Incremental harmonic balance method (IHBM) is applied to geometrically nonl
inear vibration analysis of a simply supported pipe conveying fluid. the ma
terial of which is viscoelastic of the Kelvin- Voigt type. Some unstable ph
enomena - the appearance of the peak or jumps in the pipe's amplitude frequ
ency curves, which are considered to be of importance to this kind of struc
ture, are presented in the numerical results, and the influence of several
parameters of the system on the dynamic characteristic of the pipe are also
studied. It is believed that this is the first attempt to search for the p
eriodic solution of the pipe and its intrinsic property with such a method.