Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory

Within this study, the free vibration behavior of rotating two-directional functionally graded porous sandwich microbeams is studied based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory. The effects of the thickness to material length scale parameter accompanying with the porosity volume fraction coefficient, boundary condition, aspect ratio, hub ratio, dimensionless rotation speed and gradient index on the dimensionless fundamental frequencies of the two-directional functionally graded porous sandwich microbeams are investigated. It is found that the dimensionless fundamental frequencies are significantly affected by the variation of the thickness to material length scale parameter, hub ratio, dimensionless rotation speed and porosity volume fraction coefficient. The normal deformation effect is very important especially while the variations of the dimensionless rotation speed, hub ratio and gradient index are considered. Moreover, the mode shapes of the rotating two-directional functionally graded porous sandwich microbeams are also influenced with respect to the variation of the porosity volume fraction coefficient. As a result, the optimum design of the microstructures accompanying with the lightweight and low-cost objectives can be achieved by controlling the material and porosity distribution through the body of the microstructure.