Sustainable Marine Structures

A Fuzzy Legendre-Green Function Method for Hydro-Elastic Wave Attenuation in Flexible Porous Floating Breakwaters

Yogeesh Nijalingappa

Research Fellow, INTI International University, Nilai 71800, Malaysia

Department of Mathematics, Government First Grade College, Tumkur 572102, India

Asokan Vasudevan

Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia

Manchaiah Savithramma Sunitha

Department of Mathematics, Government First Grade College, Tumkur 572102, India

Suleiman Ibrahim Mohammad

Research Fellow, INTI International University, Nilai 71800, Malaysia

Kanchugaranahalli Chandrappa Jagadeesha

Department of Mathematics, Government First Grade College, Tumkur 572102, India

DOI: https://doi.org/10.36956/sms.v8i2.3215

Received: 25 March 2026 | Revised: 6 April 2026 | Accepted: 16 April 2026 | Published: 14 May 2026

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Abstract

The present study forms a compact hydro-elastic benchmark of a flexible porous floating breakwater, with bounded parameter uncertainty. The floating member is represented as a discrete-semicontinuum Euler-Bernoulli beam in the frequency domain, and it interacts with an oscillatory-decay hydrodynamic kernel in the finite-depth approximation. A structural Green function is presented, transforming the governing boundary-value problem into the solution of a Fredholm integral equation of the second kind, which is solved by means of Legendre-Gauss-Lobatto collocation. The impact of uncertainty in flexural rigidity, structural mass, damping and depth ratio, porous dissipation and forcing amplitude is modeled by triangular fuzzy numbers; alpha-cut analysis using vertex evaluation with nesting correction propagates the uncertainty. The benchmark results show a sharp resonance region where the structural response and transmission loss become increasingly sensitive to parameter variation, while the admissible response band is narrow off-resonance. The derived formulation also provides a computationally lightweight framework for joint assessment of wave attenuation and structural demand. This study is mathematically and numerically transparent, computationally light, and easy to extend to many relevant situations. The results discussed in this study also showed that uncertainty is concentrated near the spatial region of maximum structural response and that, for the chosen benchmark, porous dissipation and forcing level are the most influential inputs.

Keywords: Coastal Protection; Spectral Collocation; Nonlocal Hydrodynamic Kernel; Porous Damping; Transmission Loss; Marine Flexural Response; α−cut Propagation

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