Modeling and solving for vibration and buckling of circular functionally graded dielectric plates reinforced by graphene platelets considering complex conditions

Abstract

The vibration and bucking behaviors of circular functionally graded (FG) dielectric plates reinforced by graphene platelets (GPL) under external electric fields are studied at the presence of many complex factors such as dielectric effect, pre-stress, gradient slope, imperfect bonding between GPL and matrix material, interface electron tunneling and Maxwell–Wagner-Sillars (MWS) polarization. Based on the effective medium theory and linear rule of mixtures, material properties of the GPL reinforced composites (GPLRC) are calculated. Dynamic differential equations of the circular FG-GPLRC dielectric plates are numerically solved by the differential quadrature method, and natural frequencies and critical loads are obtained. Trans-scale analyses for the influences of the volume fraction, geometric size, gradient distributed pattern and gradient slope on the percolation threshold, permittivity and the vibration or buckling characteristics are provided. Furthermore, variations of the natural frequencies and critical loads with electric field parameters, the pre-stress and thickness of the interphase layer are also discussed. Results show that the natural frequencies and critical loads of the plates can be changed artificially and effectively by adjusting the external electric field, pre-stress and the parameters of GPL. The larger the diameter to thickness ratio of GPL, the bigger the equivalent permittivity and the smaller the percolation threshold. When the volume fractions of GPL are less than the threshold, the mechanical properties dominate the vibration and buckling. However, when the volume fractions are bigger than the threshold, the electrical properties have significant influences. Therefore, higher macro mechanical properties can be obtained by changing the microstructure of the materials.