Summary
Second-order resonance effects in closed tubes with varying cross-sectional area are investigated. It is seen that for tubes with cross-sectional areasA(x)∼x −2 solutions for the pressure disturbances can be found, as was done by W. Chester in case of tubes with constant cross-sectional area.
Zusammenfassung
Es werden Resonanzeffekte zweiter Ordnung in Rohren mit veränderlicher Querschnittsfläche betrachtet. Ist die QuerschnittsflächeA(x)∼x −2, so können die Druckstörungen in Analogie zu Chesters Theorie analytisch berechnet werden.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Chester,Resonant Oscillations in Closed Tubes, J. Fluid Mech.18, 44 1964.
J. J. Keller,Subharmonic Non-linear Acoustic Resonances in Closed Tubes, Z. angew. Math. Phys.26, 395, 1975.
J. J. Keller,Third Order Resonances in Closed Tubes, Z. angew. Math. Phys.27, 303, 1976.
J. J. Keller,Resonant Oscillations in Closed Tubes: The Solution of Chester's Equation, Thesis Nr. 5612, ETH Zürich 1975.
G. B. Whitham,Linear and Nonlinear Waves, p. 286, Wiley Interscience, New York, 1973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Keller, J.J. Nonlinear acoustic resonances in shock tubes with varying cross-sectional area. Journal of Applied Mathematics and Physics (ZAMP) 28, 107–122 (1977). https://doi.org/10.1007/BF01590712
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01590712