Nonlinear vibration analysis of cracked pipe conveying fluid under primary and superharmonic resonances

The nonlinear vibration response of the pipe conveying fluid with a breathing transverse crack, under primary and secondary excitations is investigated. Attention is concentrated on the superharmonic resonance which is the most sensitive phenomena for small crack detection. The crack is modeled with a transverse partial cut of the pipe wall thickness. The equivalent bending stiffness of the cracked pipe is derived based on an energy method and the breathing crack model is used to simulate the transition state between the fully open and the fully closed states. Based on Von Karman's nonlinear geometric assumption and Euler-Bernoulli beam theory, the nonlinear geometric partial differential equations due to stretching effect, have been derived. The fractional viscoelastic model and the plug flow assumptions are used to model the damping and fluid flow. The coupled nonlinear partial differential equations are reduced into nonlinear ordinary differential equations by the Galerkin method. The method of multiple scales is adopted to analyze steady-state solutions for the primary and superharmonic resonances. A parametric sensitivity analysis is carried out and the effects of different parameters, namely the geometry and location of the crack, nonlinear geometric parameter, fluid flow velocity, mass ratio, fractional derivative order and retardation time on the frequency-response solution are examined. In general, this paper shows that the superharmonic response amplitude measurement is useful tool for damage detection of pipes conveying fluid in the early stages.