横振動H形振動子の共振周波数解析

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This paper deals with the analysis on the resonant frequencies of the H-type transeversely vibrating resonator suitable for low frequency below about 10kHz. A tuning-fork and a transeversely vibrating thin bar have been used, up to the present, as the resonator for frequency below about 10kHz. The resonant modes of the resonator are constant regardless to the dimentions at the time of inherent resonance. On the other hand, the modes of the H-type resonator described in this paper are dependent upon the dimensions of the resonator. Since such resonator as that having various resonant mode at inherent resonance has not been put in practical use until now, H-type resonator having different resonant modes is proposed in this paper to be practicaly. From the view point of practicability of H-type resonator, the resonant frequencies are analyzed as a function of the dimensions of the resonator. In the second chapter, the first mode vibration of the H-type resonator made of a thin steel sheet (Fig. 1) is analyzed from the analogy of the network (Fig. 2) equivalent to the transeversely vibrating mechanical system, and the convenient diagrams for design of the H-type resonator (Figs. 3, 4) and the optimal dimension to reduce the size of the resonator under the condition of constant area of the resonator are given. Furthermore, difference between the H-type resonator and a tuning-fork or a transversely vibrating bar aise made clear. (Fig. 7) The resonant modes are shown, as a fuction of the dimension of the resonator. (Fig. 6) The detailed analytical process of the vibraion modes of the resonator is given in the appendix. (Figs. A-1, A-2) Because the error of the resonant frequencies obtained from the design diagrams to measured ones is less than several percents in case of usual dimension(Fig. 4), it is proved that the design programs presented in this paper can be said to fit practical purpose. In the third chapter, as for the step-shaped H-type resonator of small size applicable to lower frequency range (Fig. 8), the result of the analysis is stated on the resonant frequency. (Figs. 9, 10) Even in this case, the calculated value of resonant frequency is nearly equal to the measured one. In the forth chapter, from the standpoint of the application of the H-type resonator as multi-mode vibrator (Figs. 12, 13), the condition imposed to the dimension is obtained that resonant frequency of the transverse vibration perpendicular to the frame-work agrees with that in the frame-work plane. (Figs. 15, 16) The multi-mode resonators can be constructed by chamfering the H-type resonator of the dimension making the resonant frequencies of the both mode mentioned above agree with each other.
社団法人日本音響学会の論文
1970-11-10

横振動H形振動子の共振周波数解析

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