Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems

Arani, A. Ghorbanpour; Kolahchi, Reza; Mortazavi, S. A.

doi:10.1007/s10999-014-9239-0

Cited by 47 publications

(6 citation statements)

References 28 publications

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“…Nonlocal piezoelasticity states that the stress tensor and the electric displacement vector depend on the strain and electric‐field of all points of the body. The constitutive equation of the nonlocal piezoelasticity can be written as

(1 - μ \nabla^{2}) σ_{i j}^{n l false(P false)} = σ_{i j}^{l false(P false)} = C_{i j k l}^{false(P false)} ε_{k l}^{false(P false)} - e_{i j k}^{false(P false)} E_{k}^{false(P false)},

(1 - μ \nabla^{2}) D_{k}^{n l false(P false)} = D_{k}^{l false(P false)} = e_{k l i}^{false(P false)} ε_{k l}^{false(P false)} + \in_{i j}^{false(P false)} E_{j}^{false(P false)},

where the parameter

μ = {false(e_{0} a false)}^{2}

denotes the small scale effect on the response of structures in nanosize, and

\nabla^{2}

is the Laplacian operator in the above equation. Also, the terms

C_{i j k l}^{false(P false)}

\in_{i j}^{false(P false)}

, and

e_{i j k}^{false(P false)}

are elastic constants, strains, dielectric constants, and piezoelectric constants, respectively.…”

Section: Nonlocal Constitutive Relationsmentioning

confidence: 99%

“…

E_{m}^{false(P false)}

is the electric field which may be written in term of electric potential (i.e.

ϕ^{false(P false)}

) as

E_{m}^{false(P false)} = - \frac{\partial ϕ^{false(P false)}}{\partial m}, m = x, y, z

…”

Section: Nonlocal Constitutive Relationsmentioning

confidence: 99%

“…Ghorbanpour Arani et al presented buckling analysis and smart control of single layered graphene sheet (SLGS) using PVDF based on nonlocal Mindlin plate theory. Nonlocal piezoelasticity based wave propagation of bonded double‐piezoelectric nanobeam‐systems was used by Ghorbanpour Arani et al . Surface stress and small‐scale effects on nonlinear vibration analysis of a single‐layer boron nitride sheet based on theories of nonlocal and surface piezoelasticity were investigated by Ghorbanpour Arani et al using differential cubature (DC) and harmonic differential quadrature (HDQ) methods.…”

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT

2016

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In the present work, nonlinear vibration analysis of polymeric nanocomposite microplates integrated with polyvinylidene fluoride (PVDF) layers as sensors and actuators is investigated. The middle layer is reinforced with carbon nanotubes (CNTs) and it's equivalent material properties are obtained by Mori–Tanaka approach. The nanocomposite and PVDF layers are subjected, respectively, to 2D magnetic and 3D electric fields. The system is rested on an elastic medium which is simulated with orthotropic Pasternak foundation. Based on the quasi‐3D sinusoidal shear deformation plate theory (SSDPT), the motion equations are derived considering surface effects using Gurtin–Murdoch theory. A partial‐differential (PD) controller is applied for the active control of the frequency through a closed‐loop control with bonded distributed PVDF sensors and actuators. Differential quadrature method (DQM) is applied in order to obtain the nonlinear frequency of microstructure. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, surface stress, elastic medium, volume percent of CNTs, applied voltage, controller, and boundary conditions on the vibration behavior of microstructure. Results depict that applying the controller, the frequency significantly decreases. This investigation may be important for the design and smart control of microdevices. POLYM. COMPOS., 39:1936–1949, 2018. © 2016 Society of Plastics Engineers

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(1 - μ \nabla^{2}) σ_{i j}^{n l false(P false)} = σ_{i j}^{l false(P false)} = C_{i j k l}^{false(P false)} ε_{k l}^{false(P false)} - e_{i j k}^{false(P false)} E_{k}^{false(P false)},

