Flapwise vibration analysis of rotating composite laminated Timoshenko microbeams with geometric imperfection based on a re-modified couple stress theory and isogeometric analysis

This paper makes the first attempt to establish a size-dependent finite element formulation by combining isogeometric analysis and a re-modified couple stress theory (RMCST) for anisotropic elasticity. The flapwise vibration of rotation composite microbeam with geometrical imperfection connected to a hub is explored. This paper employs the NURBS function as the basis function to describe the geometry and overcomes the inherent difficulty of constructing higher order continuous displacement function for modified couple stress theory based finite element formulation. Besides the angular velocity, slender ratio, scale parameter, and maximum imperfection amplitude, the effect of ply angle on the flapwise vibration of rotation composite microbeam is investigated in this paper for the first time. This investigation demonstrates that we can control the natural frequencies of rotating beam by designing composite laminates in different stacking sequences.