Nonlinear vibration analysis of fluid-conveying microtubes

Non-classical beam theory is employed to study higher modes of free vibration of a microtube conveying fluid. The modified couple stress theory is utilized to model the size-dependent vibration of the microtube structure. It is proposed that the midplane stretching of the microtube needs to be taken into account, and subsequently, the nonlinear partial differential equation of motion in a non-dimensional form has been derived. Three modes of vibration are considered in this study, and the Galerkin procedure is utilized to obtain the nonlinear equations of motion. Analytical expressions for the nonlinear frequencies are developed, and the time responses of the structural model employing the variational iteration method are presented. Results obtained from the analytical procedure were compared with those computed by using numerical method, and close agreements are observed. A parametric sensitivity study is carried out to evaluate the performance and the accuracy of the proposed analytical method from an engineering application point of view.