1F. Dunn, A. J. Averbuch, andW. D. O'Brien, Jr., "A pri- mary method for the determination of ultrasonic intensity with the elastic sphere radiometer, ,, Acustica 38, 58-61 (1977). 2T. Hasegawa andK. Yosioka, "Acousticradiationforce on fused silica spheres, and intensity determination,,, J. Acoust. Soc. Am. 58, 581-585 (1975). 3T. Hasegawa and K. Yosioka,"Acoustic-radiation forceona solid elastic sphere,,, J. Acoust. Soc. Am. 46, 1139-1143 (1969). 4L. King, "On the acoustic radiation pressure on spheres," Proc. R. Soc. London A147, 212-240 (1934). 5G.Maidanik and P. J. Westervelt, "Acoustic radiation pres- sure due to incident plane progressive waves on spherical objects,,, J. Acoust. Soc. Am. 29, 936-940 (1957). 6F. E. Fox, "Sound pressure on spheres,,, J. Acoust. Soc. Am. 12, 147-149 (1940). Absorption material mounted on a moving wall--Fluid/wall boundarycondition Earl H. Dowell, Chen-Fu Chao, and Donald B. Bliss Department ofMechanical and,4erospace Engineering, Princeton University, Princeton, New Jersey 08544 (Received 15 February1981; accepted for publication 16March 1981) The case of a structural (elastic} wall on which is mounted an absorptive material does notappear to have a self-consistent derivation of a physically correct boundary condition. Such a derivation is our goal. PACS numbers: 43.20. Fn, 43.20.Mv, 43.55.Ev LIST OF SYMBOLS C• damping coefficient of'porousmaterial Cw damping coefficient of structural wall D elastic plate bending stiffness K• spring stiffness of porous material Kw spring stiffness of structural wall rn• mass of porous material rn• mass of structural wall n normal to wall Pt internal cavity pressure w structural wall deflection w• porous material deflection Z• impedanceof porous material Z• impedance of structural wall p cavity fluid ambient density •o frequency •o• natural frequency of porous material INTRODUCTION In studies of the interior acoustics of cavities (see, for example, Refs. 1-10), various wall conditions are of interest. These include rigid walls, rigid walls on which are mounted absorptive materials, and structural walls which are characterized by mass, stiffhess, and (small) damping. Here is considered the case of a structural (elastic) wall on which is mounted an absorp- tive material. Although this case is discussed in the literature, a rigorous, self-consistent derivation of a physically correct boundary condition does not appear to be available. Such a derivation shall be our goal here. The boundary condition obtained can be used in various contexts including tlie general theory of acoustoelastic- ity described in Ref. 1. I. DISCUSSION To bring out the essential features without unneces- sary complication, first consider a one-dimensional acoustic tube. At one end the absorption material is modeled as a mass supported by a spring and dashpot. This dynamical element is, in turn, connected to an- other mass with spring and dashpot which represents the flexible wall. (See Fig. 1.) This simplified system allows one to understand the essence of the problem and, also, to generalize the results subsequently. We may now express in mathematical form various physical statements about the system elements. Wp W a)This work was performed under NASA Grant NSG1253, Langley Research Center, FIG. 1. Sketch of geometry. 244 J. Acoust. Soc. Am.70(1),July1981; 0001-4966/81/070244-02500.80; (D 1981 Acoust. Soc. Am.;Letters to the Editor 244 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.174.21.5 On: Mon, 22 Dec 2014 13:52:35