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Mitigation of wave force on a circular flexible plate by a surface-piercing flexible porous barrier

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART M-JOURNAL OF ENGINEERING FOR THE MARITIME ENVIRONMENT 2021年第2期235卷 586-599页

作者： Gayathri, R. Behera, Harekrushna SRM Inst Sci & Technol Coll Engn & Technol Dept Math Chennai 603203 TN India

Wave force acting on a circular flexible plate in the presence of a vertical surface-piercing flexible porous membrane is examined under the hypothesis of linear water wave theory. A semi-analytic solution is developed employing the Fourier-Bessel series expansion method along with the methods of separation of variables and least-squares approximation. To keep the outer flexible membrane at a desired position, clamped-moored condition is used. Appropriate orthogonal mode-coupling relationship for the eigenfunctions of the plate covered region is exploited in the expansion formulas together with the continuity of velocity and pressure for achieving the system of equations and to determine the unknowns. The effects of various physical parameters are analyzed by computing wave load on the structures, plate deflection and flow distribution. It is found that due to the presence of vertical flexible porous membrane, a significant amount of wave force on the plate is reduced. Thus, a cylindrical flexible porous membrane can be implemented to protect the inner circular flexible plate.

关键词： porous and flexible cylindrical membrane circular flexible plate least-squares approximation method orthogonal mode-coupling porous-effect parameter plate deflection flow distribution

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Wave Attenuation by Multiple Outer porous Barriers in the Presence of an Inner Rigid Cylinder

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JOURNAL OF WATERWAY PORT COASTAL AND OCEAN ENGINEERING 2020年第1期146卷

作者： Behera, Harekrushna Gayathri, R. Selvan, Siluvai Antony SRM Inst Sci & Technol Dept Math Kattankulathur 603203 Tamil Nadu India

The wave forces acting on a rigid cylinder are investigated in the presence of multiple outer porous cylindrical barriers by assuming the linear water wave theory. A Bessel series solution is obtained for the boundary value problem by using the methods of eigenfunction expansion and least-squares approximation. Two configurations of outer porous barriers are considered, namely bottom-standing and surface-piercing. As a special case, the effect of fully extended barriers is studied. The wave loads exerted on the cylinders, free surface elevations, and flow distribution around the structures are computed and analyzed for different physical parameters. The present theory is ratified with the result available in the literature for a single fully extended outer porous barrier. The study reveals that the hydrodynamic forces exerted on the inner impermeable cylinder are reduced significantly as the number of outer porous barriers is increased. Thus, multiple outer fully extended or partial porous barriers can be set up to protect the inner rigid cylinder.

关键词： Rigid and porous cylinders Least-squares approximation method porous-effect parameter Hydrodynamic wave force Free surface elevation Flow distribution

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Oblique Wave Scattering by a Floating Bridge in the Presence of a Vertical Permeable Flexible Barrier

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JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING-TRANSACTIONS OF THE ASME 2021年第2期143卷 021701页

作者： Gayathri, R. Kar, P. Behera, H. Sahoo, T. SRM Inst Sci & Technol Dept Math Chennai 603203 Tamil Nadu India IIT Kharagpur Dept OE & NA Kharagpur 721302 W Bengal India

The interaction between oblique water waves and floating bridge in the presence of a vertical partial flexible permeable barrier is studied under the assumption of the linear water wave theory in finite water depth. The associated mathematical problem is handled for a solution using the least-squares approximation method. The reflection and transmission coefficients, free surface elevation, wave force acting on the bridge and barrier are computed to study the effects of various wave and structural parameters for three different edge conditions. The study reveals that wave reflection decreases with an increase in porosity, and a reverse pattern is found in the case of wave transmission. As the normalized spacing between the barrier and the floating bridge increases, the reflection coefficient follows a periodically oscillatory pattern. Furthermore, it is noticed that regardless of the barrier configurations, the wave reflection increases for an increase in the angle of incidence. It is also found that the surface-piercing barrier is more efficient than the bottom-standing barrier as a wave barrier. Moreover, the results indicate that by placing a porous flexible barrier at an appropriate position, the wave force on the bridge can be reduced significantly.

关键词： flexible and porous barrier floating bridge least-squares approximation porous-effect parameter energy dissipation free surface elevation

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Wave attenuation by a submerged circular porous membrane

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Journal of Ocean Engineering and Science 2022年

作者： Gayathri, R. Khan, Mohamin B M Behera, Harekrushna Tsai, Chia-Cheng Department of Mathematics SRM Institute of Science and Technology Chengalpattu District Kattankulathur Tamil Nadu 603203 India Bachelor Degree Program in Ocean Engineering and Technology National Taiwan Ocean University Keelung 202301 Taiwan Center of Excellence for Ocean Engineering National Taiwan Ocean University Keelung 202301 Taiwan

