Numerical prediction of vortex-induced vibrations of a long flexible cylinder with variable cross-sections

Abstract

Long flexible cylinders with variable cross-sections are extensively used in engineering applications, yet their vortex-induced vibration (VIV) behavior under linear shear flow remains insufficiently investigated. This study proposes a novel semi-analytical method that integrates the Sturm-Liouville Eigenvalues using Theta Matrices (SLEUTH method) with the Generalized Integral Transform Technique (GITT), enabling efficient and highly accurate VIV predictions. This approach addresses the computational challenges of traditional numerical methods while accurately capturing key structural responses including the structural displacement, structural frequency, displacement envelope, and displacement evolution. Validation against existing experimental data and finite element simulations confirm the method's superior accuracy and computational efficiency. Results reveal that variations in cross-section significantly influence VIV behavior. Tapered, waist-shaped, and stepped cylinders exhibit distinct displacement distributions and frequency responses under shear flow conditions. Tapered cylinders experience amplified displacements in regions with increasing flow velocity, waist-shaped cylinders exhibit localized vibration attenuation, and stepped cylinders display abrupt transitions in displacement envelopes at geometric discontinuities. These findings lay a robust theoretical framework for analyzing VIV in variable cross-section structures, providing essential design guidance for mitigating flow-induced vibrations in offshore and marine engineering applications.