Designing gram-scale resonators for precision inertial sensors

Recent advances in glass fabrication technology have allowed for the development of high-precision inertial sensors in devices weighing of the order of grams. Gram-scale inertial sensors can be used in many applications with tight space or weight requirements. A key element of these devices' performance is the behavior of a mechanical resonator. We present a detailed study on the design of resonators for such sensors. First, we consider how the mechanical parameters of a resonator couple with an inertial sensor's performance. Then, we look at how to geometrically design resonators to achieve specific mechanical behavior without undergoing brittle failure. Both analytic tools and finite element analysis are used to this end. We then derive expressions that can be used to optimize the performance of an inertial sensor for a specific sensitive bandwidth. A simple geometry used throughout the field is studied as an example. However, the results are presented in a general form so that they can be easily adapted to any required geometry and use case. Ultimately, the results presented here guide the design of gram-scale inertial sensors and will improve the performance of devices that follow them.