Frequency Matching of Orthogonal Wineglass Modes in Disk and Ring Resonators Made From (100) Silicon

Vibrational wineglass modes in disk and rings that are made from (100) silicon are considered. It is shown that all odd-ordered wineglass modes are necessarily frequency matched, each with its orthogonal conjugate. In contrast, all even-ordered wineglass modes are likely not to be frequency matched with their orthogonal conjugate. Some specific cases are presented that show that many wineglass modes do not have a rotational periodic symmetry. This is relevant to disks and rings that are driven and sensed by surrounding gap-closing electrostatic actuators.