Surface Effects on Buckling of Double Nanobeam System Based on Nonlocal Timoshenko Model

2016 ◽  
Vol 16 (10) ◽  
pp. 1550077 ◽  
Author(s):  
S. A. H. Hosseini ◽  
O. Rahmani
Keyword(s):  
Surface Effect ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Timoshenko Model ◽  
Buckling Mode ◽  
Future Studies ◽  
Stiffness Constant ◽  
Buckling Behavior ◽  
Nonlocal Timoshenko Beam Theory

This paper is concerned with the surface effect on the buckling behavior of double nanobeam system using the nonlocal Timoshenko beam theory. The size effect is taken into consideration by using the Eringen’s nonlocal elasticity theory and the exact solution for buckling loads for simply supported boundary condition is presented. Influences of various parameters such as stiffness constant, nonlocal parameter, shear effect and buckling mode number are investigated. Also for the sake of validation, the present results are compared with those obtained from the Euler–Bernoulli model. It is shown that the proposed nonlocal model is able to produce results with high accuracy and it can be used as a benchmark in future studies on buckling of nano-sandwich structures.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory

2021 ◽  
pp. 239779142110633
Author(s):  
Reza Ebrahimi
Keyword(s):  
Nonlocal Parameter ◽  
Power Spectra ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Effective Control ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Force ◽  
Spectra Analysis ◽  
Chaotic Vibrations ◽  
Euler Bernoulli Beam

The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.

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

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
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.

Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2932-2952 ◽  
Author(s):  
Hu Liu ◽  
Zheng Lv
Keyword(s):  
Deterministic Model ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Evaluation Methodology ◽  
Probabilistic Evaluation ◽  
Nonlocal Timoshenko Beam Theory ◽  
Parametric Analyses ◽  
Foundation Parameters ◽  
Magnetic Potentials ◽  
Vibration Performance

This study is devoted to examining the vibration behaviors of magneto-electro-elastic nanobeams with consideration of nanomaterial uncertainties induced by the atom defect and manufacturing deviation. Based on the nonlocal Timoshenko beam theory, the governing equations of a magneto-electro-elastic nanobeam resting on a Winkler–Pasternak foundation and subjected to electric and magnetic potentials are derived. The material properties of the magneto-electro-elastic nanobeam are treated as uncertain parameters with well-defined bounds to overcome the extensive information required in probabilistic evaluation. The range of natural frequency of the magneto-electro-elastic nanobeam is predicted via a non-probabilistic evaluation methodology, which is validated by comparing with Monte Carlo simulation and probabilistic evaluation methodology. Then, the parametric analyses are performed to reveal the coupling effects of nanomaterial uncertainties, and nonlocal parameter, as well as elastic foundation parameters on the vibration performance of magneto-electro-elastic nanobeams. It is demonstrated that the nanomaterial uncertainties affect the mechanical behaviors of magneto-electro-elastic nanostructures significantly and the present model can be degenerated into the deterministic model as the nanomaterial uncertainty is eliminated.

Vibration of Double-Walled Carbon Nanotube-Based Mass Sensor via Nonlocal Timoshenko Beam Theory

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhi-Bin Shen ◽  
Bin Deng ◽  
Xian-Fang Li ◽  
Guo-Jin Tang
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Tube Length ◽  
Beam Model ◽  
Mass Sensor ◽  
Nonlocal Timoshenko Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Tip Mass

The potential of double-walled carbon nanotubes (DWCNTs) as a micromass sensor is explored. A nonlocal Timoshenko beam carrying a micromass at the free end of the inner tube is used to analyze the vibration of DWCNT-based mass sensor. The length of the outer tube is not equal to that of the inner tube, and the interaction between two tubes is governed by van der Waals force (vdW). Using the transfer function method, the natural frequencies of a nonlocal cantilever with a tip mass are computed. The effects of the attached mass and the outer-to-inner tube length ratio on the natural frequencies are discussed. When the nonlocal parameter is neglected, the frequencies reduce to the classical results, in agreement with those using the finite element method. The obtained results show that increasing the attached micromass decreases the natural frequency but increases frequency shift. The mass sensitivity improves for short DWCNTs used in mass sensor. The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short DWCNT sensors. Obtained results are helpful to the design of DWCNT-based resonator as micromass sensor.

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

2017 ◽  
Vol 35 (1) ◽  
pp. 65-79 ◽  
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.

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

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
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.

scholarly journals Free Vibration of Piezo-Nanowires Using Timoshenko Beam Theory with Consideration of Surface and Small Scale Effects

2014 ◽  
Vol 61 (1) ◽  
pp. 139-152 ◽  
Author(s):  
Atta Oveisi
Keyword(s):  
Timoshenko Beam ◽  
Surface Effect ◽  
Scale Effects ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Local Effect ◽  
Form Solution ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Nonlocal Timoshenko Beam Theory

Abstract This paper investigates the influence of surface effects on free transverse vibration of piezoelectric nanowires (NWs). The dynamic model of the NW is tackled using nonlocal Timoshenko beam theory. By implementing this theory with consideration of both non-local effect and surface effect under simply support boundary condition, the natural frequencies of the NW are calculated. Also, a closed form solution is obtained in order to calculate fundamental buckling voltage. Finally, the effect of small scale effect on residual surface tension and critical electric potential is explored. The results can help to design piezo-NW based instruments.

scholarly journals Free Vibration of Single Walled Carbon Nanotube Resting on Exponentially Varying Elastic Foundation

2018 ◽  
Vol 5 (1) ◽  
pp. 260-272 ◽  
Author(s):  
Snehashish Chakraverty ◽  
Subrat Kumar Jena
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Winkler Elastic Foundation ◽  
Special Cases ◽  
Edge Conditions

Abstract In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.

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