TORSIONAL DYNAMIC RESPONSE OF A CARBON NANOTUBE EMBEDDED IN VISCO-PASTERNAK’S MEDIUM

The torsional dynamics of carbon nanotubes embedded in viscoelastic medium are presented by using the nonlocal elasticity theory. The medium is considered as a foundation model which characterized by the linear Winkler’s modulus, Pasternak’s (shear) foundation modulus and the damping coefficient. The governing torsional equation is obtained and solved for nanotubes subjected to various boundary conditions and stated under different loads. The effects of some parameters like nonlocal parameter, nanotube length, Winkler’s modulus, and damping coefficient on the angular displacement of the nanotube are investigated in detail. The angular displacements are very sensitive to all parameters, especially the inclusion of the viscous damping foundation. Present results can be useful in design of future nano composites, nano electromechanical systems like nano position sensors and linear servomotors. Sample angular displacements are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak’s parameters for future comparisons.

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Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

Nanomaterials and Nanotechnology ◽

10.1177/1847980417713106 ◽

2017 ◽

Vol 7 ◽

pp. 184798041771310 ◽

Cited By ~ 7

Author(s):

Farzad Ebrahimi ◽

Mohammad Reza Barati

Keyword(s):

Boundary Conditions ◽

Elastic Foundation ◽

Nonlocal Elasticity ◽

Nonlocal Parameter ◽

Surface Elasticity ◽

Nonlocal Elasticity Theory ◽

Surface Effects ◽

Geometrical Parameters ◽

Various Boundary Conditions ◽

Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

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Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

Nonlinear Dynamics ◽

10.1007/s11071-021-06224-6 ◽

2021 ◽

Author(s):

Jan Awrejcewicz ◽

Grzegorz Kudra ◽

Olga Mazur

Keyword(s):

Elasticity Theory ◽

Nonlocal Elasticity ◽

Scale Effects ◽

Plate Theory ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Phase Portraits ◽

Small Scale ◽

Governing System ◽

Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

Journal of Vibration and Control ◽

10.1177/1077546317711537 ◽

2017 ◽

Vol 24 (17) ◽

pp. 3809-3818 ◽

Cited By ~ 15

Author(s):

Farzad Ebrahimi ◽

Mohammad Reza Barati ◽

Parisa Haghi

Keyword(s):

Elasticity Theory ◽

Nonlocal Elasticity ◽

Nonlocal Parameter ◽

Beam Theory ◽

Nonlocal Elasticity Theory ◽

Wave Dispersion ◽

Functionally Graded ◽

Wave Number ◽

Graded Material ◽

Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

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Thermo-Electro-Mechanical Vibration Characteristics of Graphene/Piezoelectric/Graphene Sandwich Nanobeams

Journal of Mechanics ◽

10.1017/jmech.2017.89 ◽

2017 ◽

Vol 35 (1) ◽

pp. 65-79 ◽

Cited By ~ 2

Author(s):

N. Kammoun ◽

H. Jrad ◽

S. Bouaziz ◽

M. B. Amar ◽

M. Soula ◽

...

Keyword(s):

Nonlocal Elasticity ◽

Natural Frequencies ◽

Nonlocal Parameter ◽

Mechanical Vibration ◽

Beam Theory ◽

Nonlocal Elasticity Theory ◽

Mode Shapes ◽

Governing Equations ◽

Numerical Examples ◽

Generalized Differential

AbstractThis paper reports an investigation on thermo-electro-mechanical vibration of graphene/piezoelectric graphene/piezoelectric/graphene sandwich nanobeams. Based on the nonlocal elasticity theory, Timoshenko beam theory and Hamilton's principles, the governing equations are developed and solved using generalized differential quadrature (GDQ) method. The effects of the nonlocal parameter, external electrical voltage, temperature change and axial force on vibration of graphene/piezoelectric/graphene sandwich nanobeams are examined. The performance and the accuracy of the presented model are highlighted through numerical examples with different boundary conditions. This study reports that the nonlocal parameter and thermo-electro-mechanical loadings have important effect on the natural frequencies and the deflection mode shapes of the graphene/piezoelectric/graphene sandwich nanobeam. The present work can serve as guideline for the design of a nanoscale graphene/piezoelectric/graphene beams based electromechanical resonator sensors.

