Journal ArticleDOI

# Effects of flexible bed on oblique wave interaction with multiple surface-piercing porous barriers

01 Apr 2021-Zeitschrift für Angewandte Mathematik und Physik (Springer International Publishing)-Vol. 72, Iss: 2, pp 1-19
TL;DR: In this paper, a flexible base surface is modelled as a thin elastic plate under the acceptance of Euler-Bernoulli beam equation, and four Fredholm-type integral equations are obtained from the boundary value problem.
Abstract: Within the framework of linearised theory of water waves, a model of oblique wave scattering by obstacles in the form of thin multiple surface-piercing porous barriers having non-uniform porosity is analysed. Herein, we consider a flexible base in an ocean of uniform finite depth. The flexible base surface is modelled as a thin elastic plate under the acceptance of Euler–Bernoulli beam equation. With the aid of eigenfunction expansion method along with mode-coupling relations, four Fredholm-type integral equations are obtained from the boundary value problem. The multi-term Galerkin approximations in terms of Chebychev polynomials multiplied by suitable weight functions are used for solving those integral equations. Analytic solutions for different hydrodynamic quantities (viz. reflection coefficients, transmission coefficients, dissipated wave energy and non-dimensional wave force) are determined, and those quantities are displayed graphically for various values of the dimensionless parameters. It is observed from the graphical representations that the permeability of the barriers and thickness of the bottom surface play a crucial role in modelling of efficient breakwaters.
##### Citations
More filters
Journal ArticleDOI
TL;DR: In this article, an interface-piercing structure is considered with the bottom possessing elasticity and the influence of porous parameters of the structure on attenuation of waves in both surface and interfacial modes for a two-layer fluid flow.

5 citations

Journal ArticleDOI
TL;DR: In this paper , the authors investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preassumption of its dynamic behavior.
Abstract: This work investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preassumption of its dynamic behavior. The two sheets were assumed to be made of the same material and under different tensions, and both penetrated into the water depth partially with unequal drafts. The viscoelastic behavior of the sheet material, which accounts for its elastic deformation and internal energy dissipation, is represented by the Voigt model. Using the eigenfunction expansion and least square determination, analytical solutions were obtained for the dual-barrier system, including the asymptotic case of a single sheet when the second sheet draft approaches zero. Subsequently, the effects of hydroelastic regimes and viscoelasticity were examined. With the single-sheet system, the wave transmission decreases as the tensioned sheet shifts from platelike to membranelike, and its material has higher internal energy dissipation (i.e., viscosity). When the size of the bottom opening increases to a gap ratio larger than ∼0.6, however, the wave transmission becomes dominated by the diffraction through the gap, and the influence of sheet material characteristics is no longer significant. With the double-sheet system, the results show that the performance of the wave barrier improves significantly by the presence of the second sheet, even with a small draft. Complex resonating patterns can be observed with increase in sheet spacing for the dual-barrier system, which reduces the wave transmission. The presence of viscosity of the double-sheet system dampens the resonance, but also reduces the wave transmission by itself through the viscous dissipation of the incident wave energy.

3 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth.
Abstract: This work investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preas...

3 citations

Journal ArticleDOI

1 citations

Journal ArticleDOI
TL;DR: In this paper , the use of submerged dual poroviscoelastic barriers with finite depth enclosing a floating compliant platform that supports utility systems, such as a solar photovoltaic system, on top is investigated as a protection measure against surface wave action.
Abstract: In this study, the use of submerged dual poroviscoelastic barriers with finite depth enclosing a floating compliant platform that supports utility systems, such as a solar photovoltaic system, on top is investigated as a protection measure against surface wave action. An analytical analysis of the wave interaction with the barrier-platform configuration is performed using eigenfunction expansion with least square approximation that takes full account of the hydroelastic behavior of the barriers. The results show that the platform displacement decreases as the barrier hydroelastic regime shifts from plate-like to membrane-like with increasing tension. In addition, a longer barrier at the incident front side of the platform yields better performance than an equal length on both sides given the same total barrier dimension. An increase in the porosity of the barriers reduces the displacement and wave loading on the barriers but leads to simultaneous higher wave transmission and larger platform displacement. The higher transmission is reduced by the internal dissipation properties of the barrier material. Overall, the dual barriers with sufficient length and appropriate poroviscoelastic properties can significantly improve the stability of the floating platform, and its performance can be tuned through varying the hydroelastic regimes and barrier-length combinations.

1 citations

##### References
More filters
Journal ArticleDOI
29 Jan 1972
TL;DR: In this article, an approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking, and experimental and theoretical results are compared and evaluated.
Abstract: A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

477 citations

Journal ArticleDOI
TL;DR: In this article, a porous wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate, and analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker.
Abstract: A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

277 citations

Journal ArticleDOI
Huaxiang Cai
TL;DR: In this article, an Iterative Learning Control (ILC) method with Extended State Observer (ESO) is proposed to enhance the tracking precision of the telescope, which can find an ideal control signal by the process of iterative learning.
Abstract: An Iterative Learning Control (ILC) method with Extended State Observer (ESO) is proposed to enhance the tracking precision of telescope. Telescope systems usually suffer some uncertain nonlinear disturbances, such as nonlinear friction and unknown disturbances. Thereby, to ensure the tracking precision, the ESO which can estimate system states (including parts of uncertain nonlinear disturbances) is introduced. The nonlinear system is converted to an approximate linear system by making use of the ESO. Besides, to make further improvement on the tracking precision, we make use of the ILC method which can find an ideal control signal by the process of iterative learning. Furthermore, this control method theoretically guarantees a prescribed tracking performance and final tracking accuracy. Finally, a few comparative experimental results show that the proposed control method has excellent performance for reducing the tracking error of telescope system.

115 citations

Journal ArticleDOI
TL;DR: Linear potential theory is applied to the analysis of wave motion through a two-layer porous structure for special cases, the characteristics of waves in nondissipative, weakly, as well as strongly as mentioned in this paper.
Abstract: Linear potential theory is applied to the analysis of wave motion through a twolayer porous structure For special cases, the characteristics of waves in nondissipative, weakly, as well as strongly

106 citations

Journal ArticleDOI
TL;DR: In this paper, the two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory.
Abstract: The two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory. Applying the method of eigenfunction expansion, these boundary value problems are converted to certain dual series relations. Solutions to these relations are then obtained by a suitable application of the least squares method. For the scattering problem, four different basic configurations of the barriers are investigated, namely, (I) a surface-piercing barrier, (II) a bottom-standing barrier, (III) a totally submerged barrier, and (IV) a barrier with a gap. The performance of these types of barriers as a breakwater are examined by studying the variation of their reflection and transmission coefficients, hydrodynamic forces and moments for different values of the porous effect parameter defined by Chwang [J. Fluid Mech. 132, 395–406 (1983)], or the Chwang parameter. For the radiation problem, three types of wavemakers, which resemble types (I), (II), and (III) of the above-mentioned configuration, are analyzed. The dependence of the amplitude to stroke ratio on other parameters is also investigated to study the features of these wavemakers.

90 citations