Analytical analysis of a discrete MEMS diatomic mass-spring Phononic Band Gap crystal for vibration stabilization applications

This paper presents the use of phononic band gap (PBG) theory for the design of mass-spring networks that can be used for vibration stabilization in MEMS sensors and/or actuators that need to display wideband immunity to vibrations over frequencies at which mechanical noise may be present. A discrete PBG crystal is a mass-spring network designed to satisfy the condition that the masses vary periodically throughout the structure. Discrete PBG crystals display a frequency selective property, both standing and traveling waves may freely vibrate at certain frequencies, yet are strongly attenuated at band gap frequencies. In this paper, the design constraints and governing analytical equations that describe discrete MEMS PBG crystals are presented. A discrete PBG crystal is then designed and fabricated in a multi-user surface micromachining process.