Primary nonlinear damped natural frequency of dielectric composite beam reinforced with graphene platelets (GPLs)

The present study deals with the primary damped natural frequency of dielectric composite beam reinforced with graphene platelet (GPL). The beam is subjected to pre-stress in the longitudinal direction and external electrical loading throughout the beam thickness direction for tuning the frequency characteristics. The material properties of the composites required for structural analysis are determined by effective medium theory (EMT) and rule of mixture. Using Timoshenko beam theory and Hamilton’s principle, the governing equations for damped nonlinear free vibration of the beam are derived and solved numerically by differential quadrature (DQ) and direct iterative methods. The effects of the attributes of the electrical loading and the GPL fillers on the damped free vibration characteristics are investigated. The analysis shows that when the GPL concentration is greater than the percolation threshold, the voltage of the electrical loading and GPL aspect ratio start to play a vital role in the damped vibration. The nonlinear damped frequency of the hinged-hinged (H–H) beam decreases by 83.8% when the voltage increases from 0 to 30 V. It is found that there exist two critical AC (alternating current) frequencies, i.e., approximate 10⁻³ Hz and 10² Hz, around which the primary damped natural frequency has a sudden jump as AC frequency either slightly increases or decreases. The vibration characteristics presented demonstrate the potential of developing smart composite structures whose vibration characteristics can be actively tuned by changing the attributes of the applied electrical loading.