Journal of Sound and Vibratiort (19ft3)Btt(2), 151-162 ACOUSTIC LOADING IN PLANAR NETWORKS M. EI_-RAHEg AND p. Wncxen Jet Propulsion Laboratory, California htstituteof Technology, Pasadena, California 91109. g.S.A. (Receiued 9 Decentber 1981, and in reuised form 15 fulv- 1982) The acoustic loading in a complex planar network of ducts is determined by a method in which Green function surface elements arc used. The networkconsists of straight ducts' elbows and branched ducts. A transfer matrixtechnique is developed in which each ductis treated separately andthe matrix of the influence coefficients ii transformed to tri-diagonal form allowing eltrcient inversion. 1. INTRODTJCTION The noise generatedby flows in duct networks is partly causedby elasticvibration of the duct walls excited by the conveyed medium. The sources of forcing functionsrange from unsteadyturbulent flow through valves [1] to separation and cavitationof the transported f'luid as it is deflected in bends and branched ducts [2]. Recently, the acoustic fluctuations generated by turbulent ffowsthrough a concentric orifice in a pipe have been investigated experimentally [3]. 'fhe acousticpressure spectrum was decomposed into its variouscircumferential harmonics for difTerent regimes of Strouhalnumber and orifice parameters. Depending on theseparameters, the spectrum encompasses cut-off frequen- ciesof the duct. Once the pressure spectrum is determined,the response of the network as an elastic wave guide can be evaluated together with the resulting exterioracoustic radiation field. In this work thc acoustic characteristics oi thc rigid wave guide and the net acoustic loadingproducedby components such as the elbow and the branched duct are investi- gated. The Ioading constitutes the applied forcing functionthat excites an elastic network. The approximation made by decoupling the elasto-acoustic problem is acceptable pro- vided the non-dimensional parameter y* : (ict) lVcn) is small compared with O (1),where / is the ratio of fluid to solid densities, i is the normalizedradius of gyration of the duct wall, cp is the speed of sound in the fluid and c6 is the characteristic speedof bending wavesin the duct wall. For a pipe with circularcross sectioni: h1'/12a, where h and a are the wall thickness and mean radius of the cross section. The acoustic pressure in the planar network is determinedby a method in which Green function surface elements are used.E,ach duct has a rectangular cross sectionand so can be modelled in two dimensions. Thc boundary of each duct is discretized into small straight and circular arc elements each carrying a source density of constantstrength. This process enables one to convert the Fredholm integralequation in the source density into a set of linear algebraic equations. Curvatureof these elements guarantees continuity of slope between adjacent elements along the curved boundary of an elbow. Fewer elements are then needed for the nurnericalprocess to converge.Further increase in computational efliciency is attained by using the transfer matrix technique. Basically, the influence coefficients including elements on the interface of conjoined ducts are determinedseparately for each duct in the network. The unknown sourcedensityvector 1-sI 0022-460X I 83 I 1001.s 1+ 1 2 $03.00/0 le 1983 Acadcrnic Press Inc, (l-ondon) Limitecl