Dynamic analysis of electrically prestressed highly aligned graphene-reinforced dielectric porous arches under large deformation

Dielectric materials offer extensive applications in mechanical and aerospace engineering due to their lightweight, flexibility, and design adaptability. When exposed to an electric field, dielectric arch structures are susceptible to large deformations, as the induced stress and deformation can lead to nonlinear dynamic behavior. This research investigates the linear and nonlinear free vibrations of electrically prestressed highly aligned graphene-reinforced dielectric porous (HA-GPLRDP) arches, taking into account electrically induced stress and large deformation. The use of highly aligned graphene platelets (GPLs) aims to enhance the dielectric performance of composites. The effective material properties of HA-GPLRDP composites, including Young's modulus and dielectric permittivity, are obtained by a two-scale effective medium theory (EMT). Using the full and incremental forms of nonlinear strains, the governing equations are derived to calculate the natural frequencies of electrically prestressed HA-GPLRDP arches under large deformation, as well as their nonlinear vibration responses. This study also involves comprehensive numerical investigations to examine the influence of the electric field, maximum distribution angle, porosity, and GPLs weight fraction. This work reveals that the symmetric and antisymmetric mode frequencies of the arch respond differently to increasing electrical voltage. In addition, it has been noted that HA-GPLRDP arches with higher porosity exhibit more pronounced nonlinear vibration at lower electrical voltage and higher AC frequency.