Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

Abstract

This article discusses about vibration analysis of single-/three-layered microsandwich Timoshenko beams with porous core and graphene platelet–reinforced composite face sheets under magnetic field and elastic foundation based on the modified strain gradient theory. It is assumed that the material properties of matrix and reinforcement vary in thickness directions. Hamilton’s principle based on the energy approach is used to obtain the governing equations of motions. The equations of motions are solved using a numerical differential quadrature method for various boundary conditions. The obtained results of this study are compared with other previous research studies, and there is a good agreement between them. Moreover, the effects of different parameters such as length-to-thickness ratio, magnetic field, various distributions of graphene platelets and porous beams, and volume fractions of graphene platelets are studied on the dimensionless natural frequencies. In fact, the main idea of this work is combination of structure reinforcement with magnetic field and graphene platelets on the sandwich porous beams at microscale, and the effects of these parameters are developed on the dimensionless natural frequencies of the microbeam. The results of the present study demonstrate that applying magnetic field and increasing its intensity lead to enhance the natural frequency. Also, it is showed that graphene platelet reinforcement with one percent of weight fraction has an effective effect on the increasing dimensionless natural frequencies of the microporous beam. Thus, it can be predicted that graphene platelets can be used instead of nanotubes because they do not have the problem of nanotube accumulation and they are more economical than nanotubes.