横振動段付音片の共振周波数と振動姿態

抄録

This paper deals with analyses and some experimental results on the free-free "steeped bar" which is stepped at one side or both sides of a uniform bar(Fig. 1). It is the purpose of this paper to obtain a guide for the design of a small sized resonator in low frequency. The stepped bar can be produced easily and can by supported at the nodal points which appear in the thick parts of the bar. These results are also useful for the design of a tuning fork. First, the fundamental mode vibration of the bar stepped at one side (Fig. 2) is analyzed with the mechanical equivalent network (Fig. 3), and the frequency-equation is obtained (Eq. 9), and the equation of the vibration mode is given (Eqs. 16, 21). The calculated and measured values of resonant frequencies are shown (Figs. 4, 5), and the resonant frequencies of the bar stepped to the thickness direction are compared with the ones of the bar stepped to the width direction (Fig. 6). The frequencies of higher modes are also shown, in (Fig. 7). It is clear from the above results that as the cross section ratio of the bar increases, the more the resonant frequency decreases, and that the minimum resonant frequency is obtained at the length ratio of 0. 1〜0. 35. Second, the fundamental vibration mode and its nodal point of the bar stepped at one side are calculated and compared with the measured values (Fig. 8). It is confirmed that the bar can be supported at a nodal point of vibration in the thick part of the bar. Lastly, an analysis on the bar stepped symmetrically at both sides is summarized and the equations of resonant frequency and vibration mode are obtained (Eqs. 25, 28, 31), and the design charts of the bar are given (Figs. 10, 11, 12). The resonant frequencies of the bar stepped at both sides come down to about 0. 7〜0. 85 times the ones of the bar stepped at one side. Accordingly, the two stepped bar is more suitable for a small size resonator in low frequency than the one stepped bar.