Second-order frequency shifts in crystal resonators under relatively large biasing fields

Frequency shifts in crystal resonators under relatively large biasing fields are studied from a perturbation procedure based on the equations for small fields superposed on finite biasing fields in an anisotropic elastic body. A general expression for second-order frequency shifts is obtained. Estimates are made on the order of magnitude of second-order frequency shifts in a quartz resonator due to relatively large normal acceleration.