On the vibration of size dependent rotating laminated composite and sandwich microbeams via a transverse shear-normal deformation theory

Abstract

In this paper, the eigenfrequencies of rotating laminated composite (LC) and sandwich microbeams with different boundary conditions (BCs) are studied. The size-dependent variational formulation of the problem is obtained based on the Modified Couple Stress Theory (MCST) by employing a transverse shear-normal deformable beam theory and finite element method (FEM) formulation. The convergence and verification studies of the developed code are carried out and computed results in terms of dimensionless fundamental frequencies (DFFs) are compared with the available ones in the open literature. Various BCs, aspect ratios, fiber orientation angles, thickness to material length scale parameter (MLSP) ratios, core thickness to face layer thickness ratios, dimensionless rotation speeds (DRSs) and hub ratios are employed for the extensive analyses. It is found that the DFFs of the LC microbeams are highly affected by the small size effect accompanying with the orthotropy ratios, DRSs, hub ratios and fiber orientation angles. The effect of the small size on the DFFs of the rotating clamped-clamped LC microbeams is more pronounced than on those of the rotating clamped-free LC microbeams. The hub ratio has a significant effect on the DFFs of the rotating LC microbeams than the rotation speed.