無限行列による段付捩り波伝搬路の解析

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This paper describes a general analysis of the torsional circular wave guide with steps based on the infinite matrix method and its application to the three-element torsional wave guide. The details of the analysis are described in Sec. 2. As a result, the dynamic characteristics of a cascade circuit with many steps can be given by the three foundamental equations, i. e. Eq. (7) for the uniform section, Eq. (16) for the velocity components and Eq. (21) for the stress components at each step. In Sec. 3, the shrot-circuit admittances (see Figs. 5 and 6), the distribution of axial resonant frequencies (see Figs. 7, 8, and 9) and the frequency filtering characteristics are investigated for several geometrical configurations of the wave guide as shown in Fig. 3. The results are discussed by comparing the exact theory with the well-known one-dimensional theory, from the point of view to apply the distributed constant design theory used in an electrical circuit to the mechanical system. In order to clarify the reason why the difference from the one-dimensional takes place, the aspects of the wave disturbance at each step are studied, through the particle velocity distribution (see Figs. 11 and 12), the condition of higher mode excitations (see Fig. 13) and the comparison of the relative axial distributions (see Fig. 14). As the results of these studies, it is stated that, i) in the inner part of vibrator, the disturbance appears conspicuously as a local deformation of radial distribution, and then the phase of the particle velocity advances forward along the propagation axis more than that of one-dimensional theory, and consequently, ii) at the input or output terminal of the vibrating circuit, we observe such phenomena as the axial resonant frequencies are lower than the values obtained by the one-dimensional theory and the frequency characteristics are widely different from designed ones. Especially, when the center frequency of a filter is taken at the resonant frequency f_3, it is noted that the admittance characteristic is deformed from the design value even if the radius of the wave guide is smaller enough than the wavelength. The working attenuation charcteristic, therefore, has a large ripple as much as a few decibel (see Fig. 10). As a solution of this problem, the authors have proposed the shortening of length of the slender wave guide as shown in Fig. 10. Finally, a number of experiments are found to support the theory very well as seen in the resonant frequency distribution shown in Figs. 7 and 15.
社団法人日本音響学会の論文
1972-03-10

無限行列による段付捩り波伝搬路の解析

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