  Stimulated Brillouin scattering recently allowed experimental excitation of
surface acoustic resonances in micro-devices, enabling vibration at rates in
the range of 50 MHz to 12 GHz. The experimental availability of such mechanical
whispering gallery modes in photonic-MEMS raises questions on their structure
and spectral distribution. Here we calculate the form and frequency of such
vibrational surface whispering gallery modes, revealing diverse types of
surface vibrations including longitudinal, transverse, and Rayleigh-type
deformations. We parametrically investigate these various modes by changing
their orders in the azimuthal, radial, and polar directions to reveal different
vibrational structures including mechanical resonances that are localized near
the interface with the environment where they can sense changes in the
surroundings.
