Frequency Equations of an Ultrasonic Vibrator for the Elastic Sensor Using a Contact Impedance Method

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Abstract
When an ultrasonic vibrator is forced to come into contact with a static load, it is known that the resonance frequency and quality factor of the vibrator are influenced by the reaction of the object. On the basic of this phenomenon, a study to measure the physical constants, such as the elastic modulus of materials, is under way. However no report concerning the accurate analysis of the relationship between the said change and the physical constants has been available. In this paper, we present the analytical result of the relationship equations. The resonance frequency is increased in the case that the body in contact is sufficiently hard, whereas it is decreased in the case that the body is soft. Frequency equations expressing both the phenomena referred to above were obtained in a unified manner. Furthermore, the appropriateness of the said equations was confirmed by experiments. It is concluded from the studied that the analytical results are in agreement with the experimental results.

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