scholarly journals The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Ping Wang
Keyword(s):  
Incident Wave ◽  
Elastic Plate ◽  
Open Water ◽  
Angular Frequency ◽  
Physical Parameters ◽  
Thin Elastic Plate ◽  
Convergence Control ◽  
Progressive Waves ◽  
Analytical Series ◽  
Hydroelastic Response

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.

Nonlinear Hydroelastic Response of a Two-Dimensional Mat-Type VLFS by the Green-Naghdi Theory

2004 ◽  
Author(s):  
Dingwu Xia ◽  
R. Cengiz Ertekin ◽  
Jang Whan Kim
Keyword(s):  
Elastic Plate ◽  
Mechanical Energy ◽  
Beam Theory ◽  
Bending Moment ◽  
Open Water ◽  
Beam Equation ◽  
Two Dimensional ◽  
Jump Conditions ◽  
Numerical Predictions ◽  
Hydroelastic Response

The two-dimensional, nonlinear hydroelasticity of a mat-type VLFS is studied within the scope of linear beam theory for the structure and the nonlinear, Level I Green-Naghdi (GN) theory for the fluid. The beam equation and the GN equations are coupled through the kinematic and dynamic boundary conditions to obtain a new set of modified GN equations. These equations model long-wave motion beneath an elastic plate. A set of jump conditions that are necessary for the continuity (or the matching) of the solutions in the open water region and that under the structure is newly derived through the use of the postulated conservation laws of mass, momentum and mechanical energy. The resulting governing equations, subjected to the boundary and jump conditions, are solved by the finite-difference method in the time domain. The present model is applicable, for example, to the study of the hydroelastic response of a mat-type VLFS under the action of a solitary wave, or a frontal tsunami wave. Good agreement is observed between the present results and other published theoretical and numerical predictions, as well as experimental data. The nonlinear results show that consideration of nonlinearity is important for accurate predictions of the bending moment of the floating elastic plate. It is also found that the rigidity of the structure also greatly affects the bending moment and displacement of the structure in this nonlinear theory.

Acoustic scattering by a finite nonlinear elastic plate. I Primary, secondary and combination resonances

1987 ◽  
Vol 414 (1846) ◽  
pp. 237-253 ◽  
Keyword(s):  
Incident Wave ◽  
Elastic Plate ◽  
Scattered Field ◽  
Acoustic Waves ◽  
Multiple Scales ◽  
Acoustic Scattering ◽  
Scattered Wave ◽  
Thin Elastic Plate ◽  
Finite Width ◽  
Wave Angle

A thin elastic plate of finite width is irradiated by time-harmonic acoustic waves. The fluid is assumed light compared with the plate mass, and the forcing term is of sufficient amplitude to necessitate the inclusion of a nonlinear term (due to mid-plane stretching) in the plate equation. The order-one scattered field is determined by the method of multiple scales when the forcing frequency approaches a free oscillation frequency (eigenfrequency) of the plate. This solution is shown to agree with previous work, for the linear problem, and can be multivalued for particular values of the plate-fluid parameters. The scattered wave may also exhibit jumps in its amplitude and phase angle as it varies with frequency, incident-wave angle or incident-wave amplitude. The non-linear term further allows the possibility of secondary and combination resonances. These are investigated and the scattered field is shown to contain terms of different frequencies to those of the incident waves. Multivalued solutions and the associated jump phenomenon are again found for these resonant cases.

The Sound Transmission Through a Baffled, Thin, Finite, Elastic Plate by Using Boundary Integral Equations

1999 ◽  
Author(s):  
Yasuhito Kawai
Keyword(s):  
Integral Equations ◽  
Elastic Plate ◽  
Boundary Integral Equations ◽  
Sound Transmission ◽  
Coupled System ◽  
Boundary Integral ◽  
Image Method ◽  
Thin Elastic Plate ◽  
Control Engineering ◽  
Sound Fields

Abstract The prediction of sound transmission through a thin elastic plate such as a window is an important problem in the field of noise control engineering. Integral equations which express sound fields in infinite half spaces which are divided off by the baffle and the elastic plate are introduced and combined with the equation of plate vibration to solve as a coupled system. The image method is used in every equation to reduce unknown functions and boundaries which should be considered. Some numerical examples are solved numerically to examine the method.

scholarly journals Coupling between the ocean and an ice shelf

1991 ◽  
Vol 15 ◽  
pp. 101-108 ◽  
Author(s):  
Colin Fox ◽  
Vernon A. Squire
Keyword(s):  
Elastic Plate ◽  
Velocity Potential ◽  
Open Water ◽  
Ocean Waves ◽  
Ocean Wave ◽  
Single Frequency ◽  
Plate Model ◽  
Ice Shelf ◽  
Long Period ◽  
Set Up

The possibility of long-period ocean waves coupling to an ice shelf is investigated. A thick elastic plate model is used for the ice shelf with comparisons made to the simpler thin-plate model. The strain set up on the ice shelf by a normally incident single frequency ocean wave is calculated by completely solving the equations governing the velocity potential for such a system. In the absence of measurements on an ice shelf, existing measurements of long-period strain on an ice tongue are used to estimate the required incident amplitude in the open water to induce the observed oscillations. It is found that the height of seas required indicates that ocean wave driving is a plausible forcing mechanism for observed oscillations.

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