Three-dimensional dynamics of curved pipes conveying fluid

The paper presents a model describing flow-induced 3D motions of a pipe. The Timoshenko-type model is adopted, accounting for geometric nonlinearities. The state of static equilibrium is governed by twelve nonlinear ordinary differential equations and the boundary problem is solved by numerical methods. Flow-induced pipe vibrations are governed by a system of six partial differential equations with coefficient terms (coefficients) depending on static solutions. The calculation procedure relies on the Galerkin approach with a spline function as a shape function. The pipe shape is defined by parametric equations. Model and the adopted method of analysis are verified through comparing research data provided by other authors. The influence of fluid flow velocity on natural frequencies and vibration modes is analysed for pipes with varied curvature, taking into account extension of the pipe centreline. •The model describing 3D spatial vibrations of the curved pipes is proposed.•The model is general and well applicable to analyses of a wide variety of systems.•The pipe shape is defined by parametric equations.•The influence of flow rate on natural frequencies and vibration modes is investigated.•Pipes of various shapes curved in planar and 3D space are examined.