| タイトル |
-
en
Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves
|
| 作成者 |
|
| アクセス権 |
open access |
| 権利情報 |
-
en
Copyright © 2006 American Institute of Physics
|
| 主題 |
|
| 内容注記 |
-
Abstract
en
The nonlinear resonance of cylindrical acoustic standing waves of an ideal gas contained between two coaxial cylinders is theoretically investigated by the method of multiple scales. The wave motion concerned is excited by a small-amplitude harmonic oscillation of the radius of the outer cylinder, and the formulation of the problem includes the wave phenomenon in a hollow cylinder without the inner one as a limiting case. The spherical standing wave in two concentric spheres is also studied in parallel. The resonance occurs if the driving frequency falls in a narrow band around the linear resonance frequency, and in the weakly nonlinear regime, no shock wave is formed in contrast to the plane wave resonance. A cubic nonlinear equation for complex wave amplitude can then be derived by the method of multiple scales. Using a first integral of the cubic nonlinear equation, we shall demonstrate that the resonant oscillation is accompanied by a periodic modulation of amplitude and phase when the dissipation effect due to viscosity and thermal conductivity is negligible. The period of the modulation varies as the minus two-thirds power of the acoustic Mach number defined at the outer cylinder or sphere and decreases with an increase in the radius ratio of the inner and outer cylinders or spheres. When the dissipation effect is small but not negligible, the modulation is slowly weakened and the resonant oscillation approaches a steady state oscillation, which corresponds to the steady solution examined in earlier works. ©2006 American Institute of Physics
|
| 出版者 |
en
American Institute of Physics
|
| 日付 |
|
| 言語 |
|
| 資源タイプ |
journal article |
| 出版タイプ |
VoR |
| 資源識別子 |
HDL
http://hdl.handle.net/2115/16865
|
| 関連 |
-
isIdenticalTo
DOI
https://doi.org/10.1063/1.2393437
|
| 収録誌情報 |
-
-
en
Physics of Fluids
-
巻18
号11
開始ページ117107
|
| ファイル |
|
| コンテンツ更新日時 |
2023-07-26 |
