Vibration analysis of a fluid-conveying curved pipe with an arbitrary undeformed configuration

A dynamic model of an extensible fluid-conveying curved pipe with an arbitrary undeformed configuration is established in a curvilinear coordinate system based on differential geometry, equilibrium equations and constitutive relations. Velocity and acceleration vectors of an arbitrary point of fluid on the centroid line of the pipe under the arbitrary undeformed configuration are obtained. The differential quadrature method is applied to discretize the physical model in the spatial domain and a set of differential-algebraic equations are obtained. A partitioned matrix method is employed to obtain natural frequencies of the fluid-conveying curved pipe and its critical velocities. A parametric study is conducted to investigate the dynamics of different fluid-conveying curved pipes. Numerical results show that the dynamics of a pipe is significantly influenced by its undeformed configuration. It is found that there are ranges of span arc angles within which the first critical velocities of arc-type pipes with different initial geometrical imperfections have dramatic changes.