Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams

Eltaher, Mohamed A.; Mahmoud, F.F.; Assie, Amr E.; Meletis, Efstathios I.

doi:10.1016/j.amc.2013.09.002

Cited by 96 publications

(51 citation statements)

References 60 publications

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“…Because of the high surface-to-volume ratio in studying nanoscale, this effect causes higher elastic modulus and mechanical strength in comparison with traditional continuum mechanic studies [11,19].…”

Section: Surface Effect Theorymentioning

confidence: 97%

“…(23) into (19), the constitutive nonlocal governing equations for EBT nanobeam by considering surface and nonlocal effects is obtained as:…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

“…Most recently, Eltaher et al [19] studied the coupling effects of surface energy and small scale on free vibration of nanobeam beast on EBT. They utilized Galerkin finite element method to solve the motion equation for simply supported nanobeam.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Investigating various surface effects on nonlocal vibrational behavior of nanobeams

Ebrahimi

Boreiry

2015

Appl. Phys. A

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In this paper, the effects of various surface parameters on free vibration behavior of nanobeams are investigated in the presence of nonlocal effect. The GurtinMurdoch model is employed for incorporating the surface parameters including surface density, surface tension and surface elasticity, while the Eringen's nonlocal elasticity theory takes into account the effect of small scales. The governing equations of motion are obtained for different materials such as aluminum and silicon with various boundary conditions. The high-precision semi-analytical differential transformation method is utilized to solve the governing equations. Then, by transforming the governing differential equations and boundary conditions into algebraic equations, the natural frequencies are obtained. The objective of the present study is to explore comprehensively the effect of different combination of various surface effects on nonlocal vibrational behavior of nanobeams for the first time. It is explicitly shown that the vibration characteristics of a nanobeam are significantly influenced by these surface effects. Moreover, it is shown that by increasing the size of beam, the influence of surface effects reduce to zero, and the natural frequency reaches its classical value. Numerical results are also presented to serve as benchmarks for future analyses of nanobeams.

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Section: Surface Effect Theorymentioning

confidence: 97%

“…(23) into (19), the constitutive nonlocal governing equations for EBT nanobeam by considering surface and nonlocal effects is obtained as:…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

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Investigating various surface effects on nonlocal vibrational behavior of nanobeams

Ebrahimi

Boreiry

2015

Appl. Phys. A

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“…It accounts for scale effect related to the size-effect and different mechanical properties, that assume the stress at a point is dependent on the strain at all points, and thus proposed that stress is a function of strain in continuum structure. Eltaher et al (2013) investigated the coupled effect of surface stress and nonlocal elasticity on vibratory system behaviors of nanobeams. The finite element model was developed to discretize the beam in domain and solved by the equation of motion numerically.…”

Section: Introductionmentioning

confidence: 99%

Analysis of nonlocal nonlinear behavior of graphene sheet circular nanoplate actuators subject to uniform hydrostatic pressure

2017

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This study investigates the scale effect on nonlinear behavior of a clamped-clamped circular graphene sheet nanoplate actuator, which is electrostatically actuated by various vdW forces, tensile loads, and hydrostatic pressures. The circular nanoplate model is developed by using Eringen's nonlocal elasticity theory. The nonlinear behavior of the circular nanoplate actuator subject to nonlocal effect, electrostatic vdW forces, tensile loads, and hydrostatic pressures, is then carefully derived, analyzed and presented. A proposed hybrid differential transformation/finite difference method is first introduced to characterize the influence of scale effect on nonlinear behavior of the circular nanoplate subject to DC loads. The modeling result shows that the pull-in voltage deviates less than 2.71% as compared to that appeared in the literature obtained by using a different approach. The validity of the proposed hybrid method is thus verified and can thus be employed to further characterize the effect of small scale for different electrostatic actuation of tensile loads and hydrostatic pressures in greater details. The structural modeling results indicate that the pull-in voltage increases obviously with increasing scale effects. Overall, the results also reveal that the hybrid method presented in this paper is effective and can be used to accurately quantify the pull-in voltage in circular nanoplate systems under different associated actuation.

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“…In another study by Sedighi [43] the dynamic pull-in behaviour of an electrically actuated nano-bridge is studied, which features a rectangular cross-section incorporating the surface and intermolecular effects. Using a nonlocal finite element model, Eltaher et al [44] examined the vibration characteristics of nano-beams accounting for the surface layer effects. Fu and Zhang [45] examined the pull-in behaviour of an electrically actuated nano-beam by incorporating the surface elasticity.…”

Section: Introductionmentioning

confidence: 99%

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

Sedighi

Ouakad

Khooran

2017

Metrology and Measurement Systems

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Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires − based on the Gurtin-Murdoch model − and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkinbased projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

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Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams

Cited by 96 publications

References 60 publications

Investigating various surface effects on nonlocal vibrational behavior of nanobeams

Investigating various surface effects on nonlocal vibrational behavior of nanobeams

Analysis of nonlocal nonlinear behavior of graphene sheet circular nanoplate actuators subject to uniform hydrostatic pressure

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

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