Validation of a Numerical Method for Determining Liner Impedance

This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, nonprogressive acoustic wave environment without ow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies. Nomenclature [A( )]; [AI]; [BI] =complex block tridiagonal matrices [A] =local element matrix a; b =length and height, respectively, of a nite element c0; 0 = ambient sound speed and density, respectively d =cavity depth E(&; ) = eld equation error function EW (&) =wall error function f =frequency in Hertz f1(&); f2(&) =one dimensional basis functions fFg =vector containing source e ects Research Scientist, Aerodynamic and Acoustics Method Branch, Fluid Mechanics Division. Principal Engineer, Research Division. Research Scientists, Structral Acoustics Branch, Fluid Mechanics and Acoustics Division.