FREQUENCY-TEMPERATURE BEHAVIOR OF SPURIOUS VIBRATIONS OF RECTANGULAR AT-CUT QUARTZ PLATES

We evaluate the frequency-temperature behavior of spurious modes in a rectangular AT-cut quartz plate resonator based on three-dimensional l inear equations. The elastic constants and three geometrical dimension s of the resonator are defined in terms of cubic polynomials of a temp erature change. Assuming that the resonator holds its rectangular plat e shape irrespective of temperature, we can determine the relationship between frequency and the dimensions of the resonator for a given tem perature using the previous technique. We compare the calculated resul ts with our own experimental data, and show that agreement between the calculated and observed data is excellent.