(1 - μ \nabla^{2}) D_{k}^{n l false(P false)} = D_{k}^{l false(P false)} = e_{k l i}^{false(P false)} ε_{k l}^{false(P false)} + \in_{i j}^{false(P false)} E_{j}^{false(P false)},

where the parameter

μ = {false(e_{0} a false)}^{2}

denotes the small scale effect on the response of structures in nanosize, and

\nabla^{2}

is the Laplacian operator in the above equation. Also, the terms

C_{i j k l}^{false(P false)}

\in_{i j}^{false(P false)}

, and

e_{i j k}^{false(P false)}

are elastic constants, strains, dielectric constants, and piezoelectric constants, respectively.…”

Section: Nonlocal Constitutive Relationsmentioning

confidence: 99%

“…

E_{m}^{false(P false)}

is the electric field which may be written in term of electric potential (i.e.

ϕ^{false(P false)}

) as

E_{m}^{false(P false)} = - \frac{\partial ϕ^{false(P false)}}{\partial m}, m = x, y, z

…”

Section: Nonlocal Constitutive Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT

2016

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“…The size-dependent wave propagation analysis of double-piezoelectric nano-beam-systems (DPNBSs) based on Euler–Bernoulli beam model was carried out by Ghorbanpour Arani et al. 26 They concluded that the imposed external voltage is an effective controlling parameter for wave propagation of the coupled system. Ke et al.…”

Section: Introductionmentioning

confidence: 99%

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

Arefi

Pourjamshidian

Arani

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.

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“…Using nonlocal elasticity theory, Eringen and his coworkers have successfully solved some important problems, such as propagation of plane waves (Eringen 1972a), propagation of Rayleigh waves (Eringen 1973), stress distribution at the tip of a crack (Eringen et al 1977) and screw and edge dislocations (Eringen 1983). Following his pioneering work, various investigations related to the use of this theory in nanostructures have been reported, including static analysis (Attia and Mahmoud 2016;Wang and Liew 2007), wave propagation (Bahrami and Teimourian 2016;Ghorbanpour Arani et al 2014;Hu et al 2008;Liu and Yang 2012), vibration characteristic (Aydogdu and Arda 2016;Brischetto 2014) as well as bending and buckling behaviors (Aranda-Ruiz et al 2012;Thai 2012) of nanostructures including nanorods (Karličić et al 2015;Narendar 2012), nanotubes (Bahaadini and Hosseini 2016;Natsuki et al 2008), nanoshafts (Arda and Aydogdu 2014), nanobeams (Eltaher et al 2016) and nanoplates (Radić et al 2014). In addition, some other size-dependent continuum theories, such as strain gradient elasticity (Fleck and Hutchinson 1997) and modified couple stress elasticity (Yang et al 2002), have emerged to study the mechanical behaviors of nanostructures (Ebrahimi and Barati 2017;Ghorbanpour Arani et al 2016;Khorshidi et al 2016;Shaat and Abdelkefi 2016;Togun and Bagdatli 2016).…”

Section: Introductionmentioning

confidence: 99%

Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium

Liu

2017

Int J Mech Mater Des

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The effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in an elastic medium is investigated by developing a nonlocal nanorod model with uncertainties. Considering limited experimental data, uncertain-but-bounded variables are employed to quantify the uncertain material properties in this paper. According to the nonlocal elasticity theory, the governing equations are derived by applying the Hamilton's principle. An iterative algorithm based interval analysis method is presented to evaluate the lower and upper bounds of the wave dispersion curves. Simultaneously, the presented method is verified by comparing with Monte-Carlo simulation. Furthermore, combined effects of material uncertainties and various parameters such as nonlocal scale, elastic medium and lateral inertia on wave dispersion characteristics of nanorod are studied in detail. Numerical results not only make further understanding of wave propagation characteristics of nanostructures with uncertain material properties, but also provide significant guidance for the reliability and robust design of the next generation of nanodevices.

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Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems

Cited by 47 publications

References 28 publications

Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT

Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium

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