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.

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.

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3974-3988 ◽  
Author(s):  
Maysam Naghinejad ◽  
Hamid Reza Ovesy
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elasticity Theory ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Principle ◽  
Various Boundary Conditions ◽  
Total Potential ◽  
Euler Bernoulli Beam

In the present article, the total potential energy principle and the nonlocal integral elasticity theory have been used to develop a novel finite element method for studying the free vibration behavior of nano-scaled beams. The formulations are based on Euler-Bernoulli beam theory and this method is able to properly analyze the free vibration of beams with various boundary conditions. By implementing the variational statements, the eigenvalue problem of the free vibration is obtained. The validation investigation is pursued by comparing the results of the current study with those available in the literature. The effects of nonlocal parameter, geometry parameters and boundary conditions on the free vibration of the Euler-Bernoulli beam are then studied.

Nonlinear Vibration of Nonlocal Piezoelectric Nanoplates

2015 ◽  
Vol 15 (08) ◽  
pp. 1540013 ◽  
Author(s):  
Chen Liu ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang ◽  
Jie Yang
Keyword(s):  
Nonlinear Vibration ◽  
Temperature Rise ◽  
Analytical Study ◽  
Constitutive Relations ◽  
Nonlocal Parameter ◽  
Winkler Foundation ◽  
Governing Equations ◽  
Electric Voltage ◽  
Direct Integration Method ◽  
The Galerkin Method

This paper presents an analytical study on the nonlinear vibration of rectangular piezoelectric nanoplates resting on the Winkler foundation. The piezoelectric nanoplate is assumed to be simply supported on all four edges and is subjected to an external electric voltage and a uniform temperature rise. Based on von Karman nonlinear strain–displacement relations and the nonlocal constitutive relations, the nonlinear governing equations and corresponding boundary conditions are derived by employing Hamilton's principle. The Galerkin method is used to obtain the nonlinear ordinary equation, which is then solved by the direct integration method. An extensive parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, temperature rise and Winkler parameter on the nonlinear vibration characteristics of piezoelectric nanoplates.

Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory

2018 ◽  
Vol 233 (1) ◽  
pp. 287-301 ◽  
Author(s):  
Behrouz Karami ◽  
Davood Shahsavari ◽  
Li Li ◽  
Moein Karami ◽  
Maziar Janghorban
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Second Order ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Size Dependent

The effective elastic-piezoelectric properties of nanostructures have been shown to be strongly size-dependent. In this paper, a nonlocal second-order shear deformation formulation is presented to study the size-dependent thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core. Temperature is considered as uniform and nonlinear distributions across plate’s thickness direction. Based on the developed nonlocal second-order shear deformation theory, the size-dependent equations of motion are derived. The nonlocal thermal buckling responses of simply supported nanoplates are solved via Navier method. The reliability of present approach is verified by comparing the existing results provided in the open literature. The influences of nonlocal parameter, gradient index, electric voltage, and Winkler–Pasternak parameters on the thermal buckling characteristics of functionally graded nanoplates are examined.

Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams

2017 ◽  
Vol 28 (15) ◽  
pp. 2007-2022 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Elastic Foundation ◽  
Power Law ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Electro Magnetic ◽  
Functionally Graded Nanobeam

This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

Buckling Analysis of Micro- and Nano-Rods/Tubes Based on Nonlocal Timoshenko Beam Theory Using Chebyshev Polynomials

2010 ◽  
Vol 123-125 ◽  
pp. 619-622 ◽  
Author(s):  
Seyyed Amir Mahdi Ghannadpour ◽  
Bijan Mohammadi
Keyword(s):  
Scale Effects ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Buckling Loads ◽  
Various Boundary Conditions ◽  
Total Potential ◽  
Nonlocal Timoshenko Beam Theory ◽  
Nano Rods ◽  
Comparison Of The Results

This paper presents the elastic buckling behavior of nonlocal micro- and nano- Timoshenko rods/tubes based on Eringen’s nonlocal elasticity theory. The critical buckling loads are obtained using the theorem of minimum total potential energy and Chebyshev polynomial functions. The present method, which uses Rayleigh–Ritz technique in this paper, provides an efficient and extremely accurate buckling solution. Numerical results for a variety of some micro- and nano-rods/tubes with various boundary conditions are given and compared with the available results wherever possible. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is promoted. The small scale effects on the buckling loads of rods/tubes are determined and discussed.

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