Monofrequency control of low-frequency quartz resonators by holographic interferometry

Abstract

The vibrations of different modes and directions are set up in a quartz resonator piezoelectric element due to anisotropy; i.e. the quartz resonator is a system of infinite number of degrees of freedom. Such system may be considered as a monofrequent one only conditionally, so that connection of operating vibration and other vibration is sufficiently slight. Under excitation of quartz resonators the stress strains of various modes are set up at once due to elastic connections. The main vibrations and their harmonics correspond to those stress strains. Moreover, a system of standing waves of a definite frequency of natural vibrations is produced in piezoelectric elements of finite dimensions. Thus, apart from the main frequency, the quartz resonators have an inherence of definite spectrum of resonance frequencies of undesirable, various intensity vibrations expressed by the amplitude-frequency characteristic (AFC) of resonators. The propagation studies have shown that during acoustic wave movement in any anisotropic body an angle other that 0 or 90 exists between the wave front and the wave direction, i.e. the waves are 'nearly longitudinal' or 'nearly transverse.' This means that the elastic waves in piezoelectric elements are longitudinal or transverse only under definite specific orientation. The method available till now for determining the quartz resonator characteristics gave the highly accurate values of spectrum frequencies and attenuation amplitudes of the main and side resonances with respect to the main resonance amplitude, but those method did not allow to determine the vibration mode precisely. The holographic interferometry method makes it possible to control the behavior of vibration modes of low-frequency piezoelectric elements of quartz resonator. Spectral characteristics of piezoelectric elements of low-frequency quartz resonator have been studied by interferograms. The existence of the same side resonators in piezoelectric elements of one and the same cut, but of different geometric dimensions can be explained by physical nature of acoustic wave propagation in an anisotropic body.