The influence of size effect on flapwise vibration of rotating microbeams

This paper deals with flapwise frequency analysis of rotating microbeams connected to a hub by incorporating size effect phenomena. Hamilton principle in conjunction with first shear deformation beam theory and symmetric-deviatoric couple stress theory (the modified version of couple stress theory developed by Yang et al.) is used to derive governing equations and corresponding boundary conditions. The classical first shear deformable beam model and also size-dependent Euler-Bernoulli beam model can be recovered from the present model. To examine free vibration behavior of the rotating microbeam, finite element formulation is developed by applying the corresponding weak form equations. Finally, the influence of size effect on free flapwise vibration behavior of a rotating cantilever microbeam is investigated by considering different parameters i.e., dimensionless material length scale parameter, dimensionless angular velocity, dimensionless radius of hub and slender ratio.