Multi-harmonic resonance of pipes conveying fluid with pulsating flow

The parametric excitation analysis of pipes conveying pulsating fluid usually focuses on the principal parametric resonance. In this paper, the principal parametric resonance and the combination resonance under parametric excitation are compared for the first time. A dynamic model of a fluid-conveying pipe with elastic torsional constraints at both ends is established. The nonlinear partial differential-integral equation is derived for governing the transverse vibration. The natural frequencies and modes of pipe are obtained. Moreover, the analytical solutions of stable region and nonlinear amplitude-frequency responses for three kinds of parametric resonances are derived. Then, the analytical results are verified numerically. The results show that there is no differential-type combination parametric resonance for pipes supported at both ends. Increasing material damping or torsional stiffness and decreasing mean velocity can increase the stable region of the pipe. However, it is interesting to note that when combination parametric resonance occurs between symmetric and antisymmetric modes, the effect of mean velocity on stability is reduced. In addition, more than one form of resonance occurs in some regions. The sum-type combination resonance is easier to be excited than the principal parametric resonance. Among them, the combination of first-fourth mode is the most sensitive to the torsional boundary, and its response is the largest. In summary, this paper demonstrates that the combination parametric resonance, which has not been researched deeply yet, can be more destructive than the principal parametric resonance.