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would be close to the shifted frequency for other reasons not discussed here. Hence, for
a tuned liquid damper application, a hysteresis in water sloshing is not a critical issue but
does however further emphasize the need to design tuned liquid dampers so they do not
operate close to the shifted resonant frequency.
Conclusions
Behavior of steady state sloshing of shallow water in a tank can depend on a prior state
of the sloshing in time. This creates two possible behaviors of sloshing of water for exact-
ly the same conditions that look quite different from each other, one being violent wave
breaking behavior with large wave heights and the other with a relatively smooth water
surface with no wave breaking and small wave heights. The hysteresis phenomenon is
known in other engineering situations and here it has been shown with rigorous experi-
ments that a sloshing of shallow water exhibits such behavior.
Acknowledgments
Assistance provided by Dr. J. Yu and Dr. T. Wakahara with the laboratory experiments is
acknowledged. Discussions with professors H. Yeh and D. Reed 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 U.S. National Science Foundation (Grant No.
CMS-9301577) and the Research Fund of the University of Iceland for this study are grate-
fully acknowledged.
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