Non-linear dynamics of supported pipe conveying pulsating fluid-II. Combination resonance

Abstract

In this paper the work presented in [N. Sri Namchchivaya, Int. J. Non-linear Mech. 24, 185-196 (1989)] is extended to study the non-linear behavior of supported pipes conveying pulsating fluid in the presence of combination resonance. The method of averaging is used to obtain a set of autonomous equations. It is found that the trivial solution of the averaged equation loses stability through a Hopf bifurcation giving rise to a periodic solution. Explicit results for the bifurcating solutions are obtained locally and globally. In addition a numerical scheme is also used to verify these results. It is found that various results obtained using different techniques agree in their common regions of validity. Numerical values of these results are evaluated for pinned-pinned and clamped-clamped pipes. © 1989.