Donald B. Bliss
Linda F. Peretti
Dept. of Mech. Eng., Duke Univ., Durham, NC 27706
A general model of the acoustic boundary condition for an absorptive liner, including bulk reaction effects, is developed. The boundary condition is an extension of the traditional impedance boundary condition modified to include the effect of gradients along the absorptive surface. Using a bulk-reacting porous material as an example, a boundary condition of this type can be constructed that is applicable over the entire frequency range, provided the liner damping is sufficiently high. The boundary condition contains frequency-dependent coefficients, in addition to the normal incidence impedance. These coefficients can be calculated theoretically or measured experimentally. A measurement procedure is described. The accuracy of the boundary condition is demonstrated by comparison with the exact solution for some simple cases. The boundary condition is converted from frequency domain to time domain by calculating the appropriate impulse response behavior. The various impulse response functions are derived by Fourier transform methods, and their behavior is discussed. The impulse functions exhibit behavior associated with viscous relaxation and wave reflection. Once the impulse response functions are known, a response to an arbitrary pressure field can be constructed. Future extensions and applications of the bulk reacting boundary condition are described briefly. [Work supported by NASA.]