Effect of linearly varying normal force upon the nonlinear modal analysis of slender beams

An improved solution to the nonlinear normal modes of a slender beam, subjected to a linearly varying normal force and end thrust, is determined, by means of an extended method of multiple time and space scales; The nonlinear free vibrations of a straight offshore riser is considered as an example. The vibration frequency of a nonlinear mode is not constant along the riser: it is seen to depend on the cross-section depth and on the vibration amplitude, thus explaining the onset of longitudinal travelling waves.

File: download