Resonant Oscillations: A Regular Perturbation Approach
- 1 July 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (7) , 1069-1075
- https://doi.org/10.1063/1.1665698
Abstract
The resonant oscillations of a gas in a closed‐end tube are treated. The time‐periodic motion is given by a regular perturbation method in which the expansion parameter is the Mach number of the resulting flow. The solution at the first order exhibits a shock traveling in the tube, but, to this order, the waves do not interact. The interaction of the waves is calculated at the second order. The perturbation procedure proceeds systematically by an application of the Fredholm alternative at each stage.Keywords
This publication has 17 references indexed in Scilit:
- Resonant thermal-acoustic oscillationsInternational Journal of Engineering Science, 1971
- Finite amplitude waves in bounded media: nonlinear free vibrations of an elastic panelProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1970
- Perturbation Theory of Nonlinear Boundary-Value ProblemsJournal of Mathematical Physics, 1969
- Resonant oscillations of water waves I. TheoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1968
- Self-sustained thermally driven nonlinear oscillations in one-dimensional magnetohydrodynamic flowInternational Journal of Engineering Science, 1967
- Periodic vibrations of systems governed by nonlinear partial differential equationsCommunications on Pure and Applied Mathematics, 1966
- Thermally driven nonlinear oscillations in one-dimensional magnetohydrodynamic flowInternational Journal of Engineering Science, 1966
- Stroboscopic-Perturbation Procedure for Treating a Class of Nonlinear Wave EquationsJournal of Mathematical Physics, 1964
- Resonant oscillations in closed tubesJournal of Fluid Mechanics, 1964
- Periodic Shock Waves in Resonating Gas ColumnsThe Journal of the Acoustical Society of America, 1960