Analysis of nonlinear shallow water waves in a tank by concentrated mass model

Satoshi Ishikawa, Takahiro Kondou, Kenichiro Matsuzaki, Satoshi Yamamura

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The sloshing of liquid in a tank is an important engineering problem. For example, liquid storage tanks in industrial facilities can be damaged by earthquakes, and conversely liquid tanks, called tuned liquid damper, are often used as passive mechanical dampers. The water depth is less often than the horizontal length of the tank. In this case, shallow water wave theory can be applied, and the results indicate that the surface waveform in a shallow excited tank exhibits complex behavior caused by nonlinearity and dispersion of the liquid. This study aims to establish a practical analytical model for this phenomenon. A model is proposed that consists of masses, connecting nonlinear springs, connecting dampers, base support dampers, and base support springs. The characteristics of the connecting nonlinear springs are derived from the static and dynamic pressures. The advantages of the proposed model are that nonlinear dispersion is considered and that the problem of non-uniform water depth can be addressed. To confirm the validity of the model, numerical results obtained from the model are compared with theoretical values of the natural frequencies of rectangular and triangular tanks. Numerical results are also compared with experimental results for a rectangular tank. All computational results agree well with the theoretical and experimental results. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear shallow water wave problems.

Original languageEnglish
Pages (from-to)171-182
Number of pages12
JournalJournal of Sound and Vibration
Volume371
DOIs
Publication statusPublished - Jun 9 2016

Fingerprint

water waves
Water waves
shallow water
dampers
Liquids
liquids
water depth
Liquid sloshing
liquid sloshing
storage tanks
static pressure
dynamic pressure
Numerical analysis
Water
Analytical models
Natural frequencies
Earthquakes
numerical analysis
resonant frequencies
waveforms

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Analysis of nonlinear shallow water waves in a tank by concentrated mass model. / Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro; Yamamura, Satoshi.

In: Journal of Sound and Vibration, Vol. 371, 09.06.2016, p. 171-182.

Research output: Contribution to journalArticle

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