Numerical study on nonlinear vibration of FG-GNPRC circular membrane with dielectric properties

Abstract

Dielectric elastomer membrane has been applied in a wide variety of engineering fields for their excellent dynamic performances. Functionally graded graphene nanoplatelet-reinforced composite (FG-GNPRC) shows great potential for developing high-performance and multifunctional structures. In this work, the damped nonlinear vibration of the FG-GNPRC dielectric membrane is investigated. The effects of damping and dielectric properties are considered in terms of energy while deriving governing equations. Taylor series expansion and differential quadrature together with direct iterative methods are used to discretize and numerically solve the obtained governing equations. The developed model and numerical solution are verified by comparing present results to existing studies. The influences of functionally graded distribution, damping, stretching ratio, dimensions of the membrane, and the attributes of the electrical field and GNP fillers on the nonlinear vibration of the structure are comprehensively investigated. It is found that compared to a uniform distribution, the membrane with functional distribution of GNP demonstrates exhibits more robust performances. The membrane with a smaller thickness-to-radius ratio is more sensitive to the external electrical field. In addition, the direct current voltage is evidenced to have a more significant effect on the nonlinear vibration when the membrane is subject to a relatively small stretching ratio. The present work suggests that the structural behavior of the FG-GNPRC membrane can be actively adjusted by varying the stretching ratio and the properties of the electrical field and the GNP filler. HIGHLIGHTS Effects of damping and dielectric properties are considered for structural behavior in terms of energy. Taylor series expansion and differential quadrature methods are combined to solve governing equations. Two transition regions in frequency ratio are identified due to AC frequency-facilitated polarization and electron tunneling. The effect of the electric field on nonlinear vibration can be regulated by varying the stretching ratio.