Nonlinear dynamics of pipes composed of Neo-Hookean hyperelastic material conveying fluid within a uniform external cross flow

Abstract

This study establishes the vibration equation for hyperelastic pipes conveying fluid, particularly focusing on scenarios where vortex-induced vibrations (VIVs) occur, incorporating both von Kármán geometric nonlinearity and Neo-Hookean hyperelastic constitutive model. In modelling procedure, slender pipe is represented as Euler-Bernoulli beam with simply supported ends. To resolve the governing equations of hyperelastic pipes, Galerkin's method together with direct numerical integration are utilized. Appropriate Galerkin's truncation number is determined through calculations, which validates the correctness of the computational approach adopted in this paper. Furthermore, this study examines the impact of various nonlinear terms induced by geometric and material nonlinearities on VIVs responses of pipes. Variations in dynamic behaviors of hyperelastic pipes under various parameters, specifically differing hyperelastic parameters and internal fluid velocities are thoroughly analyzed. Results demonstrate that a rise in internal fluid velocity significantly enhances the nonlinear characteristics exhibited by the pipe and advances the jumping phenomena. Conversely, an increase in hyperelastic parameters delays the onset of jumping phenomena. Notably, a comparative analysis between Neo-Hookean hyperelastic model and linearelastic model on dynamic response is performed, revealing that hyperelastic pipes tend to slightly advance the occurrence of jumping phenomena.