Variational Principles of Nano Laminated Composite Plates with Flexoelectric Effect

Flexoelectric effect is strengthened in dielectrics at nanoscale so that it could not be neglected. In this work, a laminated composite plate with flexoelectric core and two coverings of CNTRCs is modeled. The variational principles of the plate with generalized supporting conditions are derived considering both the flexoelectricity of the piezoelectric core and the reinforcement of the CNTRCs. According to it, the governing equation and boundary conditions with any supporting types are obtained. Then the analytical solutions to the displacements and resonant frequencies of the plate with two different boundary conditions for free vibration are given. The numerical results prove that the flexoelectric effect relies on the scale seriously. Moreover, the CNTRCs coverings can improve the bending stiffness of the whole plate. Therefore, the bending responses such as resonant frequency and bending deflection can be adjusted and optimized by changing the ratio of the CNTs to the matrix. It’s hopeful to provide the theoretical basis of numerical calculation of electronic devices with laminated structures at nanoscale.