  Recent advances in glass fabrication technology have allowed for the
development of high-precision inertial sensors in devices weighing in 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 behaviour 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 behaviour 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 optimise 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
they can easily be 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.
