Generalized Equation for the Force-Frequency Characteristics of Circular Quartz Plates with Three-Point Support and Its Application to Supporting of an SC-Cut Plate

Abstract

A generalized equation which expresses the force-fre- quency characteristics of a circular disk plate supported by three un- symmetrical points is derived from the concept of balance of applied forces and the superposition of virtual force pairs. Optimum support- ing angles of an SC-cut plate, which is less immune to radially applied forces, are computed and the validity of the equation is confirmed with experiment. It is proposed that the most probable expansion coefficients of the force-frequency characteristics should be compiled from exten- sive experimental results.