Modeling of coupling mechanisms and frequency separation in double disk resonators

We present modeling expressions for the coupling mechanisms in vertically stacked disk resonators. Using lumped modeling techniques, analytic expressions for coupling mechanisms in a stack of two disks are derived. The modeling results are compared to those of high-fidelity finite element analyses and show that the analytic expressions derived can be used to predict frequency separation between radial extensional modes. The established model is useful for gaining insight into parameter sensitivity when designing a stacked double disk resonator.