Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

Effect of compression on wave diffraction by a floating elastic plate

In the present paper, the water wave diffraction by a two-dimensional floating elastic plate is analyzed in the presence of compressive force. The solutions in the cases of infinite and finite water depths are derived based on integro-differential equation method in the presence of compressive force under the assumption of small amplitude water wave theory and plate deflection. Further, wave diffraction by the floating elastic plate is analyzed under the assumption of shallow water approximation. The role of compressive force and its limiting values are obtained by using the hydroelastic analysis of the flexural gravity waves. The limiting values of oblique angle of incidence are obtained in different cases and the effect of compressive force on the oblique angle is analyzed. Effect of compressive force and angle of incidence on the hydroelastic behavior of the floating plate are studied by analyzing the reflection coefficients in different cases.     

Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier–Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier–Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.     

Behavior of a floating elastic plate during vibrations of a bottom segment

The Wiener-Hopf technique is used to obtain an analytical solution for the problem of vibrations of a floating semi-infinite elastic plate due to earthquake-induced vibrations of a bottom segment. An explicit solution is obtained ignoring the inertial term. The surface-wave amplitudes and ice-plate deflection are studied numerically as functions of the frequency and position of the vibrating bottom segment, ice thickness, and fluid depth.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 98–108, March–April, 2005.     

Shock wave interaction with porous plates

Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate, decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate thickness has a minimal effect.     

The effect of porosity on shock interaction with a rigid, porous barrier

This work investigates the pressure amplification experienced behind a rigid, porous barrier that is exposed to a planar shock. Numerical simulations are performed in two dimensions using the full Navier–Stokes equations for a M = 1.3 incoming shock wave. An array of cylinders is positioned at some distance from a solid wall and the shock wave is allowed to propagate past the barrier and reflect off the wall. Pressure at the wall is recorded and the flowfield is examined using numerical schlieren images. This work is intended to provide insight into the interaction of a shock wave with a cloth barrier shielding a solid boundary, and therefore the Reynolds number is small (i.e., Re = 500 to 2000). Additionally, the effect of porosity of the barrier is examined. While the pressure plots display no distinct trend based on Reynolds number, the porosity has a marked effect on the flowfield structure and endwall pressure, with the pressure increasing as porosity decreases until a maximum value is reached.      

Nonlinear water wave interaction with floating bodies in SPH

A weakly compressible SPH solver is presented for applications involving nonlinear interaction between water waves and floating bodies. A complete algorithm able to compute fully coupled viscous Fluid–Solid interactions is described. No slip boundary condition on the solid surface is enforced through a ghost–fluid technique and the global loads are evaluated through the momentum exchange between fluid and ghost particles. A dedicated algorithm is developed to manage the intersection between the free surface and the solid profile. An explicit synchronous algorithm is proposed for the full coupling between fluid and rigid bodies. Stability, convergence and conservation properties are tested on several freely floating test cases and a final validation of the full algorithm is performed for the interaction between a 2-D box and a wave packet.     

Low-frequency wave propagation in an elastic plate floating on a two-layered fluid

For some technical applications related to the ice–sea interaction, it is necessary to predict waveguide properties of elastic plates floating on a relatively thin layer of water, which has a non-uniform density distribution across its depth. The issue of particular concern is propagation of low-frequency waves in such a coupled waveguide. In the present paper, a stratified fluid is modelled as two homogeneous, inviscid and incompressible layers with slightly different densities. The lighter layer of fresh water lies on top of the heavier layer of salty water. The former one produces fluid loading at the pre-stressed plate, whereas the latter one is bounded by the sea bottom. The classical asymptotic methods are employed to identify significant regimes of wave motion in such a three-component waveguide. Dispersion diagrams obtained from approximate dispersion relations are compared with their exact counterparts. The phenomena of veering and generation of waves with zero group velocity induced by pre-stress are identified and quantified.     

Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid

The scattering of water waves by a flexible porous membrane barrier in a two-layer fluid having a free surface is analysed in two dimensions. The membrane barrier is extended over the entire water depth in a two-layer fluid, each fluid being of finite depth. In the present analysis, linear wave theory and small amplitude membrane response are assumed. The porous membrane barrier is tensioned and pinned at both the free surface and the seabed. The associated mixed boundary value problem is reduced to a linear system of equations by utilizing a general orthogonality relation along with least-squares approximation method. Because of the flow discontinuity at the interface, the eigenfunctions involved have a discontinuity at the interface and the orthogonality relation used is a generalization of the classical one corresponding to a single-layer fluid. The reflection and transmission coefficients for the surface and internal modes, the free surface and interface elevations and the nondimensional membrane deflection are computed for various physical parameters like the nondimensional tension parameter, porous-effect parameter, fluid density ratio, ratio of water depths of the two fluids to analyse the efficiency of a porous membrane as a wave barrier in the two-layer fluid.     

