Geometrically exact equation of motion for large-amplitude oscillation of cantilevered pipe conveying fluid

摘要: Theoretical modeling and dynamic analysis of cantilevered pipes conveying fluid are presented with particular attention to geometric nonlinearities in the case large-amplitude oscillations. To derive a new version nonlinear equation motion, rotation angle centerline pipe is utilized as generalized coordinate describe motion pipe. By using variational operations on energies system respect either lateral displacement or centerline, two kinds equations cantilever derived first based Hamilton’s principle. It interesting that these governing geometrically exact, different-looking but essentially equivalent. With aid Taylor expansion, one newly developed can be degenerated into previous Taylor-expansion-based expressed form displacement. Then, proposed linearized determine stability system. Finally, analyses conducted current exact model. shown would undergo limit-cycle oscillation after flutter instability induced by internal flow. As expected, quantitative agreement between model achieved when amplitude relatively small. However, remarkable difference results amplitudes predicted models occur for The main reason model, high-order have been neglected applying thus yielding some deviation oscillations generated. Consequently, more reliable fluid.