Dynamics of an Euler Elastica Pipe with Internal Flow of Fluid

The equations of motion for a cantilever Euler elastica pipe are deduced applying a generalized set of Lagrange equations for non-material volumes. Based on an exact planar nonlinear beam theory the strain energy for the pipe is derived. The classical Lagrange terms and the additional terms due to moving mass entering and exiting the system result in a set of nonlinear equations of motion for the cantilever pipe with internal flow. A possible dimensional reduction and comparison to existing works are performed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)