Vibration analysis of conveying fluid pipe via He's variational iteration method

•Variational iteration method is applicable to analysis of pipe conveying fluid.•Critical flow velocity and frequencies of pipe conveying fluid are deserved.•Mode shapes of pipe conveying fluid are shown.•The present method is a more precise one than existing computation method.

In this paper, a recently new semi-analytical method, i.e., He's variational iteration method is developed to apply to free vibration analysis of conveying fluid pipe. The critical flow velocity and frequency of pipe conveying fluid are obtained with considering the various boundary conditions. The results are compared with the ones of different transform method, and prove VIM that has the same precision and efficient with DTM. The mode shapes of cantilevered pipe and both ends with elastic support pipe are shown under different flow velocity.