A Polar Form Rayleigh Wave Gyroscope

In this paper it is shown that a circular acoustic cavity bounded by a set of circular reflector grooves and formed from elastically isotropic material, can support degenerate resonant behavior for circular wave-fronted Rayleigh waves. The Rayleigh wave response to a time-harmonic, cyclically symmetric line-load possessing both in-plane and out of plane components, located within a circular acoustic cavity is determined. The forced response, both inside and outside the acoustic cavity, is expressed in terms of the family of Bessel functions whose order is determined by the cyclic order of the circular line-load. It is shown that significant accumulative reflection of the circular wave-fronted Rayleigh waves from the reflective array can occur and that the axisymmetric design satisfies the conditions for degenerate resonance. Thus, the resonator has potential application as a Coriolis gyroscope sensitive to angular rates applied about the polar axis of the resonator.