A new type of piezo-electric flexural vibrator in the form of balanced cantilevers

The flexural vibrator, designed to vibrate at about 1 kc/s, basically consists of identical cantilever arms extending from a common area to form a symmetrical element. Two distinct shapes have been considered¿the H and the `zigzag¿. Some of the H elements have uniform cross-section while others are arranged to have most of their mass at the free ends in order to reduce the frequency for a specimen of given length. The `zigzags¿ have folded arms of any number of sections (increasing the number of sections reduces the frequency). The theory of the various forms and their frequency equations are derived. Conditions for perfect balance of the reactions at the supports are discussed. Measurements have been made on H and `zigzag¿ forms made from quartz slices ZYb¿(¿ = 0 ¿ 10°) and on `zigzag¿ form from e.d.t.XYltl ¿, 90°, 90°. Frequency, temperature behaviour, Q-factor and displacement patterns of the elements are compared with theory. Since some of the conventional driving methods proved unsatisfactory a short Section is included on circuits.