Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory

Abstract

In this paper, a nonlinear theoretical model for three-dimensional vibration analysis of curved microtubes conveying fluid with clamped–clamped ends is developed and analyzed based on a modified couple stress theory and the Hamilton’s principle. This new theoretical model contains a material length scale parameter that can capture the size effect. In-plane and out-of-plane bending motions, axial motion and twist angle of the microtube are considered in the proposed model. The Lagrange nonlinear axial strain is adopted to obtain the static deformation induced by internal fluid flow. The derived equations of motion are discretized through the Galerkin method. Linearized equations around the static deformation are obtained from the discretized equations, and then the evolution of in-plane and out-of-plane natural frequencies for the curved microtube with various values of flow velocity and material length scale parameter is investigated. The results show that size effect on the vibration properties is significant when the characteristic size of the microtube is comparable to the internal material length scale parameter, and no instabilities are possible for curved microtubes if the nonlinear axial deformation is considered. Therefore, both the size effect and the axial nonlinearity have to be incorporated in the design of curved microscale beam/tube devices and systems.