Wave interaction with an array of porous walls in a two-layer ocean of varying bottom topography

Meccanica - Oblique wave scattering by a breakwater consisting of an array of thin porous walls in a two-layer ocean with varying bottom topography is investigated by using linear wave theory....     

Wave trapping by porous barrier in the presence of step type bottom

The present study deals with the trapping of oblique wave by porous barrier located near a rigid wall in the presence of a step type bottom bed. The solution of the physical problem is obtained using the eigenfunction expansion method and multi-mode approximation associated with modified mild-slope equation. Assuming that the porous structure is made of materials having fine pores, the mathematical problem is handled for solution by matching the velocity and pressure at interface boundaries. Various numerical results are computed and analyzed to understand the role of bed profiles, structural porosity, depth ratio, oblique angle of incidence, distance between barrier and step edge and, the distance between the porous barrier and rigid wall in optimizing wave reflection and load on the structure/rigid-wall. A comparison of results on wave trapping by porous barriers over flat and undulated bed reveals that for the same distance between the porous barrier and rigid wall, more number of times optimum reflection occurs in case of undulated bed. The present study is likely to be of immense importance in the design of coastal structures for protecting coastal infrastructures.     

Wave scattering by a floating porous elastic plate of arbitrary shape: A semi-analytical study

In this paper, a semi-analytical model based on linear potential flow theory and an eigenfunction expansion method is developed to study wave scattering by a porous elastic plate with arbitrary shape floating in water of finite depth. The water domain is divided into the interior and exterior regions, corresponding to the domain beneath the plate and the rest extending towards infinite distance horizontally, respectively. The unknown coefficients in the potential expressions are determined by satisfying the continuity conditions for pressure and velocity at the interface of the two regions, together with the conditions for the motion/force at the edge of the plate, where the Fourier series expansion method is employed to deal with the terms associated with the radius function. A plate with three shapes – circular, cosine and elliptical – and three edge conditions are considered. We find that the largest deflection of the plate with a simply supported edge and a clamped edge is more sensitive to the change in porosity when the porosity is small. The power dissipated by an elliptical plate with its major axis perpendicular to the incident wave direction is the largest among the case studies for the majority of the porosity values tested.     

Eigenvibrations of a flexible platform floating on shallow water

The spectral problem for a flexible platform (airport) floating on shallow water is examined. The platform is modeded by a flexible plate of finite width and infinite length. A waveguide eigenmode is detected which propagates along the platform and attenuates exponentially away from it. The remaining eigenmodes are outgoing and growing exponentially away from the platform. All the eigenmodes can be excited only by external action on the platform. The behavior of the platform under external loading is examined. Lavrent'ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 173–181, January–February, 2000.     

Air shock wave interaction with an obstacle covered by porous material

The interaction between an air shock wave and a rigid wall covered by a porous screen is investigated numerically and experimentally. A mathematical two velocity with two stress tensors model is used for studying the wave processes in saturated porous media. The process of reflection of a step-type wave from a rigid wall covered with a porous layer is considered, the effect of the porous medium and wave parameters on the reflection is analyzed, and the numerical results are compared with the experimental data.Received: 30 July 2002, Accepted: 24 December 2002, Published online: 27 May 2003     

Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.     

Computation of the stress resultants of a floating Mindlin plate in response to linear wave forces

In this paper, we focus on the computation of stress resultants of a floating elastic plate using the Mindlin plate theory. The proposed method makes use of the linear wave theory and shallow-draft assumption. However, the usual Kirchhoff theory is replaced by the Mindlin theory for the plate. For a single frequency, the coupled water-plate problem is solved using a higher-order-coupled finite element–boundary element method. The solutions for the stress-resultants computed using the proposed method are more satisfactory than these based on the Kirchhoff plate theory.     

Hydroelastic impact of a horizontal floating plate with forward speed

The hydroelastic responses of a horizontal plate impacting with the water at both forward and downward speeds are investigated theoretically. The longitudinal bending behavior of a horizontal elastic plate is approximated by the behavior of longitudinal strips represented as an Euler-beam model. A simplified method of hydroelastic responses of the plate is extended to the cases with forward speed and compressive force, for which the hydrodynamic pressure is found by solving a two-dimensional boundary value problem based on the linearized wave theory. In order to validate the theoretical model, a fully-coupled algorithm in LS-DYNA and the available experimental measurements are used for the predictions of the hydrodynamic pressure and deformations of the horizontal plates impacting with water at vertical velocities. The effects of the forward speed and compressive force which can occur at the bottom of ship ships, are investigated theoretically for the plates with different edge boundary conditions. The critical values of the forward speed and longitudinal compression are discussed regarding the plates with various longitudinal lengths.