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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.

This research investigates the free vibration of a rotating annular microplate under the flexoelectric effect. Initially, the Kirchhoff plate theory assumptions are used to express the displacement fields. After considering the displacement field, strains and their gradients are derived and substituted into the electric enthalpy and kinetic energy expressions. Subsequently, by applying Hamilton’s principle to the aforementioned equations, the electric and mechanical equations are computed. To derive the equations of motion, initially, the polarization vectors and their gradients are derived from the electric equations and associated boundary conditions. Subsequently, these are incorporated into the mechanical equations, which also encompass electric components. It is notable that by removing the time-dependent terms from the in-plane equations of motion, the static displacement due to rotation at each speed is obtained. After deriving the equations of motion and boundary conditions, these equations are non-dimensionalized using non-dimensionalizing relations. In the next step, Hamilton’s principle is used to discretize the equations and boundary conditions. Consequently, by applying the generalized differential quadrature method and extracting the stiffness and mass matrices resulting from the transverse equation of motion and boundary conditions, the natural transverse frequency of the rotating annular microplate under the flexoelectric effect is calculated. The results of this research are useful for promoting the use of rotating annular microplants under flexoelectric effect for microelectromechanical systems designers with high efficiency.

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.

A size-dependent electromechanical Euler–Bernoulli micro/nanobeam is proposed to address the nonlinear vibration and instability regions on the basis of nonlocal strain gradient theory (NSGT) and von-Karman hypothesis. The micro/nanopiezoelectric sandwich beam is axially influenced by the parametric excitation. Moreover, the electric enthalpy energy density is employed to consider the effect of flexoelectricity. The nonlinear equations of motion are derived with the aim of Hamilton’s variational approach. In this study, the electrostatic and Casimir forces are considered. The multiple time scales method is employed to solve the equation. Based on the outcomes of this research, it can be claimed that the flexoelectric and piezoelectric parameters have a pivotal influence on the amplitude response and dynamic instability regions. Furthermore, the applied voltage enlarges the distance between the bifurcation points and has a softening effect on micro/nanobeam. This work tries to provide a comprehensive understanding of flexoelectric micro/nanosandwich beam and prepare valuable information for designing flexoelectricity-based micro/nanostructures such as actuators, sensors, switches and resonators.

Flexoelectric effect and its influence on the application of multifunctional ferroelectrics have been investigated. Theory of flexoelectric coupling has indicated that mechanical strain gradient can impact polarization in a way analogous to electric field. Experimentally, magnitudes of the flexoelectric coefficients have been measured in ferroelectric, incipient ferroelectric and relaxor ferroelectric perovskites. Present data of flexoelectricity suggests that such unconventional electromechanical coupling could make unique contribution to properly engineered ferroelectric thin films and nanostructures. Flexoelectric effect is expected to intensify at small dimensions and get large enough at nanoscale to significantly impact phase transition and functional response in ferroelectrics.

Flexoelectric effect describes the electromechanical coupling between the strain gradient and its internal polarization in all dielectrics. Despite this universality, the resulting flexoelectric field remains small at the macroscopic level. However, in nanosystems, the size-dependent effect of flexoelectricity becomes increasingly significant, leading to a notable flexoelectric field that can strongly influence the material’s physical properties. This review aims to explore the flexoelectric effect specifically at the nanoscale. We achieve this by examining strain gradients generated through two distinct methods: internal inhomogeneous strain and external stimulation. In addition, advanced synthesis techniques are utilized to enhance the properties and functionalities associated with flexoelectricity. Furthermore, we delve into other coupled phenomena observed in thin films, including the coupling and utilization of flexomagnetic and flexophotovoltaic effects. This review presents the latest advancements in these areas and highlights their role in driving further breakthroughs in the field of flexoelectricity.