Topology optimization of MEMS resonators with target eigenfrequencies and modes

In this paper we present a density based topology optimization approach to the synthesis of industrially relevant MEMS resonators. The methodology addresses general resonators employing suspended proof masses or plates, where the first structural vibration modes are typically of interest and have to match specific target eigenfrequencies. As a significant practical example we consider MEMS gyroscope applications, where target drive and sense eigenfrequencies are prescribed, as well as an adequate distance of spurious modes from the operational frequency range. The 3D dynamics of the structure are analysed through Mindlin shell finite elements and a numerically efficient design procedure is obtained through the use of model order reduction techniques based on the combination of multi-point constraints, static approximations and static reduction. Manufacturability of the optimized designs is ensured by imposing a minimum length scale to the geometric features defining the layout. Using deterministic, gradient-based mathematical programming, the method is applied to the design of both single mass and tuning fork MEMS resonators. It is demonstrated that the proposed methodology is capable of meeting the target frequencies and corresponding modes fulfilling common industrial requirements.