Nonlinear free vibration of graphene platelets (GPLs)/polymer dielectric beam

Nonlinear free vibration of graphene platelets (GPLs) reinforced dielectric composite beam subjected to electrical field is analysed. Effective medium theory is adopted to approximate the overall Young's modulus and dielectric permittivity of the GPLs reinforced composite. The Poisson's ratio and mass density of the composites are estimated by rule of mixture. Based on Timoshenko beam theory, governing equations for beam vibration are established by using Hamilton's principle and nonlinear von Kármán strain-displacement relationship. Numerical solution to the governing equations is obtained through differential quadrature method. The effects of GPL concentration and size, and the electrical voltage and AC (alternating current) frequency upon the nonlinear vibration of the GPL reinforced composite beam are investigated. The results demonstrate that there exists a threshold for GPL weight fraction in the polymer matrix, above which the electrical field plays a dominant role on the vibration behaviours. Increasing the voltage of the electrical field will enhance the ratio of nonlinear frequency to linear frequency. A transition region for the AC frequency is observed, within which the vibration characteristics varies dramatically. The analysis conducted in present work is envisaged to provide guidelines for designing GPL reinforced smart composites and structures