Inducing a nonreflective airborne discontinuity in a circular duct by using a nonresonant side branch to create mode complexity

Abstract

A nonreflective airborne discontinuity is created in a one-dimensional rigid-walled duct when the mode complexity introduced by a nonresonant side branch reaches a maximum, so that a sound wave can be spatially separated into physical regions of traveling and standing waves. The nonresonance of the side branch is demonstrated, the mode complexity is quantified, and a computational method to optimize side-branch parameters to maximize mode complexity in the duct in the presence of three-dimensional effects is presented. The optimal side-branch parameters that maximize the mode complexity and thus minimize reflection are found using finite element analysis and a derivative-free optimization routine. Sensitivity of mode complexity near the optimum with respect to side-branch parameters is then examined. The results show reflection from the impedance discontinuity in the duct can be reduced nearly to zero, providing a practical means of achieving a nonreflective discontinuity for a plane wave propagating in a duct of finite length.

Analytical Solutions for Side-branch Impedance Producing Spatial Localization of Acoustic Waves in Ducts with Varying Cross Sections

“…Though the change of the side-branch impedance is small with respect to the CSA parameters, the corrections were required because we have seen that the localization of traveling and standing waves was very sensitive to the impedances. 2 The traveling-wave measure using side-branch impedances with and without corrections for CSA variation were compared using 3D FEA. The traveling-wave measures plotted against a 1 , when the side-branch impedances were calculated by Eqs.…”

“…Recently, a nonresonant damped side branch has been used for spatial separation (localization) of acoustic traveling and standing waves in a duct with constant cross-sectional area (CSA), where the acoustic impedance of the side branch required to produce this localization is found analytically as a function of wavenumber and side-branch location. [1][2][3] In structural dynamics, spatial separation of traveling and standing waves has also been studied for a non-dispersive taut string with an attached spring-dashpot support and a vibration absorber, 4,5 a dispersive taut string on a partial viscoelastic foundation, 6 and an Euler-Bernoulli beam with one or two spring-dashpot supports. 7 The ducts, strings and beams stud-ied for localization of waves were all assumed to have constant geometries, as in the case of the duct 1,2 shown in Fig.…”