On size-dependent lead-lag vibration of rotating microcantilevers

In the current study, flexural frequency characteristics of rotating microcantilevers due to lead-lag vibration (vibration in the plane of rotating axis) is investigated by implementation of modified couple stress theory. This higher-order elasticity theory interprets the size-dependent mechanical behavior of microstructures by employing only one material length scale parameter besides two Lamé parameters. The coupled stretching-bending equations and related boundary conditions are presented based on both Euler–Bernoulli and Timoshenko beam theories. The two-node beam elements are developed to evaluate the lead-lag vibration characteristics of rotating microcantilevers. The achieved results indicate that the flexural frequencies have an ascending trend with respect to the size-dependency. Moreover, it is found that by increasing the angular velocity and hub radius, the influence of the size-dependency on flexural frequencies lessens. The effect of size-dependent shear deformation on flexural frequencies is examined by comparison of the results obtained via Euler–Bernoulli beam model with those resulted from the Timoshenko beam model. Finally, it is indicated that the divergence instability predicted via linear approach is not correct for both macro and micro scales.