Hysteresis in Shallow Water Sloshing
Publication: Journal of Engineering Mechanics
Volume 133, Issue 10
Abstract
Hysteresis in sloshing of shallow water in horizontally excited tanks is explored experimentally. In particular the wave response to relatively large shaking amplitude near the resonant frequency is investigated for two tank configurations: a tank with horizontal bottom and vertical walls, and a tank with horizontal bottom and sloping beaches. The hysteresis behavior is clearly observed within a narrow frequency range around the shifted resonant frequency. The wave response is either in the form of smooth nonbroken waves or in the form of violent breaking waves for exactly the same set of parameters depending only on how the target oscillation frequency is tuned: i.e., whether the forcing frequency of the prior state is higher or lower than the target frequency. The consequence is that it is not possible to define a unique value for the jump frequency as it depends on the direction of the frequency tuning.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Assistance provided by Dr. J. Yu and Dr. T. Wakahara with the laboratory experiments is acknowledged. Discussions with Professor D. Reed at the University of Washington are appreciated. Dr. S. Masri is thanked for arranging the use of the shaking table facility at the University of Southern California. The support of the United States National Science Foundation (Grant Nos. NSFCMS-9301577 and NSFCMS-0245206) and the Research Fund of the University of Iceland for this study are gratefully acknowledged.
References
Faltinsen, O. M. (1974). “A nonlinear theory of sloshing in rectangular tanks.” J. Ship Res., 18, 224–241.
Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A., and Timokha, A. N. (2000). “Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth.” J. Fluid Mech., 407, 201–234.
Faltinsen, O. M., and Timokha, A. N. (2001). “Adaptive multimodal approach to nonlinear sloshing in a rectangular rank.” J. Fluid Mech., 432, 167–200.
Faltinsen, O. M., and Timokha, A. N. (2002). “Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth.” J. Fluid Mech., 470, 319–357.
Frandsen, J. B. (2004). “Sloshing motions in excited tanks.” J. Comput. Phys., 196(1), 53–87.
Frandsen, J. B. (2005). “Numerical predictions of tuned liquid tank structural systems.” J. Fluids Struct., 20(3), 309–329.
Fujino, Y., Pacheco, B. M., Chaiseri, P., and Sun, L.-M. (1988). “Parametric studies on tuned liquid damper (TLD) using circular containers by free-oscillation experiments.” Struct. Eng./Earthquake Eng., 5, 381–391.
Fujino, Y., Sun, L., Pacheco, B. M., and Chaiseri, P. (1992). “Tuned liquid damper (TLD) for suppressing horizontal motion of structures.” J. Eng. Mech., 118(10), 2017–2030.
Gardarsson, S., Yeh, H., and Reed, D. (2001). “Behavior of sloped-bottom tuned liquid dampers.” J. Eng. Mech., 127(3), 266–271.
Gardarsson, S. M. (1997). “Shallow-water sloshing.” Ph.D. thesis, Univ. of Washington, Seattle.
Gardarsson, S. M. (2007). “Hysteresis in shallow water sloshing—Data website.” ⟨http://www.hi.is/~sigmg/JEM_2007/hysteresis-data⟩ (May 3, 2007).
Hill, D. F. (2003). “Transient and steady-state amplitudes of forced waves in rectangular basins.” Phys. Fluids, 15(6), 1576–1587.
Koh, C. G., Mahatma, S., and Wang, C. M. (1994). “Theoretical and experimental studies on rectangular liquid dampers under arbitrary excitations.” Earthquake Eng. Struct. Dyn., 23(1), 17–31.
Lepelletier, T. G., and Raichlen, F. (1988). “Nonlinear oscillations in rectangular tanks.” J. Eng. Mech., 114(1), 1–23.
Ockendon, H., and Ockendon, J. R. (2001). “Nonlinearity in fluid resonances.” Meccanica, 36(3), 297–321.
Ockendon, J. R., and Ockendon, H. (1973). “Resonant surface waves.” J. Fluid Mech., 59, 397–413.
Reed, D., Yeh, H., Yu, J., and Gardarsson, S. M. (1998a). “Tuned liquid dampers under large amplitude excitation.” J. Wind. Eng. Ind. Aerodyn., 74–76, 923–930.
Reed, D., Yu, J., Yeh, H., and Gardarsson, S. (1998b). “Investigation of tuned liquid dampers under large amplitude excitation.” J. Eng. Mech., 124(4), 405–413.
Sun, L. M., Fujino, Y., Pacheco, B. M., and Isobe, M. (1989). “Nonlinear waves and dynamic pressures in rectangular tuned liquid damper (TLD)—Simulation and experimental verification.” Struct. Eng./Earthquake Eng., 6, 251–262.
Yeh, H., and Chang, K.-T. (1994). “On propagation of edge-wave packets.” Proc., Waves—Phys. and Numer. Modeling, M. Isaacson and M. Quick, eds., Univ. of British Columbia, Vancouver, 270–279.
Information & Authors
Information
Published In
Copyright
© 2007 American Society of Civil Engineers.
History
Received: May 18, 2006
Accepted: Nov 7, 2006
Published online: Oct 1, 2007
Published in print: Oct 2007
Notes
Note. Associate Editor: Nikolaos D. Katopodes
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.