Wave action over a submerged circular flexible porous membrane is investigated and the impact of porosity in dampening the far-field wave amplitude is examined in a scattering of incoming waves. The unknown potential for the free surface and the membrane-covered regions are obtained by coupling the respective boundary conditions and Darcy's law for permeable structure. The associated boundary value problem is solved using the method of expansions of the eigenfunctions as Fourier-Bessel series. To understand the efficiency of the present study, wave force excitation on the circular membrane, far-field scattering wave amplitude, energy dissipation, and flow distribution are computed and examined. The study shows that on the leeward side of the membrane the wave amplitude reduces drastically. In addition, the submergence depth has a significant impact on wave energy dissipation. This model will be beneficial in developing the mechanism to minimize wave force on coastal structures for a variety of marine operations. In addition, this structure has minimal environmental effects on different coastline processes and can therefore be used in a variety of coastal/ocean applications. © 2022

关键词： Circular membrane Eigenfunction expansion method Flow distribution Plane wave integration porous-effect parameter

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Reduction of hydroelastic response of a flexible floating structure by an annular flexible permeable membrane

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JOURNAL OF ENGINEERING MATHEMATICS 2019年第1期118卷 73-99页

作者： Selvan, Siluvai Antony Behera, Harekrushna Sahoo, Trilochan SRM Inst Sci & Technol Dept Math Kattankulathur Tamil Nadu India IIT Kharagpur Dept Ocean Engn & Naval Architecture Kharagpur 721302 W Bengal India

In the present study, hydroelastic response mitigation of a very large floating circular structure by an annular flexible permeable membrane is studied under the assumption of the linearized theory of water waves and small amplitude structural response. The very large floating structure is modeled based on small amplitude plate theory, while the flexible annular membrane is modeled using the two-dimensional string equation. Darcy's law is used to model wave past the permeable annular membrane. To keep the structures in position, both the floating structures are assumed to be moored on the circular boundaries. The velocity potentials are expanded in terms of the Fourier-Bessel series in the open water, membrane-, and plate-covered regions. The solution of the physical problem is obtained using the matched eigenfunction expansion method along with the orthogonality of the vertical eigenfunctions in the open water region. On the other hand, orthogonal mode-coupling relation, satisfied by the vertical eigenfunctions in the floating flexible plate-covered region, is used when there is no spacing between the outer and the inner structures. The wave forces exerted on the inner and outer structures, deflection of the plate, and flow distribution around the inner plate are analyzed using numerical computations to understand the hydroelastic response of the inner elastic plate in the presence of the outer porous membrane. The effects of various wave and structural parameters such as wavenumber, porous-effect parameter, tensile force, width of the outer membrane, spring constants associated with the mooring joints, and the spacing between the structures are examined. The study reveals that the porous-effect parameter and the width of the annular membrane play an important role in reducing the wave forces on the inner plate. Moreover, due to the reflection and dissipation of a major part of the wave energy concentrating near the free surface, the inner floating structure experi

关键词： Annular porous membrane Circular elastic plate Eigenfunction expansion method Mooring edge porous-effect parameter Plate deflection Wave force

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Fredholm integral equation technique for hydroelastic analysis of a floating flexible porous plate

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EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 2018年 67卷 291-305页

作者： Koley, S. Mondal, R. Sahoo, T. Dhirubhai Ambani Inst Informat & Commun Technol Gandhinagar 382007 India Harbin Inst Technol Shenzhen Grad Sch Inst Turbulence Noise Vibrat Interact & Control Shenzhen Peoples R China Indian Inst Technol Dept Ocean Engn & Naval Architecture Kharagpur 721302 W Bengal India

Oblique surface gravity wave scattering by a floating flexible porous plate is investigated in water of finite and infinite depths under the assumption of small amplitude water wave theory and structural response. Using the Greens function technique, the boundary value problems are converted into a system of Fredholm type integral equations in terms of the velocity potentials and their normal derivatives along the plates which are handled for solutions using Simpsons quadrature formula. Energy relations are derived to check the accuracy of the computed results. Various results of physical interests are computed and analyzed to study the roles of structural flexibility and porosity, wave period and angle of incidence on wave scattering by the plate. Certain results are analyzed to study the effect of edge conditions on the scattering of surface waves by the flexible porous plate. It is observed that depending on the heading angle of the incident waves, with suitable positioning of the plate, tranquility zone can be created by a flexible floating plate. Moreover, the study reveals that a major part of the wave energy can be dissipated with the introduction of structural porosity which will be of immense help in the creation of a tranquility zone for the protection of various marine facilities and infrastructures. (C) 2017 Published by Elsevier Masson SAS.

