Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory

Ebrahimi, Farzad; Barati, Mohammad Reza

doi:10.1140/epjp/i2017-11320-5

Cited by 70 publications

(29 citation statements)

References 46 publications

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“…Regardless of time dependency and on the basis of Equation (45), the natural frequencies of the beam were extracted nondimensionally to be better plotted in an illustration as Ω = ω L 2 h ρ C 11 and X = x L . In terms of predicting the static and dynamic responses of piezoelectric-flexoelectric nanostructures, the previous published research studied many conditions, e.g., the effect of nonlocal parameter [29,34,38], different edge conditions [31], thermal environment [36], surface effect [36,37], elastic substrate [39], etc. ; therefore, the present study focuses on the influence of flexoelectricity on a nanobeam with internal viscoelasticity.…”

Section: Frequency Analysismentioning

confidence: 99%

“…The differential quadrature (DQ) method discretized the equations of frequency, and a direct iterative process computed the values of the frequencies. Ebrahimi and Barati [38] analytically researched the vibration response of a piezoelectric nanobeam embedded on the Winkler-Pasternak foundation. They considered classical beam theory and took flexoelectricity and surface effects together in the frequency equations.…”

Section: Introductionmentioning

confidence: 99%

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On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan

Eremeyev

2020

Symmetry

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The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton’s principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material.

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Section: Frequency Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan

Eremeyev

2020

Symmetry

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“…It is thus essential to quantify and understand the vibration behaviors of piezoelectric nanobeams. As a universal electromechanical mechanism in all piezoelectric materials, flexoelectricity has been reported to have strong influence on the vibration responses of piezoelectric nanobeams [7][8][9]. As a result, the study of flexoelectric effect on vibration responses of embedded piezoelectric nanobeams may provide valuable information for the above mentioned potential applications of piezoelectric nanobeams.…”

Section: Introductionmentioning

confidence: 99%

“…However, some researchers point out that nonlocal elasticity theory should be incorporated to the strain gradient theory for more accurate prediction of mechanical behavior of nanostructures [13][14][15]. On this basis, to include the nonlocal effect in vibration analysis of piezoelectric nanobeams, Ebrahimi and Barati [8] investigated the vibration characteristics of a flexoelectric nanobeam resting on Winkler-Pasternak elastic foundation based on nonlocal elasticity theory. In this study, Hamilton's principle was used to derive the governing equations of motion and a Galerkin-based method was applied to obtain the natural frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

2018

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In this study, vibration characteristics of a piezoelectric nanobeam embedded in viscoelastic medium are investigated based on nonlocal Euler-Bernoulli beam theory. In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived by using Hamilton's principle, where nonlocal effect, piezoelectric effect, flexoelectric effect and viscoelastic medium are considered simultaneously. Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions. The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved. The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium and electrical loadings.

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Size‐dependent continuum‐based model of a flexoelectric functionally graded cylindrical nanoshells

Babadi

Beni

2020

Math Methods in App Sciences

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Flexoelectricity is dependent on the strain gradient, which is high in microscale and nanoscale, leading to its considerable effect on the electromechanical behavior of structures in microscale and nanoscale. Using the Love's theory for thin shells and the modified flexoelectricity theory, governing coupled equations of the functionally graded magneto‐electro‐elastic (FGMEE) cylindrical nanoshells were formulated along with their boundary conditions using the Hamilton's principle and variation method. It is worth noting that the governing coupled equations of FGMEE cylindrical nanoshell with an electric potential‐independent polarization parameter, where the polarization is independent of the electric potential, are considered the major novelty of this study. To show the ability and uniqueness of the formulation, free vibrations of the shell were examined in a specific state, regardless of the magnetic field effect under the clamped–clamped boundary condition. The effects of different parameters including geometry, size effect, and external voltage on the vibration frequency of the nanoshell were investigated. According to the results, the vibration behavior of the flexoelectric nanoshell is largely dependent on the size effect. Given the application of this structure in sensors and actuators, the external voltage has a considerable effect on the electromechanical behavior of the structure in the presence of the flexoelectric effect.

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Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory

Cited by 70 publications

References 46 publications

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

Size‐dependent continuum‐based model of a flexoelectric functionally graded cylindrical nanoshells

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