Some Experimental Studies of the Vibrations of Quartz Plates

Numerous modes of vibration of zero-and thirty-degree cut circular and rectangular crystalline quartz plates were studied experimentally. Various methods were employed in studying these modes which are piezo-electrically excited. The behavior of lycopodium powder applied to the vibrating faces proved to be the most fruitful source of information. A number of photographs of the patterns thus formed are produced and described. Although of limited utility two mechanical devices also were employed in these studies. The direction of maximum radial displacement was determined for the two active lower frequency modes of zero-degree circular plates. It was found that these directions are nearly parallel to directions of critical values of Young's modulus. Facts were disclosed concerning specially oriented rectangular plates and rods. Experimental values of Young's modulus based on vibration frequencies of the latter were found to agree closely with corresponding values computed from a known theoretically derived expression. Rough experimental verification of the direction of one of the critical values of Young's modulus was obtained. Equations are derived for the modulus of rigidity and Poisson's ratio for crystalline quartz as functions of orientation, and graphs of these two functions as well as of Young's modulus are given. Methods are indicated, which may prove advantageous, of rigidly mounting quartz plates.