Strain gradient theory-based vibration analyses for functionally graded microbeams reinforced by GPL

Abstract On the basis of modified strain gradient theory (MSGT), the free vibration of graphene nanoplatelets (GPL) reinforced functionally graded (FG) microbeam on elastic foundation is studied. Firstly, material properties of the composites are calculated by Halpin-Tsai model and linear mixed model. Then, the MSGT and Reddy beam theory are adopted to establish the fundamental equations of the microbeam on the elastic foundation. And the governing differential equations related to the size effect are derived by the Hamiltonian principle and solved by the Navier method. Finally, the influences of the graded distribution, mass fraction, geometric shape of GPL and size effect on the vibration behaviors are discussed in detail. Results show that these parameters have significant influence on the natural frequencies. The methods to improve the natural frequencies of the microbeams are proposed considering the influence of internal microstructure on the overall characteristics. The research results are of great significance to design this kind of micro-nano structures.