关键词： Floating elastic plate porous-effect parameter Fredholm integral equation Greens function Wave scattering

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An integro-differential equation approach to study the scattering of water waves by a floating flexible porous plate

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GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS 2018年第5期112卷 345-356页

作者： Koley, Santanu Sahoo, Trilochan Birla Inst Technol & Sci Pilani Dept Math Hyderabad India Indian Inst Technol Kharagpur Dept Ocean Engn & Naval Architecture Kharagpur W Bengal India

In the present manuscript, the hydroelastic response of a flexible porous plate, floating in water of finite as well as infinite depths, is studied under the assumption of a linearized wave-structure interaction theory. Using Green's integral theorem, the associated boundary value problems are converted into integro-differential equations in terms of the plate deflection. To solve the derived integro-differential equations, the plate deflection is approximated as a superposition of the horizontal eigenfunctions in the plate-covered region. As a result, approximate explicit expressions are obtained for the physical quantities of interests such as reflection and transmission coefficients. The accuracy of the present numerical computations are analysed by comparing the results with the standard results available in the literature. It may be noted that the aforementioned physical problem is similar in nature with that of Koley etal. but the solution technique is completely different. As various results associated with the floating flexible porous plate are presented in Koley, Mondal and Sahoo (Eur. J. Mech. B- Fluid., 2018, vol. 67, 291-305) and therefore in this paper, the major emphasis is on the solution technique and only a few results are provided for comparison purpose.

关键词： Floating flexible plate integro-differential equation porous-effect parameter

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effect of bottom topography on wave scattering by multiple porous barriers

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MECCANICA 2018年第4-5期53卷 887-903页

作者： Kaligatla, R. B. Tabssum, S. Sahoo, T. Indian Inst Technol ISM Dhanbad Dept Appl Math Dhanbad 826004 Bihar India Indian Inst Technol Kharagpur Dept Ocean Engn & Naval Architecture Kharagpur 721302 W Bengal India

Scattering of obliquely incident surface gravity waves by multiple porous barriers is studied in the presence of step type varying bottom topography. The bottom bed consists of a finite interval of uneven geometry which is connected by two semi-infinite intervals of uniform water depths. An array of porous barriers are located on water of uniform depth on the lee side of bottom variations. Using small amplitude wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem which is handled for solution using coupled eigenfunction expansion in uniform bottom regions and modified mild-slope equation in varying bottom region. Further, certain jump conditions are used for the conservation of mass flux at slope discontinuities in bottom profile. To understand the effect of variations in bottom topography on wave scattering by multiple porous barriers, physical quantities such as reflection and transmission coefficients, wave forces on the barriers are computed and analyzed for different values of depth ratio, varying bottom parameter, porous-effect parameter, incident wave angle, spacing between the barriers and slope length of varying bottom. In the presence of ripple bottom bed, effect of multiple porous barriers on Bragg scattering is analyzed. Certain drift in Bragg reflection is noticed due to propagation of oblique incident waves over step type ripple beds.

关键词： Multiple porous barriers Mild-slope equation porous-effect parameter Reflection and transmission coefficients Wave scattering

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Scattering of oblique waves by permeable vertical flexible membrane wave barriers

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APPLIED OCEAN RESEARCH 2017年 62卷 156-168页

作者： Koley, S. Sahoo, T. Indian Inst Technol Ropar Dept Math Rupnagar 140001 India Indian Inst Technol Kharagpur Dept Ocean Engn & Naval Architecture Kharagpur 721302 W Bengal India

The interaction of obliquely incident surface gravity waves with a vertical flexible permeable submerged membrane wave barrier is investigated in the context of three-dimensional linear water wave theory. From the general forfnulation of the submerged membrane barrier, the performance of bottom-standing, surface-piercing and fully extended membrane wave barriers are analyzed for various values of wave and structural parameters. The analytic solution of the physical problem is obtained using eigenfunction expansion method and a coupled boundary element-finite difference method has been used to get the numerical solution. In the boundary element method, since the boundary condition on the membrane barrier is not known a priori, the membrane response and velocity potentials are solved simultaneously using appropriate discretization with the help of finite difference scheme. The convergence of the analytic and numerical solution techniques is discussed. The study reveals that for suitable combination of wave and structural parameters, approximately (45-50)% incident wave energy can be dissipated irrespective of membrane barrier configurations. Further, in certain situations, nearly full wave reflection and zero transmission occur for all barrier configurations. The study will be useful in the design of flexible permeable membrane to act as an effective wave barrier for creation of tranquility zone in the marine environment. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Surface gravity waves Flexible membrane porous-effect parameter Eigenfunction expansion method Boundary element method Finite difference method

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Wave Trapping by Dual porous Barriers Near a Wall in the Presence of Bottom Undulation

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Journal of Marine Science and Application 2017年第3期16卷 286-297页

作者： R.B. Kaligatla Manisha T. Sahoo Department of AppliedMathematics Indian Institute of Technology (ISM) Dhanbad Dhanbad 826004 India Department of Ocean Engineering and Naval Architecture Indian Institute of Technology Kharagpur Kharagpur 721302 India

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/infrastructures in coastal environment.

关键词： porous barriers mild-slope equation reflection coefficient wave trapping porous-effect parameter

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