  A single-axis Microelectromechanical system gravimeter has recently been
developed at the University of Glasgow. The sensitivity and stability of this
device was demonstrated by measuring the Earth tides. The success of this
device was enabled in part by its extremely low resonant frequency. This low
frequency was achieved with a geometric anti-spring design, fabricated using
well-established photolithography and dry etch techniques. Analytical models
can be used to calculate the results of these non-linear oscillating systems,
but the power of finite element analysis has not been fully utilised to explore
the parameter space before now. In this article, the results of previous
analytical solutions are replicated using finite element models, before
applying the same techniques to optimise the design of the gravimeter. These
computer models provide the ability to investigate the effect of the
fabrication material of the device: anisotropic <100> crystalline silicon. This
is a parameter that is difficult to investigate analytically, but finite
element modelling is demonstrated here to provide accurate predictions of real
gravimeter behaviour by taking anisotropy into account. The finite element
models are then used to demonstrate the design of a three-axis gravimeter
enabling the gravity tensor to be measured - a significantly more powerful
surveying tool than the original single-axis device.