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Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/09544062211038029 ◽

2021 ◽

pp. 095440622110380

Author(s):

Jianshi Fang ◽

Bo Yin ◽

Xiaopeng Zhang ◽

Bin Yang

Keyword(s):

Angular Velocity ◽

Boundary Conditions ◽

Elasticity Theory ◽

Nonlocal Elasticity ◽

Slenderness Ratio ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Functionally Graded ◽

Different Boundary Conditions ◽

Gradient Variation

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton’s principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

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Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study

International Journal of Applied Mechanics ◽

10.1142/s1758825115500362 ◽

2015 ◽

Vol 07 (03) ◽

pp. 1550036 ◽

Cited By ~ 20

Author(s):

Omid Rahmani ◽

S. A. H. Hosseini ◽

M. H. Noroozi Moghaddam ◽

I. Fakhari Golpayegani

Keyword(s):

Boundary Conditions ◽

Torsional Vibration ◽

Analytical Study ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Stress Theory ◽

Various Boundary Conditions ◽

Crack Location ◽

Nonlocal Stress ◽

Torsional Spring

In this paper, the torsional vibration of cracked nanobeam was studied based on a nonlocal elasticity theory. The location of the crack is simulated by a torsional spring which links segments of nanobeam together. Also, different boundary conditions, including clamped–free, clamped–clamped and clamped–torsional spring, were considered. Furthermore, a detailed parametric study was conducted to investigate the influence of crack location, nonlocal parameter, length of nanobeam, spring constant and end supports on the torsional vibration.

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Thermally Induced Asymmetric Buckling of Circular Monolayer Graphene

Journal of Nanomaterials ◽

10.1155/2013/416189 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Haw-Long Lee ◽

Win-Jin Chang

Keyword(s):

Boundary Condition ◽

Mode Shape ◽

Nonlocal Elasticity ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Monolayer Graphene ◽

Small Length ◽

Length Effect ◽

Thermally Induced ◽

Different Order

The asymmetric buckling behaviors of circular monolayer graphene with clamped boundary condition subjected to temperature change are analytically studied based on the nonlocal elasticity theory, including the small length effect. The axisymmetrical and asymmetric critical buckling temperatures and mode shape of different order modes are obtained. According to the analysis, the asymmetric critical buckling temperature of monolayer graphene is larger than the axisymmetric one. The axisymmetrical and asymmetric critical buckling temperatures decrease with increasing nonlocal parameter. In addition, nodal diametrical lines and nodal circles can be found from the modal shapes. In order to avoid destruction of the sensors due to buckling of the structure, they can be placed at the nodal diametrical lines or nodal circles.

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Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.4.109 ◽

2013 ◽

Vol 4 ◽

pp. 968-973 ◽

Cited By ~ 22

Author(s):

Mohammad Rahim Nami ◽

Maziar Janghorban

Keyword(s):

Elasticity Theory ◽

Shear Deformation ◽

Static Analysis ◽

Nonlocal Elasticity ◽

Deformation Theory ◽

Nonlocal Parameter ◽

Shear Deformation Theory ◽

Nonlocal Elasticity Theory ◽

Shear Stresses ◽

Rectangular Plates

In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates.

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Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

Journal of Mechanics ◽

10.1017/jmech.2014.46 ◽

2014 ◽

Vol 30 (5) ◽

pp. 443-453 ◽

Cited By ~ 27

Author(s):

M. Sobhy

Keyword(s):

Boundary Conditions ◽

Natural Frequency ◽

Plate Theory ◽

Equations Of Motion ◽

Nonlocal Parameter ◽

Nonlocal Elasticity Theory ◽

Graphene Sheets ◽

Elastic Foundations ◽

Various Boundary Conditions ◽

Mechanics Of Composite Materials

AbstractIn this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

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