Nonlinear Oscillations in Rectangular Tanks

Lepelletier, Thierry; Raichlen, Fredric

doi:10.1061/(asce)0733-9399(1988)114:1(1)

Cited by 96 publications

(44 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of interest are how the transient maximum amplitude compares to the steady-state value and how the nonlinear beating period varies with the parameters of the problem. Lepelletier and Raichlen [6] solved the shallow-water equations numerically and demonstrated good agreement between their calculations and experiments. Representing a different approach, Wu et al [7] used finite elements to investigate three-dimensional sloshing in inviscid rectangular basins of finite depth.…”

Section: Introductionmentioning

confidence: 76%

Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison

Hill

Frandsen

2005

J Eng Math

View full text Add to dashboard Cite

The problem of water waves generated in a horizontally oscillating basin is considered, with specific emphasis on the transient evolution of the wave amplitude. A third-order amplitude evolution equation is solved analytically in terms of Jacobian elliptic functions. The solution explicitly determines the maximum amplitude and nonlinear beating period of the resonated wave. An observed bifurcation in the amplitude response is shown to correspond to the elliptic modulus approaching unity and the beating period of the interaction approaching infinity. The theoretical predictions compare favorably to fully nonlinear simulations of the sloshing process. Due to the omission of damping, the consideration of only a single mode, and the weakly nonlinear framework, the analytical solution applies only to finite-depth, non-breaking waves. The inviscid numerical simulations are similarly limited to finite depth.

show abstract

Section: Introductionmentioning

confidence: 76%

Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison

Hill

Frandsen

2005

J Eng Math

View full text Add to dashboard Cite

show abstract

“…The comparison of the maximum wave elevation computed by the present model with that of the linear theory of [4] is shown in Figure 11.…”

Section: Numerical Examplesmentioning

confidence: 97%

“…The comparisons of the maximum wave elevation computed by the present model with that of the experiment taken from [4] are shown in Figure 12. At or near the resonant zone, the present model gives much better predictions than the linear potential theory, and for those frequencies away from the resonance (V B0.94 and V \ 1.07), the numerical results agree well with the experimental data.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Figure 3 shows the comparison of the maximum surface elevations with horizontal sinusoidal excitation computed from the linear potential theory and from the analysis model considering the fluid viscosity. Owing to the fluid viscosity at or near the resonant zone, the fluid sloshing is heavily damped (see Figures 7 and 8), the wave elevation would not grow linearly with time [4], and a steady state is achieved. When far away from the resonant zone, the results computed from the two theories almost coincide.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…To make use of the experimental results taken from Reference [4], the rectangular tanker with length L=0.6095, water depth H =0.06 is considered first. The fluid viscosity is v= 0.00094 and the fluid density is z =1000.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

A boundary element method and spectral analysis model for small-amplitude viscous fluid sloshing in couple with structural vibrations

Yuelong

Xue

Kurita³

2000

Int. J. Numer. Meth. Fluids

View full text Add to dashboard Cite

A nonlinear numerical model for sloped‐bottom tuned liquid dampers

Olson

Reed

2001

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

Shaking-table data for a tuned liquid damper with a sloped bottom of 30 • with the horizontal are investigated using a non-linear numerical model previously developed by Yu, Jin-kyu, Nonlinear characteristics of tuned liquid dampers. Ph.D. Thesis, Department of Civil Engineering, University of Washington, Seattle, WA, 98195 (1997). Sti ness and damping parameters for this model are obtained and compared with those previously derived for box-shaped tanks. The values for these parameters re ect the softening spring behaviour of the sloped-bottom system in contrast to the hardening system evident for the boxshaped TLD. Consequently, the sloped-bottom tank should be tuned slightly higher than the fundamental structural frequency in order to obtain the most e ective damping.

show abstract

Nonlinear Oscillations in Rectangular Tanks

Cited by 96 publications

References 6 publications

Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison

Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison

A boundary element method and spectral analysis model for small-amplitude viscous fluid sloshing in couple with structural vibrations

A nonlinear numerical model for sloped‐bottom tuned liquid dampers

Contact Info

Product

Resources

About