Nonlinear dynamics of cantilevered hyperelastic pipes conveying fluid: Comparative study of linearelasticity and hyperelasticity

Abstract

In light of the softness and lightweight characteristics, hyperelastic pipes are prone to large deformation. Intending to provide accurate predictions of their large deformation vibrations, the present study aims to establish a rotation-angle-based geometrically exact model for cantilevered pipes conveying fluid composed of hyperelastic materials. Additionally, given the presence of nonlinear geometric relations, it is imperative to assess the role of hyperelasticity in the nonlinear dynamics of fluid-conveying pipes in comparison to linearelastic pipes. The modeling process integrates the Mooney-Rivlin hyperelastic model with a geometrically exact description of the pipe. And the final governing equation is developed through energy analysis and the extended Hamilton's principle. Subsequently, Galerkin's method and the finite difference method are employed to address the governing equation. Following the verification of the proposed model, parametric studies are conducted in the form of planar oscillation diagrams, time histories, phase trajectories, and bifurcation diagrams. The findings of the present study highlight three critical insights. Firstly, the hyperelastic model introduces numerous complicated nonlinear terms as function of the rotation angle with high-order nonlinearity. In the present study, at least fifth-order nonlinear terms should be preserved to adequately predict large deformation vibrations. Secondly, the Mooney-Rivlin hyperelastic model imparts a hardening effect in comparison to the linearelastic model, significantly reducing vibration amplitudes. Lastly, the third-order approximate model is demonstrated to be inadequate in predicting large deformation vibrations at high flow velocity, as it contains the approximation on not only the geometric description but the hyperelasticity-related terms.