Coupled dynamic instability of graphene platelet-reinforced dielectric porous arches under electromechanical loading

Graphene platelet-reinforced dielectric porous (GPLRDP) arches are a kind of multifunctional structures, which can be used to design various dielectric resonators and soft robotic components. This work studies the coupled dynamic instability of GPLRDP arches under electromechanical loading. It is assumed that the presence of voids is uniformly distributed in the arch structure, while graphene platelets (GPLs) are uniformly dispersed inside the skeleton of such voids. The effective medium theory (EMT) is used to determine the effective dielectric permittivity and Young's modulus of such structures. Based on the Hamilton principle, the governing equations of this problem are formulated. The differential quadrature method (DQM) and the Bolotin method are then used for solving the arch system to identify the coupled dynamic instability region. In this study, we observe the coupling effect of parametric and forced resonance phenomena. A series of numerical experiments are also carried out to examine the influence of porosities, GPL weight fractions, boundary conditions, and electrical voltage levels on the critical excitation frequency and coupled dynamic instability behavior of GPLRDP arches. It is found that the coupled dynamic instability region becomes wider and shifts to low frequency as the effect of porosity increases. When the signal amplitude of AC frequency is within a certain range, there is an abrupt increase of the critical excitation frequency under a high level of DC voltage. The numerical results of this work demonstrate that the location and size of the coupled dynamic instability region can be actively controlled by adjusting the material and structural parameters.