Free Vibration Analysis of Rotating Microbeams Based on the Modified Couple Stress Theory

Free vibration analysis of rotating microbeams including the size effects are presented in this paper. The formulation is based on the Modified Couple Stress theory. According to the Euler-Bernoulli beam model the shear deformation is neglected. The Hamilton s principle is applied to the strain and kinetic energies relations to derive the equations of motion. The Galerkin discretization approach is implemented to determine the natural frequencies. Validation of the results is confirmed via comparison with the existing results in the literature. The effects of mass moment of inertia, rotation speed, Poisson s ratio and the beam thickness to the material length scale parameter ratio are also investigated. The results illustrate that in low to moderate beam thickness to material length scale parameter ratio, the classical theory delivers quite different flapping frequencies while in high ratios the classical theory results converge to the modified couple stress theory. In contrast, the axial frequencies are not affected by the size effects. In addition, the mass moment of inertia has a softening effect on the natural flapping frequencies, and it plays an important role for determination of the flapping natural frequencies, especially in the higher modes. Finally, Poisson s ratio has a softening effect on the predicted flapping frequencies by the modified couple stress theory.