Effect of compression on wave diffraction by a floating elastic plate (original) (raw)
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Scattering of waves by articulated floating elastic plates in water of infinite depth
Marine Structures, 2005
The wave scattering by an articulated floating elastic plate in water of infinite depth is analyzed in the linearized theory of water waves. Using the geometrical symmetry of the articulated plate, the associated boundary value problem in the half-plane is reduced to two boundary value problems in the quarter plane, whose solutions are derived by the direct application of a mixed-type Fourier transform and the corresponding mode-coupling relation. The articulated plate is modeled as the assembling of two semi-infinite thin elastic plates which are attached by connectors. The hydroelastic behavior of the floating elastic plate is investigated by analyzing the stiffness of the connectors on the reflection and transmission characteristics of the flexural gravity waves. The phase and group velocity, reflection and transmission coefficient and the vertical displacement response of the elastic plate are computed and analyzed to understand the effect of articulation on the wave motion below the plate. r
Scattering of water waves by a submerged thin vertical elastic plate
Archive of Applied Mechanics, 2013
The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green's function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green's integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.
Geophysical & Astrophysical Fluid Dynamics, 2014
Expansion formulae associated with the interaction of oblique surface gravity waves with a floating flexible plate in the presence of a submerged horizontal flexible structure are derived using Green's integral theorem in water of finite and infinite water depths. The associated Green's functions are derived using the fundamental solution associated with the reduced wave equation. The integral forms of the Green's functions and the velocity potentials are advantageous over the eigenfunction expansion method in situation when the roots of the dispersion relation coalesce.As an application of the expansion formulae, diffraction of oblique waves by a finite floating elastic plate in the presence of a submerged horizontal flexible membrane is investigated in water of finite depth. The accuracy of the numerical computation is demonstrated by analysing the convergence of the complex amplitude of the reflected waves and the energy relation. Effect of the submerged membrane on the diffraction of surface waves is studied by analysing the reflection and transmission coefficients for various parametric values. Further, the derivation of long wave equation under shallow water approximation is derived in a direct manner in the appendix. The concept and methodology can be easily extended to deal with acoustic wave interaction with flexible structures and related problems of mathematical physics and engineering.
Water wave scattering by a floating elastic plate over a plane incline
The Quarterly Journal of Mechanics and Applied Mathematics, 2012
The effect of a shoreline on the interaction between surface water waves and a floating elastic plate is investigated on the basis of linear theory by considering the fluid motion over a plane inclined bed. The use of a radiation condition at the shoreline that removes reflected waves there both simulates energy dissipation in the shoaling region and allows comparisons to be made with the case of constant water depth. The model applies equally to floating sea ice and 'very large floating structures'. A Green's function approach reduces the underlying boundary value problem to a pair of coupled integral equations to which Galerkin's method is applied. A sample of numerical results is given from which inferences may be drawn about the influence of the sloping bed. Discrete eigenvalues in sheet length are observed at which the formal scattering problem has no solution.
Hydroelastic Response to Oblique Wave Incidence on a Floating Plate with a Submerged Perforated Base
Journal of Marine Science and Engineering
A hydroelastic model is developed of a floating flexible structure in the presence of a submerged perforated base connected with mooring lines under oblique wave action. Using the velocity decomposition method, the analytical solution of the referred model is obtained in finite water depth. The convergence of the analytical solution for different oblique wave incidences is examined, and the present results of deflection amplitude are compared with experimental datasets and the numerical results available in the literature. The effects of oblique wave incidence, along with various design parameters on the reflection, transmission, and dissipation coefficients, as well as structural displacements, are analysed through hydroelastic analysis. Further, the effect of oblique incidence angle on the free oscillation hydroelastic waves in two wave modes is investigated by deriving the free motion velocity potential in a wave basin.
Scattering of water waves by inclined thin plate submerged in finite-depth water
Archive of Applied Mechanics (Ingenieur Archiv), 2001
The problem of water wave scattering by an inclined thin plate submerged in water of uniform ®nite depth is investigated here under the assumption of irrotational motion and linear theory. A hypersingular integral equation formulation of the problem is obtained by an appropriate use of Green's integral theorem followed by utilization of the boundary condition on the plate. This hypersingular integral equation involves the discontinuity in the potential function across the plate, which is approximated by a ®nite series involving Chebyshev polynomials. The coef®cients of this ®nite series are obtained numerically by collocation method. The quantities of physical interest, namely the re¯ection and transmission coef®cients, force and moment acting on the plate per unit width, are then obtained numerically for different values of various parameters, and are depicted graphically against the wavenumber. Effects of ®nite-depth water, angle of inclination of the plate with the vertical over the deep water and vertical plate results for these quantities are shown. It is observed that the deep-water results effectively hold good if the depth of the mid-point of the submerged plate below the free surface is of the order of one-tenth of the depth of the bottom.
Scattering of surface waves by a semi-infinite floating elastic plate
Physics of Fluids, 2001
A new inner product is developed based on the Fourier analysis to study the scattering of surface waves by a floating semi-infinite elastic plate in a two-dimensional water domain of finite depth. The eigenfunctions for the plate-covered region are orthogonal with respect to this new inner product. The problem is studied for various wave and geometrical conditions. Especially, the influence of different edge conditions on the hydrodynamic behavior is investigated and compared. The edge conditions considered in the present study involve ͑i͒ a free edge, ͑ii͒ a simply supported edge, and ͑iii͒ a built-in edge. The hydrodynamic performance of an elastic plate is characterized for various conditions in terms of wave reflection and transmission, plate deflection, and surface strain. It is observed that the hydrodynamic behavior depends on the wave conditions, the geometrical settings, and the edge conditions. The built-in edge condition induces the maximum wave reflection and the minimum wave transmission. The free edge condition leads to the maximum plate deflection.
Zeitschrift für angewandte Mathematik und Physik, 2016
In this paper, we present an alternative method to investigate scattering of water waves by a submerged thin vertical elastic plate in the context of linear theory. The plate is submerged either in deep water or in the water of uniform finite depth. Using the condition on the plate, together with the end conditions, the derivative of the velocity potential in the direction of normal to the plate is expressed in terms of a Green's function. This expression is compared with that obtained by employing Green's integral theorem to the scattered velocity potential and the Green's function for the fluid region. This produces a hypersingular integral equation of the first kind in the difference in potential across the plate. The reflection coefficients are computed using the solution of the hypersingular integral equation. We find good agreement when the results for these quantities are compared with those for a vertical elastic plate and submerged and partially immersed rigid plates. New results for the hydrodynamic force on the plate, the shear stress and the shear strain of the vertical elastic plate are also evaluated and represented graphically.