Yh. Lin et Yk. Tsai, NONLINEAR VIBRATIONS OF TIMOSHENKO PIPES CONVEYING FLUID, International journal of solids and structures, 34(23), 1997, pp. 2945-2956
This paper presents a finite element approach for nonlinear vibration
analysis of Timoshenko pipes conveying fluid. An approach using the co
ncept of fictitious loads to account for the kinematic corrections was
applied to establish the finite element model, without the need to es
tablish the nonlinear-equations of motion. Computation of System respo
nses was carried out by iteratively updating the nodal coordinates unt
il convergence was reached. The formulation and implementation of the
approach were verified first by comparing the analysis results with th
ose available in the literature for the case of both slender and short
beams undergoing static large deformations and the case of flow induc
ed vibration of a slender cantilever pipe with supercritical flow spee
ds. Limit cycle and its associated vibration-amplitude for the flow in
duced vibration problem were discussed. Further analysis was conducted
for assessment of the effects of. flow speed and fluid/pipe mass rati
o on the limit cycle vibration amplitude. The influence of slenderness
ratio on the limit cycle amplitude was also reported. (C) 1997 Elsevi
er Science Ltd.