This paper presents the experimental results of attenuation(ATT)characteristics of some lined and splitter ducts. A rectangular air passage with one or more inner surfaces covered with a fibrous acoustical material is used for the mesurements of ATT. The experimental apparatus is schematically shown in Fig. 1 and 2. The flow resistance of some acoustical materials versus volumetric density is given in Fig. 3. Typical distribution of local sound pressure intensity in a cross section is shown in Fig. 4. The noise reduction rate for the distance along the axis of the duct can be calculated from the integrated mean value of the sound pressure distribution for each section plotted against the distance as shown in Fig. 5. It is shown that the sound pressure linearly decreases with logarithmic distance Z. Fig. 6 to 8 show the experimental results of ATT for various thicknesses of acoustical material, where a dotted line shows the calculated value from the Bruel's formula. The ATT of a lined duct depends primarily on the thickness and the flow resistance value. It is also shown that the peak value of ATT moves to the side of lower frequency with increase of the thickness and flow resistance of the acoustical material. The number of sound waves in an acoustical material can be determined theoretically from the flow resistance value, showing that the number is larger than that of sound in air, because the velocity of sound decreases in the acoustical material. Fig. 9 and 10 show the reduction of wave length in the material as a function of fill-up ratio multiplied by the flow resistance value. The ATT of a lined duct can be expressed by Eq. 3, in which K is defined as the absorption coefficient of the acoustic material. Fig. 11 shows the variation of K with the flow resistance of the acoustical material. Similar experiments were performed for a splitter duct by varying the thickness of acoustical material. A peak of ATT also exists at the wave length of sound nearly equal to the interval of arrangement of the acoustical material as shown in Fig. 14. Fig. 15 and 16 show the variation of the coefficient K of a splitter duct of types D_A and D_B with the flow resistance of acoustial material. Again, the ATT can be estimated from the flow resistance of the acoustical material. The coefficient K are compared in Fig. 17 for lined duct, splitter duct of type D_A and D_&ltA′&gt in which each duct is divided by a steel plate along the center line. A practical dissipative type muffler for a boiler fan was designed and constructed based on these results as shown in Fig. 18. The attenuation characteristics of muffler were measured as shown in Fig. 19, where a dotted line shows the designed value. (A chain line and points show the attenuation characteristics of the muffler for an induction fan. ) It is shown that the attenuation characteristics of the dissipative type mufflers can be estimated well by the method described here.

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Impacting vibration, that is a mechanical vibration accompanied with impact, is usually complicated and can hardly be analyzed, owing to extreme nonlinearity of the impact. Then, a general method of analog computer simulation applicable to impacting vibration of a multi-degree-of-freedom system has been investigated. In the collinear impact of two bodies A and B (Fig. 1 (a)), the relation between the gap (x_A-x_B) and the contact force f_i is given by Fig. 1 (b) or Eq. 1. In Eq. 1, the negative gap represents local deformation at the impact point. The stiffness of the local deformation s_n is assumed to be constant. It can be considered that a virtual elastic component of nonlinear stiffness s_N is always connected between the impact points of two bodies. In the impedance analogy, the reciprocal of s_N corresponds to a nonlinear capacitance C_N. By use of this C_N, an electrical equivalent circuit of a vibration system with impact is given in Fig. 2, where f_&ltAk&gt and f_&ltBk&gt are the external forces applied to the mechanical terminals A_k and B_k, respectively, and x^^^. _A and x^^^. _B are the velocities of the impact points A_1 and B_1, respectively. The nth mode equivalent circuit inside the black box in Fig. 2 can be given as Fig. 3 (a) or (b). A computing element simulating the C_N, which has an ideal characteristic as shown in Fig. 4 (b), can be constructed as Fig. 4 (a) provided that D_1 is an ideal diode. The actually obtained characteristic, however, is unsatisfactory for the exact simulation as shown by crosses (×) in Fig. 5. Then, a clipping circuit shown in Fig. 7 is added in cascade to the output terminal of Fig. 4 (a). Thus, such an improved characteristic as shown by dotts (・) in Fig. 5 is obtained. This element is named an 'impact-element' and represented by the symbol shown in Fig. 9. A setup diagram for analog computer simulation of the nth mode is shown in Fig. 10 (a) and it is represented by diagramatic symbol as in Fig. 10 (b). A block diagram for simulating the whole vibration system represented by the equivalent circuit shown in Fig. 2 is set up as in Fig. 8 by use of the symbols of Fig. 9 and Fig. 10 (b). By the above-mentioned method, simulation of some impacting vibrations has been done. Simulated waveforms obtained for models given in Fig. 11 and 13 are shown in Fig. 12 and 14, respectively. These results indicate that the simulation method mentioned here is available and effective for simple analyses of impacting vibrations.

