Sustainable Marine Structures

A Green Function Collocation Method for Fuzzy Hydroelastic Response of Floating Beams

Suleiman Ibrahim Mohammad

Department of Business Administration, School of Business, Al al-Bayt University, Mafraq 25113, Jordan

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

Yogeesh Nijalingappa

Research Fellow, INTI International University, Nilai 71800, Malaysia

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

Mohammed El Khider

Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai P.O. Box 14143, United Arab Emirates

Asokan Vasudevan

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

Shashikumar Honnavalli Channabasavaiah

Department of Mathematics, Government First Grade College, Tiptur 572201, Karnataka, India

DOI: https://doi.org/10.36956/sms.v8i2.3208

Received: 18 March 2026; Revised: 6 April 2026; Accepted: 17 April 2026 | Published: 22 May 2026

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Abstract

Hydroelastic deformation is a key response in large, flexible floating marine structures, and uncertainty in structural and hydrodynamic properties can strongly affect predicted amplitudes, especially near resonance. This study presents a green function collocation method for the fuzzy hydroelastic analysis of a floating beam under bounded uncertainty that is not well described by probability. A frequency-domain nonlocal beam model with finite-depth hydrodynamic coupling is developed, and the structural green function is used to transform the governing equation into a Fredholm integral equation of the second kind, which is then discretized using Chebyshev collocation. Triangle fuzzy numbers of uncertain flexural rigidity, structural mass, damping, depth ratio and forcing amplitude are modeled and propagated via alpha-cut reconstruction. For the deterministic benchmark, the method picks up a sharp resonance peak at  = 3.1244 (denotes the nondimensional frequency at resonance). The collocation solution converges monotonically, with a rate of practical error decrease on the order of seconds; the final crisp value for midspan amplitude when at resonance is 10.668. Under fuzzy uncertainty, the midspan-amplitude interval expands from the crisp value at α = 1 to [0.6127, 11.7440] at α = 0. Flexural rigidity and structural mass drive the spread; damping and forcing amplitude are secondary drivers, and depth ratio has only a weak effect over this benchmark range. The results demonstrate method stability, efficiency and applicability in early uncertainty-aware design assessment.

Keywords: Hydroelasticity; Chebyshev Nodes; Wave-Structure Interaction; Alpha-Cut Propagation; Fredholm Integral Equation; Nonlocal Hydrodynamic Kernel; Marine Flexural Dynamics

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