膨張形消音器の円筒状空胴の特性

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概要

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• In the previous paper(this Journal 25(3)1969, p. 122), the author shown that the characteristics of an expansion chamber of a muffler in the distributed constant range are explained in terms of the equivalent open-circuit transmission admittance Y_f of the chamber. In this paper, by analyzing Y_f obtained from the solution of wave equation, the characteristics of the cylindrical chamber of the expansion chamber type muffler are investigated and are compared with the results of experiment. The solution of wave equation in the cylinder, Fig. 2, is obtained under the condition that the input opening is regarded as a circular piston and the output opening is closed. If losses are negligible, the sound pressure on the output-side plate of the cylinder is given by Eq. (21)in the case that the input opening is co-axial with the cylinder, and a rough approximation becomes to Eq. (26)in the case of non co-axial. Typical curves of the first three terms of Eq. (21)are shown in Figs. 3 and 4. In case of a long cylinder, only the first term appears in the region ka<λ_<01>=1. 2197π as Fig. 3, and Y_f becomes to Eq. (23). But in case of a short cylinder, the first and second terms must be considered even in the region ka<λ_<01> as shown in Fig. 4. In the region ka>λ_<01>, the sound pressure on the plate is considerably high, and so |Y_f| is small and the noise reduction may not be expected so much. In general, the effective upper limit for noise reduction is regarded as ka=λ_<10>=0. 5861π in the case that the input and output openings are both non co-axial, and it is regarded as ka=λ_<01> in the other cases. In term of frequency, they are shown by Eqs. (27)and(24)respectively. When the loss at the wall of the cylinder is considered, the approximate expression of |Y_f| in the effective frequency range is given by Eq. (36)assuming that the loss is not so large, where R_0, R_l and R_a are the acoustical resistance densities of the input-side plate, the output-side plate and the side wall of the cylinder respectively. It is obvious that the loss makes the minimum value of |Y_f| larger. The measured upper limit frequencies are in good agreement with Eqs. (24)and(27)as shown in Figs. 7, 8 and 9, and Fig. 8 shows that a very short co-axial chamber acts such as a resonator. The relationship between the upper limit frequency and the diameter of the cylinder is shown in Fig. 10. As for the effect of the loss at the wall of the chamber, the results of measurement are larger than the results of calculation as shown in Figs. 12 and 13. But it becomes clear that the loss at the wall compensates the dips of the characteristic curve of |Y_f| caused by the resonance in the axial direction.

• 社団法人日本音響学会の論文
• 1973-04-10

著者

• 奥田 襄介

  熊本大学工学部

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