Size-dependent vibration analysis of a microbeam in flow based on modified couple stress theory

This paper develops and analyzes a theoretical model for flexural vibrations of microbeams in flow with clamped–clamped ends. Based on a modified couple stress theory and the Hamilton’s principle, the governing equations for three-dimensional vibration of a curved microbeam are derived with the consideration of the fluid force induced by external flow. Meanwhile, as a special case, the reduced equation for a straight microbeam in flow is obtained. This new theoretical model contains a material length scale parameter that can capture the size effect. The differential quadrature method (DQM) is introduced to formulate the discrete forms of the governing equations. Based on the numerical calculations, the effects of several system parameters, i.e. the open angle, the characteristic size of the microbeam and the flow velocity, on the natural frequencies and stability of the system are discussed. The results show that, with a sufficiently high flow velocity, the static buckling instability may occur for both curved and straight microbeams in flow, which should be considered in the design and applications. Furthermore, the size effect on the vibration properties is significant when the characteristic size of the microbeam is comparable to the internal material length scale parameter.