Journal of the Horological Institute of Japan

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Our thesis is mainly concerned with the study on a mechanical vibrator - a ring with added masses - followed from the theoretical point of view. The ring with which we deal is the one in which a small part is removed from a perfect ring and masses are added at the free end of the rest. Given the equation of motion of the ring, the fundamental, the second and the third modes of vibration are obtained. As the factors relating to the ring, the Young's modulus, the density of the material, the area and the radius of gyration of the section, the shape of the ring. and added masses are considered. The results about a nodal point of the ring vibration are as follows: In the fundamental mode of vibration. a nodal point can be formed at the intersecting point of the ring with the ring axis of symmetry, by the proper addition of the weight of the masses. And also the internal stress in the ring reaches a maximum at the point. In the second and thd third modes of vibration. however, no nodal point can be formed in any case. The vibration modes derived from the theoretical calculation can be proved by the present experiment. Moreover, it can also be proved, by the other experiment that a ring which has a nodal point and is supported there becomes a vibrator or a resonator with the highest quality factor, as compared with the other kindes of ring.

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