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.

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.

Buckling and post-buckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings

2014 ◽  
Vol 14 (03) ◽  
pp. 1350067 ◽  
Author(s):  
C. Liu ◽  
L. L. Ke ◽  
Y. S. Wang ◽  
J. Yang ◽  
S. Kitipornchai
Keyword(s):  
Temperature Rise ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Electric Voltage ◽  
Energy Functionals ◽  
Size Dependent ◽  
Total Potential ◽  
Nonlocal Timoshenko Beam Theory ◽  
Post Buckling ◽  
Minimum Total Potential Energy

Buckling and post-buckling behaviors of piezoelectric nanobeams are investigated by using the nonlocal Timoshenko beam theory and von Kármán geometric nonlinearity. The piezoelectric nanobeam is subjected to an axial compression force, an applied voltage and a uniform temperature rise. After constructing the energy functionals, the nonlinear governing equations are derived by using the principle of minimum total potential energy and discretized by using the differential quadrature (DQ) method. A direct iterative method is employed to determine the buckling and post-buckling responses of piezoelectric nanobeams with hinged–hinged, clamped–hinged and clamped–clamped end conditions. Numerical examples are presented to study the influences of the nonlocal parameter, temperature rise and external electric voltage on the size-dependent buckling and post-buckling responses of piezoelectric nanobeams.

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.

AN INVESTIGATION ON THE CHARACTERISTICS OF BENDING, BUCKLING AND VIBRATION OF NANOBEAMS VIA NONLOCAL BEAM THEORY

2014 ◽  
Vol 11 (06) ◽  
pp. 1350085 ◽  
Author(s):  
SOUMIA BENGUEDIAB ◽  
ABDELWAHED SEMMAH ◽  
FOUZIA LARBI CHAHT ◽  
SOUMIA MOUAZ ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Scale Effects ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Small Scale ◽  
Shear Stresses ◽  
Nonlocal Timoshenko Beam Theory ◽  
Walled Carbon Nanotubes

In the present study, a nonlocal hyperbolic shear deformation theory is developed for the static flexure, buckling and free vibration analysis of nanobeams using the nonlocal differential constitutive relations of Eringen. The theory, which does not require shear correction factor, accounts for both small scale effects and hyperbolic variation of shear strains and consequently shear stresses through the thickness of the nanobeam. The equations of motion are derived from Hamilton's principle. Analytical solutions for the deflection, buckling load and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories. Present solutions can be used for the static and dynamic analyses of single-walled carbon nanotubes.

Sign in / Sign up

Export Citation Format

Share Document