Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Yan, Zhao; Jiang, Liying

doi:10.1098/rspa.2012.0214

Cited by 112 publications

(40 citation statements)

References 47 publications

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“…Elastic properties are c 11 = 102 GPa, c 12 = 31 GPa and c 66 = 35.5 GPa; piezoelectric and dielectric constants are e 31 = −17.05 C/m 2 and κ 33 = 1.76 × 10 −8 C/(V m) [28]. The mass density is taken as ρ = 7600 kg/m 3 .…”

Section: Resultsmentioning

confidence: 99%

“…For a thin piezoelectric plate with large ratio of in-plane dimension to thickness, we adopt the assumption that the electric field exists only in the z-direction since the electric field components in the x − y plane are negligible compared with those in the thickness direction [16,28]. For a nanoscale dielectric material considering the flexoelectric effect, the constitutive equations can be expressed as [16,17,29] …”

Section: Governing Equationsmentioning

confidence: 99%

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Electromechanical responses of piezoelectric nanoplates with flexoelectricity

2015

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Flexoelectricity, representing the coupling between electrical polarizations and strain gradients, should be taken into account in the analysis of electromechanical responses of nanostructures where large strain gradients are expected. In this paper, we will explore the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported piezoelectric nanoplate by using the Kirchhoff plate theory. The governing equations and corresponding boundary conditions are deduced from Hamilton's principle, and the analytical solutions are obtained for the deflection and natural frequency. The results indicate that the deflections predicted by the present model are smaller than those calculated by the classical one which only considers piezoelectricity, while the frequencies exhibit the opposite trend. In addition, the flexoelectric effect is more prominent for thinner plates; the differences of the deflections or frequencies between the two models are gradually diminishing with an increase in the plate thickness. The current work may contribute to the understanding of the higher-order electromechanical coupling mechanism. Moreover, the modified plate model can be utilized to accurately design novel piezoelectric nanoplate-based sensors in nanoelectromechanical systems.

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Section: Resultsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

2015

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“…Consequently, the equilibrium position and energy of each atom near the surface can differ significantly from those in the interior. Such effects have been identified as a main mechanism leading to the size effects associated with the elastic moduli, resonant frequency, and thermal conductivity of nanoscale materials [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Elastic Theory of Nanomaterials Based on Surface-Energy Density

Chen

Yao

2014

Journal of Applied Mechanics

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Recent investigations into surface-energy density of nanomaterials lead to a ripe chance to propose, within the framework of continuum mechanics, a new theory for nanomaterials based on surface-energy density. In contrast to the previous theories, the linearly elastic constitutive relationship that is usually adopted to describe the surface layer of nanomaterials is not invoked and the surface elastic constants are no longer needed in the new theory. Instead, a surface-induced traction to characterize the surface effect in nanomaterials is derived, which depends only on the Eulerian surface-energy density. By considering sample-size effects, residual surface strain, and external loading, an explicit expression for the Lagrangian surface-energy density is achieved and the relationship between the Eulerian surface-energy density and the Lagrangian surface-energy density yields a conclusion that only two material constants-the bulk surface-energy density and the surface-relaxation parameter-are needed in the new elastic theory. The new theory is further used to characterize the elastic properties of several fcc metallic nanofilms under biaxial tension, and the theoretical results agree very well with existing numerical results. Due to the nonlinear surface effect, nanomaterials may exhibit a nonlinearly elastic property though the inside of nanomaterials or the corresponding bulk one is linearly elastic. Moreover, it is found that externally applied loading should be responsible for the softening of the elastic modulus of a nanofilm. In contrast to the surface elastic constants required by existing theories, the bulk surface-energy density and the surface-relaxation parameter are much easy to obtain, which makes the new theory more convenient for practical applications.

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“…(19) and (20) into Eq. (6), the components of the stress field of the surface layer of the ith nanowire are obtained as follows:…”

Section: Governing Equations Of the Nanosystem Based On The Hobtmentioning

confidence: 99%

“…Until now, the surface elasticity theory of Gurtin-Murdoch has been widely used for a wide range of problems associated with nanostructures. For instance, statics deformation [6][7][8][9][10], buckling behavior [11][12][13][14][15][16][17][18][19][20], and vibrations [21][22][23][24][25][26][27][28] of elastic nanobeams/nanoplates/nanowires have been investigated accounting for the surface effect.…”

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confidence: 99%

Elastic buckling of current-carrying double-nanowire systems immersed in a magnetic field

Kiani

2016

Acta Mech

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Axial buckling analysis of magnetically affected double-nanowire systems carrying electric current is of high interest. Using Lorentz and Biot-Savart laws, the magnetic forces on each nanowire are appropriately evaluated. By employing Timoshenko and higher-order beam theories, the governing equations of the nanosystem are extracted in the context of the surface elasticity theory of Gurtin-Murdoch. By applying a meshless technique, the critical buckling load of the nanosystem is calculated. In a particular case, the predicted results by the suggested numerical methodology are also verified with those of the assumed mode method, and a reasonably good agreement is achieved. The influences of the electric current, magnetic field strength, interwire distance, and surface energy effect on the buckling behavior of the nanosystem are examined. The capability of the Timoshenko beam theory in capturing the predicted results by the higher-order beam theory is also explained.

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Cited by 112 publications

References 47 publications

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Elastic Theory of Nanomaterials Based on Surface-Energy Density

Elastic buckling of current-carrying double-nanowire systems immersed in a magnetic field

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