Analytical Solution for Static and Dynamic Analysis of Graphene-Based Hybrid Flexoelectric Nanostructures

Abstract

Owing to their applications in devices such as in electromechanical sensors, actuators and nanogenerators, the consideration of size-dependent properties in the electromechanical response of composites is of great importance. In this study, a closed-form solution based on the linear piezoelectricity, Kirchhoff’s plate theory and Navier’s solution was developed, to envisage the electromechanical behaviors of hybrid graphene-reinforced piezoelectric composite (GRPC) plates, considering the flexoelectric effect. The governing equations and respective boundary conditions were obtained, using Hamilton’s variational principle for achieving static deflection and resonant frequency. Moreover, the different parameters considering aspect ratio, thickness of plate, different loadings (inline, point, uniformly distributed load (UDL), uniformly varying load (UVL)), the combination of different volume fraction of graphene and piezoelectric lead zirconate titanate are considered to attain the desired bending deflection and frequency response of GRPC. Different mode shapes and flexoelectric coefficients are also considered and the results reveal that the proper addition of graphene percentage and flexoelectric effect on the static and dynamic responses of GRPC plate is substantial. The obtained results expose that the flexoelectric effect on the piezoelastic response of the bending of nanocomposite plates are worth paying attention to, in order to develop a nanoelectromechanical system (NEMS). Our fundamental study sheds the possibility of evolving lightweight and high-performance NEMS applications over the existing piezoelectric materials.

Flexoelectricity and surface effects on coupled electromechanical responses of graphene reinforced functionally graded nanocomposites: A unified size-dependent semi-analytical framework

“…The deflection continues to decrease as the flexoelectric coefficient increases in magnitude. We observe the same trend of results in published literature (Shingare and Naskar, 2021c) which affirms the validity of our present model (EKM) further. In addition to this, in all three distributions, there exists a significant reduction in the magnitude of deflection in between f 14 = 10 −6 C/m and f 14 = 10 −8 C/m whereas after f 14 = 10 −8 C/m, this reduction is almost negligible.…”

“…8. From figures 7 and 8, it can be observed that the results obtained from EKM and Ritz solutions are found to be in excellent agreement with the results estimated by Shingare and Naskar (2021c). Concerning the issue of non-linearity mentioned in previous Section 2.5.1, these figures also clearly indicate that the effect of neglecting non-linear terms is acceptable even in flexoelectric cases (f 14 ≠ 0).…”

“…The above two conclusions are precisely matching with the discussions presented in the preceding sections as per Kerr and Alexander (1968). In the following subsections, the validation study is performed with respect to existing literature (Shingare and Naskar, 2021c;Yang et al, 2015) considering two illustrative cases for the static and dynamic analysis of flexo-surface FGPM nanoplates.…”

“…Convergence study for transverse deflection of UD-FGPM nanoplates under three iterations. We have first examined the static and dynamic responses of a non-FGM flexoelectric nanoplate from (Shingare and Naskar, 2021c) using the present model where we just neglect the surface effects (ξ c and σ 0 = 0) on the upper and lower surface. This nanoplate is made of hybrid graphene reinforced piezoelectric composite (GRPC) material where all the edges are simply supported and a transverse load of 0.1MPa is acting upon it.…”

Compound influence of surface and flexoelectric effects on static bending response of hybrid composite nanorod

“…A piezoelectric micro/nanoscale structure such as beams, plates, rods, and panels is found to be having massive capabilities for numerous applications including energy harvesters which contain sensors, actuators, parallel plate capacitors, and nanogenerators. 3–10 Nanoscale beams and rods are extensively used in several NEMS applications. Precisely from the past couple of years, piezoelectric/non-piezoelectric materials have fascinated great interest for producing energy harvesters to generate the electric response on the application of mechanical load to the structure.…”