Theoretical study of micro/nano-scale bistable plate for flexoelectric energy harvesting

Chen, Lihua; Pan, Shiqing; Fei, Yaying; Zhang, Wei; Yang, Fei

doi:10.1007/s00339-019-2539-3

Cited by 12 publications

(4 citation statements)

References 21 publications

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“…The dynamic responses of nanoplates with flexoelectric effect in Kirchhoff plates was proposed by [26,27]. Other studies incorporating nonlinear effects in dynamic response of flexoelectric systems can be found in [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of flexoelectric systems in the frequency domain with isogeometric analysis

2022

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A numerical procedure based on Isogeometric Analysis (IGA) is developed to analyze the dynamic response of flexoelectric systems in the frequency domain. In materials or composites with an effective flexoelectric response, a polarization can be induced by local strain gradients. In general, these effects are small in the static regime. However, larger effects may be induced by dynamic loads, and can be used in energy harvesters converting mechanical vibrations into electrical energy. In this work, the equations describing frequency response of flexoelectric systems under dynamic loads are first described. Then, an IGA discretization procedure is employed to handle the C 1 continuity of the displacement fields. The conditions of both open and close-circuits are formulated. The numer-

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis of flexoelectric systems in the frequency domain with isogeometric analysis

2022

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“…The pioneering contributions with respect to gradient effects are attributed to the nonlocal theory developed by Mindlin [20] who formulated a comprehensive linear model for the deformation of an elastic body based on the functional dependence of the potential energy density on both strain as well as its first and second gradients. Since then, and more systematically in recent years, a significant volume of associated works has been disseminated in the literature pertaining to various modeling aspects such as topology optimization of multimaterial flexoelectric composites [21][22][23], numerical and/or analytical determination of the effective properties of flexoelectric structures [24][25][26][27][28][29], bending and vibration analysis of flexoelectric beams [30][31][32][33], dynamic analysis and control of flexoelectric plates and shells [34][35][36][37][38], and many others. Ever since the rapid growth of the additive manufacturing industry has significantly facilitated fabrication of composites and metamaterials with arbitrary architectures, it stands to reason that the development of models that predict their behavior and properties a priori is a step in the right direction.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic homogenization of flexoelectric composite plates with periodically varying thickness

Kalamkarov

Hadjiloizi

Georgiades

2022

Mathematics and Mechanics of Solids

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A micromechanical model for the analysis of structurally periodic flexoelectric plates with periodically varying thickness is developed on the basis of asymptotic homogenization. The period of thickness variation is small and comparable to the plate thickness; accordingly, the plate is usually referred to as having a “rapidly varying thickness.” The stipulation for rapidly varying thickness is important because it is envisioned that the developed model can be applied to a broad range of thin plates, both stratified as well as plates endowed with an arbitrary distribution of reinforcements attached to the surface or embedded within the plate. The microscopic problem is implemented in two steps pertaining, respectively, to first- and second-gradient asymptotic homogenization. Each level of homogenization culminates in its own set of unit cell problems from which the effective coefficients of the homogenized structure can eventually be obtained. These effective coefficients couple the force and moment resultants as well as the averaged electric displacement with the first and second gradients of the macroscopic displacement and electric potential. Once the effective coefficients are obtained, the macroscopic problem is invoked, which provides a set of four differential equations from which the macroscopic variables of mechanical displacement and electric potential can be obtained. The model is illustrated by means of laminated flexoelectric composites as well as simple rib-reinforced plates. It is shown that in the limiting case of a thin, purely elastic plate, the derived model converges to the familiar classical plate model.

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“…Yao [41][42][43][44][45] separated the end of the upper piezoelectric layer from the base layer in the traditional piezoelectric cantilever beam and conducted an experimental study on broadband energy collection and dynamic response of the L-shaped piezoelectric cantilever beam. Chen [46,47] studied a micro/nanoscale bistable plate electrical-thermalmechanical coupling system for energy harvesting and analyzed the voltage-modal frequency response of a nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

Theory of Nonlinear Vibrations for Antisymmetric Cross‐Ply Bistable Laminated Shells

Zhang

2021

Shock and Vibration

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In this paper, on the basis of taking the von Karman nonlinear factors into consideration, the constitutive equation of the antisymmetric cross-ply laminated composite was used to calculate the internal force and internal moment of the bistable structure, and the dynamic equilibrium equation and the compatible equation were constructed, respectively. The two equations were combined to establish a nonlinear dynamic model for the antisymmetric cross-ply laminated glass fiber resin bistable shell. Then, the finite element numerical simulation software ABAQUS was adopted to perform simulation modeling and numerical analysis on a series of bistable specimens, so as to study the impact of different geometric parameters on the frequencies, mode shapes, and other vibration characteristics of the antisymmetric laminated fiber resin bistable shell. Galerkin discretization was conducted on the vibration partial differential equation. Since there are only even-order partial differential terms of deflection w with respect to x and y in the vibration partial differential equation at this time, the form of series obtained by each term is the same, which simplifies the discretization of the dynamic equilibrium equation and the compatible equation. Finally, the two equations after discretization were merged to obtain the three-degree-of-freedom nonlinear ordinary differential equation of the antisymmetric cross-ply laminated glass fiber resin bistable shell. The system averaged equation was acquired by perturbation analysis through a multiscale method, and the periodic solution of the antisymmetric laminated bistable system was studied. Moreover, the system’s nonlinear dynamic behavior characteristics such as bifurcation and chaos were explored when the main resonance Ω is close to ω 1 and ω 2 , respectively, and the internal resonance is 1 : 2 : 3.

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Theoretical study of micro/nano-scale bistable plate for flexoelectric energy harvesting

Cited by 12 publications

References 21 publications

Dynamic analysis of flexoelectric systems in the frequency domain with isogeometric analysis

Dynamic analysis of flexoelectric systems in the frequency domain with isogeometric analysis

Asymptotic homogenization of flexoelectric composite plates with periodically varying thickness

Theory of Nonlinear Vibrations for Antisymmetric Cross‐Ply Bistable Laminated Shells

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