Out‑of‑Plane Strain Included Formulation for Free Vibration and Bending Analyses of a Sandwich GPL‑Reinforced Microbeam Based on the MCST

Abstract

Purpose To study free vibration and bending analyses of a sandwich microbeam with a functionally graded (FG) porous core and two polymeric face sheets reinforced with graphene nanoplatelets (GPLs). Methods In this paper, the modifed couple stress theory (MCST) and a quasi-3D trigonometric shear deformation beam theory are employed. The resultant material properties are examined using the rules of micromechanical. The equations derived through energy method are solved by Navier’s method to obtain the natural frequencies and defection of the nanobeam for a simply-supported boundary condition. Results Trueness of the results are justifed through comparison with the new recently published materials. Parametric static and dynamic results are presented for investigating efect of signifcant parameters on the frequencies and defections of the sandwich microbeam, such as porosity parameter, distribution of the pores, the thickness of the core, volume fraction and distribution pattern of the GPLs, thickness-to-length scale parameter, and foundation coefcients. Conclusions The results show that the VA distribution type has the biggest defection and the AV one has the lowest value of static bending.