  We have studied the first three symmetric out-of-plane flexural resonance
modes of a goalpost silicon micro-mechanical device. Measurements have been
performed at 4.2K in vacuum, demonstrating high Qs and good linear properties.
Numerical simulations have been realized to fit the resonance frequencies and
produce the mode shapes. These mode shapes are complex, since they involve
distortions of two coupled orthogonal bars. Nonetheless, analytic expressions
have been developed to reproduce these numerical results, with no free
parameters. Owing to their generality they are extremely helpful, in particular
to identify the parameters which may limit the performances of the device. The
overall agreement is very good, and has been verified on our nano-mechanical
version of the device.
