S. OIE and R. TAKEUCHI: FLEXIBLE PLATE WITH POROUS LAYERS MOUNTED

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5 S. OIE and R. TAKEUCHI: FLEXIBLE PLATE WITH POROUS LAYERS MOUNTED

8 "generalized efficiency coefficient of radiation" for amplitude proposed in the previous paper15) and its absolute value generally has the values less than unity under Assump. (iii) introduced in Sec. 3 (see Fig. 4(b) in this paper). Therefore, it is expected that the transmission loss of the panel with the porous layers is usually larger than the one of the panel with the non-porous layers which have the same mechanical constants as those of the porous layers, such as the Young's modulus Em, the J. Acoust. Soc. Jpn. (E) 1, 2 (1980) (a) Fig. 4 (a) Directional characteristics of sound transmission loss at frequency 5kHz. (b) 140

S. OIE and R. TAKEUCHI: FLEXIBLE PLATE WITH POROUS LAYERS MOUNTED of the "generalized efficiency coefficient of radiation" sound transmission loss near the coincidence frequency.

9 S. OIE and R. TAKEUCHI: FLEXIBLE PLATE WITH POROUS LAYERS MOUNTED of the "generalized efficiency coefficient of radiation" sound transmission loss near the coincidence frequency. Our treatment may explain this phenomenon to some extent provided that the suitable values 5kHz for the porous material used in Figs. 3 and 4(a). From Figs. 3 and 4, it may be able to say that the effect of porous property of the mounted layer becomes more significant for the incident wave of higher frequency and of larger incident angle. Of course, the exceptions may be found because of the interference effect between the sound wave radiated from the core plate and the sound wave caused by the vibration of fluid excited inside of the porous material. As mentioned in Sec. 1, the several authors1-3) have experimentally investigated the effect of the mounted porous layers upon the sound transmission loss of the composite plate and have concluded as follows: while the effect of the mounted porous layers is significant in the high frequency range, it is little in the low frequency range. The existing theoretical treatment by the other authors4-6) dose not directly describe the decrease of the effect of the mounted porous layers in the low frequency range because of the assumptions that the mechanical contacts between the bare panel and the porous layers are negligible and that the porous layers are at rest. Therefore, their treatment requires the additional corrections as follows: in the very low frequency range, the increase of sound transmission loss by the porous property of the mounted layers is zero, and the appropriate transmission loss is obtained by connecting a smooth curve from the curve in the very low frequency range to the one in the high frequency range.5) On the other hand, our treatment directly describe the tendency of the experimental results without any additional corrections. Of course, there is the limit of application in our treatment because of the assumptions introduced in Sec. 2 and Sec. 3. Additionally, it has been pointed out that the application of porous materials abates the decrease of sound transmission loss near the coincidence frequency. This effect may be arisen mainly from the mechanical properties of the porous materials because it is expected from the numerical example in Fig. 3 that the effect of the porous property itself merely cause the monotonous increase of sound transmission loss over a fairly wide frequency range and dose not cause the extraordinary increase of of the loss factors are chosen. REFERENCES 1) K. A. Mulholland, "The effects of sound-absorbing materials on the sound insulation of single panels," Appl. Acoust. 2, 1-7 (1969). 2) S. M. Brown, J. Niedzielski, and G. R. Spalding, "Effect of sound -absorptive facings on partition airborne-sound transmission loss," J. Acoust. Soc. Am. 63, (1978). 3) S. Takayama and K. Kido, "Multi-layer sound insulation structure using glass fiber," Preprints of T. G. IECE Jpn. EA78-44 (1978) (in Japanese). 4) L. L. Beranek and G. A. Work, "Sound transmission through multiple structures containing flexible blankets," J. Acoust. Soc. Am. 21, (1949). 5) T. J. Schultz, Noise and Vibration Control, ed. by L. L. Beranek (McGraw-Hill, New York, 1971), Chap ) R. A. Mangiarotty, "Optimization of the mass distribution and the air spaces in multi-element sound proofing structures," J. Acoust. Soc. Am. 35, (1963). 7) S. Oie and R. Takeuchi, "On the sound insulation characteristics of the single panel with porous materials applied on its surfaces," J. Acoust. Soc. Jpn. 35, (1979) (in Japanese). 8) H. Oberst, "Uber die Dampfung der Biegeschwingungen dunner Bleche durch fest haftende Belage," Acustica 2, Akus. Beih (1952). 9) E. M. Kerwin, "Damping of flexural waves by a constrained viscoelastic layer," J. Acoust. Soc. Am. 31, (1959). 10) T. Nicholas, "The effects of rotary inertia and shear deformation on the flexural vibrations of a two-layered viscoelastic-elastic beam," The 38th Symposium on The Shock and Vibration (1968), pp ) K. S. Pister, "Flexural vibration of thin laminated plates," J. Acoust. Soc. Am. 31, (1959). 12) C. Zwikker and C. W. Kosten, Sound Absorbing Materials (Elsevier, New York, 1949), Chaps. 2 and 3. 13) S. Oie and R. Takeuchi, "Sound radiation from a surface of porous material," J. Acoust. Soc. Jpn. 34, (1978) (in Japanese). 14) S. Oie and R. Takeuchi, "Some considerations on acoustic properties of porous plate," J. Acoust. Soc. Jpn. (in Japanese) 35, 3-10 (1979). 15) S. Oie and R. Takeuchi, "Sound radiation from a vibrating plane wall having a porous layer on it," J. Acoust. Soc. Jpn. (E), (submitted). 141

Proceedings of Meetings on Acoustics

Proceedings of Meetings on Acoustics Volume 9, 0 http://acousticalsociety.org/ ICA 0 Montreal Montreal, Canada - 7 June 0 Structural Acoustics and Vibration Session asa: History and Application of Constrained