  We experimentally demonstrate the controlled enhancement of the mechanical
quality factor Q of GaAs disk optomechanical resonators. Disks vibrating at 1.3
GHz with a mechanical shield integrated in their pedestal show a Q improvement
by a factor 10 to 16. The structure is modeled numerically and different modes
of vibration are observed, which shed light on the Q enhancement mechanism. An
optimized double-disk geometry is presented that promises Q above the million
for a large parameter range.
