Sustainable Marine Structures

Fuzzy Finite Difference Analysis of Wave-Induced Vibration in Fixed Offshore Platforms

Suleiman Ibrahim Mohammad

Department of Business Administration, School of Business, Al al‑Bayt University, Mafraq 25113, Jordan; Research Fellow, 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 Almakki

School of Engineering, Architecture and Interior Design, Amity University Dubai, Dubai P.O. Box 345019, United Arab Emirates

Asokan Vasudevan

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

Mohammed El Khider

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

DOI: https://doi.org/10.36956/sms.v8i3.3207

Received: 18 March 2026 | Revised: 6 April 2026 | Accepted: 13 May 2026 | Published Online: 2 July 2026

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Abstract

This study presents a fuzzy finite difference framework for the wave-induced lateral vibration of a fixed offshore platform idealized as an equivalent cantilever. The motivation is that key inputs in offshore response analysis, including hydrodynamic coefficients, structural stiffness, wave height, and damping, are often bounded but not known precisely enough to support a fully probabilistic description. The governing Euler-Bernoulli vibration model is driven by a linearized Morison-type load, and the uncertain quantities , and are represented by triangular fuzzy numbers. Alpha-cut decomposition reduces the fuzzy problem to one with an equivalent family of deterministic corner problems, and an implicit finite difference scheme is used to solve each corner problem. The mesh-converged deterministic first-mode frequency of the representative benchmark is 0.134 Hz, and its time-asymptotic top-displacement amplitude is 37.22 mm. As α decreases from 1 to 0, the fuzzy peak response widens from a precise value at  to an interval [28.06, 47.87] mm at α = 0, of width 19.81 mm. The results provide insight that inertia coefficient , followed by wave height H and elastic modulus E are the most influential variables upon response width. The parametric framework produces various nested fuzzy response sets while ensuring stable mesh-converged solutions, as well as an interpretable uncertainty band, enabling a preliminary serviceability assessment process. The study serves as a simplified benchmark model, and the assumptions, such as equivalent-cantilever idealization and linearisation of drag, are explicitly stated. 

Keywords: Hydrodynamic Uncertainty; Alpha‑Cut Propagation; Morison Loading; Implicit Time Stepping; Interval Response Envelopes; Marine Structural Dynamics; Fuzzy Finite Differences

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