. be excitable (and thereby practically usable) and the mode shapes have to exhibit desirable deformations with a required amplitude within the spatial region of interest. Finally, the functionality of these devices have to be guaranteed under varying environmental conditions, making the design process a highly complex matter.

The aim of the proposal this project is to enable numerical-simulation-based efficient design optimization of miniaturized multi-resonant systems. Because such simulations require time-consuming computations of large scale systems of differential algebraic equations, we will search for optimal designs by intimately combining two advanced numerical techniques, namely Topology Optimization and Model Order Reduction, in a way that will significantly speed up the simulation process. Although the results will be achieved in a domain-specific manner, the methodology will be relevant for the design of a broad range of dynamic systems in mechatronics.

This figure shows a typical application for topology optimization (TO), which is compliance minimization. Starting from a full block, TO manipulates the material distribution to obtain a structure with minimal compliance for a given load case and desired mass of the final structure.


Model order reduction (MOR) projects system matrices into suitable and significantly lower dimensional subspaces, using some projection matrices V and W. It does so such that the accuracy of the model is not noticably compromised. By using the reduced model instead of the full model, the computation time can be significantly reduced.