Discussion Forum

Hi all,

I have now been trying for some time to analyse the support loss contribution to the Q factor of beam resonators, with application to resonant sensing. The resonator I am most interested in is a Xylophone Bar Resonator - see the literature for details. It is essentially a thin beam supported at the node points of its first free-free mode by two transverse ligaments. The support loss occurs where the ligaments are connected to the substrate. I have attacked the problem analytically by assuming clamped boundary conditions for the ligaments, finding the force components under this assumption, and using these results to drive elastic waves into an infinite half-plane. This model can be used to derive the energy dissipated per cycle, and hence the Q factor, by integrating the convolution of the force and displacement.

I want to compare this result to numerical simulation using COMSOL, and to test the validity of the infinite halfplane approximation. I have a parametrised geometry, and can calculate the required displacement for given halfplane size,etc. However, this of course gives me only the ratio of the required displacement to that of the resonator (due to the lack of energy loss from the model).

Is there a good way to approximate an infinite halfplane numerically? Perhaps absorbtion at the boundaries? How to model this? Any ideas?

Harry G