Flexoelectric effect in dielectrics under a dynamic load

Sládek, J.; Sládek, V.; Repka, Miroslav�; Deng, Qian

doi:10.1016/j.compstruct.2020.113528

Cited by 20 publications

(6 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Results for complex influence of micro-inertia effect, piezoelectric, and flexoelectric properties of the material are presented in Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 and Figure 13 . In our calculations, the direct flexoelectricity coefficients

and

are considered as

[ 43 ]. For finite values of flexoelectric parameters the imaginary part of phase velocity c 2 is different from zero, which yields a finite attenuation of the wave amplitude.…”

Section: Numerical Solution and Resultsmentioning

confidence: 99%

“…The equations of motion can be derived by using variational principles [ 40 , 41 , 42 ]. Bearing in mind the variations of internal energy

and kinetic energy

in the Hamilton principle

with assuming no body sources for the work of external loading

, the governing equations (i.e., the equation of motion and the Gauss law) become (see [ 39 , 43 ] for more details)

where

is nabla operator, and the media without free electric charges are considered. Note that focusing on micro-inertia effect in the present study, the employed simplified model does not involve the micro-stiffness effects represented in the density of internal energy by coupling terms

and

[ 44 ].…”

Section: Formulation and Theoretical Treatment Of The Problemmentioning

confidence: 99%

See 1 more Smart Citation

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Hrytsyna

Sládek

2021

Nanomaterials

Self Cite

View full text Add to dashboard Cite

The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

show abstract

and

are considered as

[ 43 ]. For finite values of flexoelectric parameters the imaginary part of phase velocity c 2 is different from zero, which yields a finite attenuation of the wave amplitude.…”

Section: Numerical Solution and Resultsmentioning

confidence: 99%

“…The equations of motion can be derived by using variational principles [ 40 , 41 , 42 ]. Bearing in mind the variations of internal energy

and kinetic energy

in the Hamilton principle

with assuming no body sources for the work of external loading

, the governing equations (i.e., the equation of motion and the Gauss law) become (see [ 39 , 43 ] for more details)

where

and

[ 44 ].…”

Section: Formulation and Theoretical Treatment Of The Problemmentioning

confidence: 99%

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Hrytsyna

Sládek

2021

Nanomaterials

Self Cite

View full text Add to dashboard Cite

show abstract

“…The frequency of the mechanical wave (≈ GHz) is much lower than the electric polarization occurs instantaneously with a frequency (>THz). Thus, the frequency of electromagnetic field changes due to the dynamic flexoelectric effect is much higher than that of mechanical field, the quasi-static approximation is assumed for electric fields and the dynamic flexoelectric effect is neglected in this study [31]. In this case, the variation of the kinetic energy K within the time duration [0, t] is…”

Section: Flexoelectricity Theorymentioning

confidence: 99%

“…In the past decade, several numerical methods have been proposed to study the flexoelectric effect in flexoelectric solids, such as the mesh free Galerkin method [18,19], the isogeometric analysis [20,21], the higher-order FEM [22][23][24], and the mixed finite element method (MFEM) [7,[25][26][27][28][29]. Previous works mainly focused on the flexoelectric effect under the static load, and only a few investigations involved the dynamics of the process [30,31]. Unfortunately, even for those works on dynamic cases, neither the mechanical wave propagation nor the converse flexoelectric effect has been considered.…”

Section: Introductionmentioning

confidence: 99%

Modeling mechanical waves propagation in flexoelectric solids

Zhou,

Tian,

Deng

et al. 2024

Smart Mater. Struct.

Self Cite

View full text Add to dashboard Cite

In this paper, the propagation of mechanical waves in flexoelectric solids with the consideration of both the direct and converse flexoelectric effects is studied via a collocation mixed finite element method (MFEM). The dynamic effects associated with mechanical waves propagation are accounted by introducing the kinetic energy in the Hamilton's principle. In the proposed collocation MFEM, a quadratic polynomial is independently assumed for each component of the mechanical strain and electric field. The independently assumed mechanical strain and electric field are collocated with their counterparts computed from the displacement and electric potential at 9 Gaussian quadrature points. Thus, except for the fundamental field variables, no additional degrees of freedom (DOFs) are introduced. By performing the numerical experiments using the collocation MFEM, it is found that due to the direct flexoelectric effect, the propagation of mechanical waves can result in electric polarization in materials. Besides, the converse flexoelectric effect can induce mechanical waves when there are non-uniform transient electric field applied to the material. Numerical results indicate that by increasing the loading speed of the time varying mechanical displacement load, the direct flexoelectric effect associated with the mechanical strain gradient could be significantly enhanced.

show abstract

“…Xue [45] presented a flexoelectric micro cantilever energy harvester with a broad bandwidth. A few papers incorporated strain gradient inertial effects in the formulation (see [46][47][48][49]). A review paper summarizing the different dynamic flexoelectric formulations can be found in [50].…”

Section: Introductionmentioning

confidence: 99%

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

2022

View full text Add to dashboard Cite

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-

show abstract

Flexoelectric effect in dielectrics under a dynamic load

Cited by 20 publications

References 74 publications

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Modeling mechanical waves propagation in flexoelectric solids

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

Contact Info

Product

Resources

About