Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation

In this study, fluid conveying continuous media was considered as micro beam. Unlike the classical beam theory, the effects of shear stress on micro-structure's dynamic behavior not negligible. Therefore, modified couple stress theory (MCST) were used to see the effects of being micro-sized. By using Hamilton's principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Micro beam was considered as resting on an elastic foundation. The obtained equations of motion were became independence from material and geometric structure by nondimensionalization. Approximate solutions of the system were achieved with using the multiple time scales method (a perturbation method). The effects of micro-structure, spring constant, the occupancy rate of micro beam, the fluid velocity on natural frequency and solutions were researched. MCST compared with classical beam theory and showed that beam models that based on classical beam theory are not capable of describing the size effects. Comparisons of classical beam theory and MCST were showed in graphics and these graphics also proved that obtained mathematical model suitable for describe the behavior of normal sized beams.