LAUSR

The dynamic characteristics of imperfect pipes conveying fluid in the pre-buckling and post-buckling states are investigated. In this paper, the novel motion equation of fluid-conveying imperfect pipe supported at both ends is derived by considering the geometric imperfection and the geometric nonlinearity induced by mid-plane stretching. The imperfect configurations are chosen as the first bucked modes of pined–pined and clamped–clamped pipes. The exactly analytical solutions for static response are obtained due to the fluid flow. In the linear vibration analysis, the equation is discretized by the Galerkin method and solved as a linear eigenvalues problem. Excellent agreement is observed between the present solution and the available literature. Compared with the supercritical pitchfork bifurcation of the perfect pipe conveying fluid, the results show that the cusp bifurcation occurs in the imperfect pipe when increasing the flow velocity. In the post-buckling state, there are three equilibrium configurations composed of two asymmetry stable branches and an unstable branch. The critical velocity firstly increases and then decreases when the imperfect amplitude increases. The numerical results indicate that initial imperfect amplitude and flow velocity have a complex influence on the natural frequency of the imperfect pipe. The first natural frequency increases when the initial imperfect amplitude increases. The three branches of the imperfect pipe in the post-buckling state provide more interesting and essential dynamic behaviors.