On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

Resonant surface waves and chaotic phenomena

1987 ◽  
Vol 183 ◽  
pp. 543-565 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna
Keyword(s):  
Surface Tension ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Chaotic Behaviour ◽  
Chaotic Motions ◽  
Chaotic Phenomena ◽  
Rectangular Container ◽  
Effect Of Surface

Surface waves in a rectangular container subjected to vertical oscillations are studied. Effects of energy dissipation along the lines of Miles (1967) and the effect of surface tension are included. Sufficient conditions, for two modes to dominate the motion, are given. The analysis is along the lines of Miles (1984a) and Holmes (1986). A complete bifurcation analysis is performed, and the modal amplitudes and phases are shown to have chaotic behaviour. This result is obtained under assumptions different from those of Holmes (1986). The conclusions regarding chaotic motions are based on a theorem of šilnikov (1970).

Dynamic analysis of rectangular liquid containers in three-dimensional space

2006 ◽  
Vol 33 (5) ◽  
pp. 501-507 ◽  
Author(s):  
M R Kianoush ◽  
H Mirzabozorg ◽  
M Ghaemian
Keyword(s):  
Current Practice ◽  
Seismic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Fe Analysis ◽  
Lumped Mass ◽  
Mass Model ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Three Dimensional Space

A new method for seismic analysis of containers in three-dimensional space is introduced in which the effects of both impulsive and convective components and their corresponding damping are accounted for in time domain. A case study is performed to investigate the behaviour of a concrete rectangular container under the effects of horizontal and vertical ground motions using the scaled earthquake components of the 1940 El-Centro earthquake record. Two-dimensional behaviour of the tank is assumed. The results of the study are compared with those obtained using the current practice and those determined from finite element (FE) analysis based on a lumped mass model. The results of the FE analysis with the equivalent added masses and rigid walls are in good agreement with those from the current practice. Compared with the proposed method, however, the current practice overestimates the response of the container. Also, the vertical excitation leads to a significant response in the container, but combining the effects of horizontal and vertical excitations reduces the response of the structure in the considered system.Key words: liquid, rectangular container, sloshing, staggered method, three-dimensional space, vertical excitation.

scholarly journals Three-dimensional surface velocities of Storstrømmen glacier, Greenland, derived from radar interferometry and ice-sounding radar measurements

2003 ◽  
Vol 49 (165) ◽  
pp. 201-209 ◽  
Author(s):  
Niels Reeh ◽  
Johan Jacob Mohr ◽  
Søren Nørvang Madsen ◽  
Hans Oerter ◽  
Niels S. Gundestrup
Keyword(s):  
Steady State ◽  
Vertical Velocity ◽  
Three Dimensional ◽  
Greenland Ice Sheet ◽  
Mass Conservation ◽  
Ablation Rate ◽  
Radar Interferometry ◽  
Surface Velocity ◽  
Outlet Glacier ◽  
Dimensional Surface

AbstractNon-steady-state vertical velocities of up to 5 m a−1 exceed the vertical surface-parallel flow (SPF) components over much of the ablation area of Storstrømmen, a large outlet glacier from the East Greenland ice sheet. Neglecting a contribution to the vertical velocity of this magnitude results in substantial errors (up to 20%) also on the south–north component of horizontal velocities derived by satellite synthetic aperture radar interferometry (InSAR) measurements. In many glacier environments, the steady-state vertical velocity component required to balance the annual ablation rate is 5–10 m a−1 or more. This indicates that the SPF assumption may be problematic also for glaciers in steady state. Here we derive the three-dimensional surface velocity distribution of Storstrømmen by using the principle of mass conservation (MC) to combine InSAR measurements from ascending and descending satellite tracks with airborne ice-sounding radar measurement of ice thickness. The results are compared to InSAR velocities previously derived by using the SPF assumption, and to velocities obtained by in situ global positioning system (GPS) measurements. The velocities derived by using the MC principle are in better agreement with the GPS velocities than the previously calculated velocities derived with the SPF assumption.

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