Static and dynamic properties of functionally graded materials sandwich microbeams based on sinusoidal shear deformation theory

The static bending and free vibration of functionally graded (FG) sandwich microbeams were investigated based on the modified couple stress theory (MCST) and the sinusoidal shear deformation theory. The two types of FG sandwich microbeams were taken into consideration. Governing equations were derived by using the Hamilton' principle. Analytical solutions of bending and vibration with simply supported boundary condition were obtained in the basis of the Navier's solution procedure. The results with general boundary conditions were obtained by using the Ritz method. The numerical results demonstrate that the static and dynamic behavior of FG sandwich microbeams is size-dependent and affected by the microbeam's nondimensional thickness, FG index, the ratio of length to thickness and the structure type. This study may be helpful for the design and performance optimization of the FG sandwich structures.