A phononic crystal can control the acoustic coupling between a resonator and its support structure. We micromachine a phononic bandgap shield for high Q silicon nitride membranes and study the driven displacement spectra of the membranes and their support structures. We find that inside the observed bandgaps, the density and amplitude of non-membrane modes are greatly suppressed, and membrane modes are shielded from an external mechanical drive by up to 30 dB.
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