Nonlinear vibrations of Timoshenko pipes conveying fluid

This paper presents a finite element approach for nonlinear vibration analysis of Timoshenko pipes conveying fluid. An approach using the concept of fictitious loads to account for the kinematic corrections was applied to establish the finite element model, without the need to establish the nonlinear equations of motion. Computation of system responses was carried out by iteratively updating the nodal coordinates until convergence was reached. The formulation and implementation of the approach were verified first by comparing the analysis results with those available in the literature for the case of both slender and short beams undergoing static large deformations and the case of flow induced vibration of a slender cantilever pipe with supercritical flow speeds. Limit cycle and its associated vibration amplitude for the flow induced vibration problem were discussed. Further analysis was conducted for assessment of the effects of flow speed and fluid/pipe mass ratio on the limit cycle vibration amplitude. The influence of slenderness ratio on the limit cycle amplitude was also reported. © 1997 Elsevier Science Ltd