scholarly journals Nonlinear Hydroelastic Interaction among a Floating Elastic Plate, Water Waves, and Exponential Shear Currents

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ping Wang ◽  
Yongyan Wang ◽  
Xintai Huo
Keyword(s):  
Elastic Plate ◽  
Water Waves ◽  
Opposite Effect ◽  
Phase Speed ◽  
Horizontal Velocity ◽  
Wave Crest ◽  
Current Case ◽  
Floating Elastic Plate ◽  
Wave Trough ◽  
Hydroelastic Interaction

Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil-Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current.

Theory of the almost-highest wave. Part 2. Matching and analytic extension

1978 ◽  
Vol 85 (4) ◽  
pp. 769-786 ◽  
Author(s):  
M. S. Longuet-Higgins ◽  
M. J. H. Fox
Keyword(s):  
Phase Velocity ◽  
Wave Height ◽  
Water Waves ◽  
Phase Speed ◽  
Wave Crest ◽  
Analytic Extension ◽  
Radius Of Curvature ◽  
Maximum Height ◽  
Branch Points ◽  
Method Of Calculation

Most methods of calculating steep gravity waves (of less than the maximum height) encounter difficulties when the radius of curvature R at the crest becomes small compared with the wavelength L, or some other typical length scale. This paper describes a new method of calculation valid when R/L is small.For deep-water waves, a parameter ε is defined as equal to q/2½c0, where q is the particle speed at the wave crest, in a frame of reference moving with the phase speed c. Hence ε is of order (R/L)½. Three zones are distinguished: (1) an inner zone of linear dimensions ε2L near the crest, where the flow is described by the inner solution found previously by Longuet-Higgins & Fox (1977); (2) an outer zone of dimensions O(L) where the flow is given by a perturbed form of Michell's solution for the highest wave; and (3) a matching zone of width O(L). The matching procedure involves complex powers of ε.The resulting expression for the square of the phase velocity is found to be \[ c^2 = (g/k)\{1.1931-1.18\epsilon^3\cos(2.143\ln \epsilon + 2.22)\} \] (see figures 5a, b), which is in remarkable agreement with independent calculations based on high-order series. In particular, the existence of turning-points in the phase velocity as a function of wave height is confirmed.Similar expressions, valid to order ε3, are found for the wave height, the potential and kinetic energies and the momentum flux or impulse of the wave.The velocity field is extended analytically across the free surface, revealing the existence of branch-points of order ½, as predicted by Grant (1973).

scholarly journals The dynamic pressure in deep-water extreme Stokes waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170095 ◽  
Author(s):  
Tony Lyons
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Dynamic Pressure ◽  
Stokes Wave ◽  
Wave Crest ◽  
Maximum Principles ◽  
Nonlinear Water Waves ◽  
Stagnation Points ◽  
Wave Trough ◽  
Crest Line

In this paper, we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maximum principles are applied to analyse the dynamic pressure in the fluid body by means of an excision process. It is shown that the dynamic pressure attains its maximum value beneath the wave crest and its minimum beneath the wave trough, while it decreases in moving away from the crest line along any streamline. This article is part of the theme issue ‘Nonlinear water waves’.

EFFECT OF INITIAL CONTACT LOCATION ON MULTIASPERITY NANOCONTACT: QUASICONTINUUM SIMULATION

NANO ◽  
2014 ◽  
Vol 09 (01) ◽  
pp. 1450004
Author(s):  
WU-GUI JIANG ◽  
SHUANG XU ◽  
ZHENG-WEI WANG
Keyword(s):  
Contact Process ◽  
Copper Substrate ◽  
Wave Crest ◽  
Initial Contact ◽  
Displacement Curve ◽  
Quasicontinuum Method ◽  
Contact Stage ◽  
Wave Trough ◽  
Contact Models ◽  
Microscopic Deformation

Two nanocontact models with different initial contact locations are built to simulate the process of the multiasperity nanocontact for investigating the effect of initial contact location on the nanocontact process by using the quasicontinuum method. The indenter is initially located on the top of the middle wave crest (MWC) of the substrate and the top of the wave trough on the left side (LWT) of the substrate, respectively. The microscopic deformation mechanism, the load–displacement curve and the nanohardness–displacement curve are examined. It is found that the deformation mechanisms in the two multiasperity contact models are different. During the initial contact stage, in the MWC model, the twinning deformation dominates the whole contact process, while in the LMT model many Lomer-Cottrell locks are generated in the copper substrate, which inhibits the occurrence of twinning deformation.

Directional Stability and Control of Ships in Waves

1972 ◽  
Vol 16 (03) ◽  
pp. 205-218
Author(s):  
Haruzo Eda
Keyword(s):  
Automatic Control ◽  
Gain Control ◽  
Small Region ◽  
Wave Crest ◽  
Following Seas ◽  
Directional Stability ◽  
Wave Trough ◽  
Calm Water ◽  
Hull Forms ◽  
And Control

The stability and oscillatory motions of ships (automatically steered and unsteered) in the horizontal plane were examined on a digital computer for the case of regular following seas. Available hydrodynamic data for Series 60 hull forms were used. Analysis of directional stability was made for the case of zero encounter frequency (i.e., the ship runs at high speeds equal to the wave celerity). The ship (which is hydrodynamically stable without automatic control in calm water) is directionally unstable in following seas except for the small region near the ascending node of the waves. Addition of automatic control can give the ship directional stability when it is located on the wave trough, but not when it is located on the wave crest. At relatively high frequency (i.e., at low speeds in following seas), the rudder and control system are almost incapable of reducing oscillatory motion. Violent rudder activity in following seas can be decreased by reducing the yaw-rate-gain control constant and by increasing the rudder-response-time constant.

scholarly journals Motions of a Very Large Floating Elastic Plate in Waves

1997 ◽  
Vol 1997 (182) ◽  
pp. 285-294 ◽  
Author(s):  
Shuuichi Nagata ◽  
Hisafumi Yoshida ◽  
Hiroshi Isshiki ◽  
Yutaka Ohkawa
Keyword(s):  
Elastic Plate ◽  
Floating Elastic Plate
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