Discussion Forum

I have been working on a clamping loss dissipation and need some help.

Following the paper "Attachment loss of micromechanical and nanomechanical
resonators in the limits of thick and thin support structures" (attached)
and "Elastic wave transmission at an abrupt junction in a thin plate with
application to heat transport and vibrations in mesoscopic systems" (attached)
clamping loss is due to strain energy in the clamps that is lost to the
base of the structure from the resonator. For a thick base it should scale
as 1/L^5. (equation 17).
Also from the second paper it is predicted that out of plane flexural modes
scale as w/L and in plane modes as (w/L)^3. (see conclusions)

I tried to reproduce this result using Comsol, attached is the m-file and
output file for the thick base approximation.

I simulated the beam attached to a 'large' base and then found the
resonance frequency. I then integrated over the sub-domain to calculate
the total strain energy. I assumed the the clamping losses are given by
the ratio of the strain energy in the base to the total strain energy of
the system. When plotting the dissipation against beam length (all other
parameters held constant) I found a 1/L^0.96 dependency which seemed to
approach 1/L as I improved the mesh.

I do not see why the attachment loss paper should not hold and was hoping
I could demonstrate these results in Comsol.

Any ideas?