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A theory of the excitation of a clarinet was proposed in case that no performer's lips were applied to the reed of the instrument, by assuming the interaction between the air column and the reed and considering the vibration of reed as a bending vibration of beam. The results of calculation were compared with those of experiment on a model clarinet specially prepared in order to make both experimental condition and theoretical assumption coincide. In Section 2, the method of calculation of the resonance frequency of reed itself is shown ; the calculation was based on the assumption that the reed vibration is well represented by one-dimensional bending vibration of beam. Section 3 depicts the equation (Eq. (14)) of motion of the reed of instrument and the wave equation (Eq. (13)) of air column. These equations were solved simultaneously and from the results of analysis the frequency equation was obtained, which gave the dependence of the excited frequency (including higher order modes) on the physical blowing condition of the instrument. In Section 4, an example of the excited frequency calculated from the frequency equation is first shown (Fig. 7) based on presumable values of the material constants for a standard reed, together with the resonance frequency of the reed. Next, for confirming the above mentioned theoretical results, calculation was performed for the excitation of an instrument with metal reeds of precisely defined material constants and geometrical form. Table 4 and Figs. 8 and 9 show the observed and calculated results of the excited frequency of the model clarinet mentioned above as a function of the pipe length. And for comparison, the resonance frequency of reed itself calculated by the method described in Section 2 is presented in the same table and figures, in which it is shown that the results of calculation and experiment coincide satisfactorily well. It was also made clear that the excited frequency of the clarinet without application of performer's lips is deviated to some extent from the resonance frequency of reed, and that the change of excited frequency due to the pipe length is nearly proportional to the resonance frequency of the air column. In this case, the change of excited frequency was small compared with that of resonance frequency of the air column, and there existed a frequency region in which the clarinet was difficult or perfectly not to be excited according to a certain relation existing between the resonance frequency of reed and that of air column (See Figs. 8 and 9).

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This paper presents the experimental results of swaying and rocking vibration tests on small bodies resting on the surface of a foundation. The experiments were conducted for the purpose of clarifying the spring and damping effects of real soil in the horizontal and rotational directions, because the resonance of a vibration pickup mounted on the surface of the ground causes considerable error on the measurement of the ground surface vibration. The experiments were conducted on a foundation of Kanto loam. The results obtained are summarized below. The approximate expressions for the spring constant and the damping coefficient in the horizontal and rotational directions for an elastic half-space were introduced using the Groud Compliance given of Tajimi (Eqs. (9)-(12)). The measured swaying spring constant is proportional to the radius of the contact area and rocking spring constant is proportional to the third power of the radius, as theoretically predicted. The measured value of the swaying spring constant is nearly identical to that of the static spring constant assuming a uniform contact pressure distribution, and the value of the rocking spring constant lies between the two calculated values obtained assuming rigid base and triangular contact pressure distributions (Figs. 5 and 7). The measured values of the swaying and rocking spring constants increase as the average contact pressure increases (Figs. 6 and 8). The measured value of the dimensionless natural frequency of the coupled swaying and rocking vibration system lies between two calculated values, one of which was calculated assuming a rigid base pressure distribution both in the horizontal and rotational directions, while the other was calculated assuming a uniform distribution in the horizontal direction and a triangular pressure distribution in the rotational direction (Fig. 10). The influence of the soil viscosity on the damping effects was investigated. The expressions for the damping coefficient due to soil viscosity were introduced assuming the foundation to be a Voigt solid (Eqs. (21)-(25)). The measured value of the magnification factor is nearly identical to the value calculated using a damping coefficient assuming the soil to be a visco-elastic material (Fig. 11).

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