Size-Dependent Free Vibration Of Microbeams Submerged In Fluid

The size-dependent free vibration of microbeams submerged in fluid is presented in this paper based on the modified couple stress theory. Two different cross-section shapes of microbeams are considered, i.e. the circular cross-section and rectangular crosssection. This nonclassical microbeam model is introduced for capturing the size effect of microstructures. In this fluid and structure coupled system, the effect of hydrodynamic loading on microbeams can be expressed by the added mass method. By using Hamilton's principle and differential quadrature (DQ) method, we can derive governing equations of microbeams in fluid, and then rewrite them in the discretized form. The frequencies and mode shapes for microbeams are determined by proposing an iterative method. Numerical examples are given to show the effect of fluid depth, fluid density, length scale parameter, slenderness ratio, boundary condition and cross-section shape on the vibration characteristics.