Nonlinear Stability of Differential Surge Chambers
Publication: Journal of Hydraulic Engineering
Volume 118, Issue 11
Abstract
Surge oscillations in a differential surge chamber have two degrees of freedom and are characterized by nonlinearities. The linear approximation provides stability criteria for small perturbations around the equilibrium state, and the Thoma stability criterion applies to the differential chamber. Large surge oscillations are investigated with direct numerical integration on two phase planes. The analysis indicates that the system reveals itself as a supercritical Hopf bifurcation—the exchange of stability from an asymptotically stable spiral to an unstable spiral approaching a stable limit cycle. The total chamber area is the controlling parameter. The bifurcation point corresponds to the Thoma criterion. For a surge chamber with an‐area larger than the Thoma value, an unstable limit cycle may exist around the equilibrium state on each phase plane, and it defines the domain of asymptotic stability. If the chamber area is less than the Thoma value, the case of soft self‐excitation with a stable limit cycle inside and an unstable one outside may occur, Stability in the large and instability in the small dominate the system.
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Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 118 • Issue 11 • November 1992
Pages: 1526 - 1539
Copyright
Copyright © 1992 ASCE.
History
Published online: Nov 1, 1992
Published in print: Nov 1992
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