C213 共鳴器列を取り付けた管の中に密封した空気柱の衝撃波を伴わない大振幅振動

概要

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Shock-free, high-amplitude resonant oscillations of an air column in a closed tube has been achieved experimentally by connecting a periodic array of Helmholtz resonators, and a nonlinear frequency response has been obtained. In order to explain this response theoretically, a weakly nonlinear theory is developed by assuming a one-dimensional model in which a boundary-layer effect is taken into account as a perturbation. Focusing on a behavior near the lowest resonance frequency, a small detuning from the resonance frequency is considered, which leads to introduction of a slow time-scale for a complex wave amplitude. Making use of the method of multiple scales, an amplitude equation is derived, as a secular-free condition, from the boundary conditions, and a nonlinear frequency response is derived from the steady solution to the equation. It is found from this that the experimental response curve is explained qualitatively, but quantitative agreements are still open.
日本流体力学会の論文
2002-07-23