scholarly journals Dynamic Behavior of Multi-Layered Viscoelastic Nanobeam System Embedded in a Viscoelastic Medium with a Moving Nanoparticle

2016 ◽  
Vol 33 (5) ◽  
pp. 559-575 ◽  
Author(s):  
Sh. Hosseini Hashemi ◽  
H. Bakhshi Khaniki
Keyword(s):  
Dynamic Behavior ◽  
Viscoelastic Medium ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Function Technique ◽  
Small Scale ◽  
Transform Method ◽  
Damping Parameter ◽  
Moving Nanoparticle

AbstractIn this paper, dynamic behavior of multi-layered viscoelastic nanobeams resting on a viscoelastic medium with a moving nanoparticle is studied. Eringens nonlocal theory is used to model the small scale effects. Layers are coupled by Kelvin-Voigt viscoelastic medium model. Hamilton's principle, eigen-function technique and the Laplace transform method are employed to solve the governing differential equations. Analytical solutions for transverse displacements of double-layered is presented for both viscoelastic nanobeams embedded in a viscoelastic medium and without it while numerical solution is achieved for higher layered nanobeams. The influences of the nonlocal parameter, stiffness and damping parameter of medium, internal damping parameter and number of layers are studied while the nanoparticle passes through. Presented results can be useful in analysing and designing nanocars, nanotruck moving on surfaces, racing nanocars etc.

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

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.

Effects of Elastic Restraints on the Fundamental Frequency of Nonlocal Nanobeams with Tip Mass

2019 ◽  
Vol 24 (3) ◽  
pp. 520-530
Author(s):  
Malesela K. Moutlana ◽  
Sarp Adali
Keyword(s):  
Fundamental Frequency ◽  
Scale Effects ◽  
Beam Theory ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Nano Scale ◽  
Scale Structures ◽  
Elastically Restrained ◽  
Elastic Restraints ◽  
Tip Mass

The fundamental frequencies of an elastically restrained nanobeam with a tip mass are studied based on the nonlocal Euler-Bernoulli beam theory. The nanobeam has a torsional spring at one end and a translational spring at the other end where a tip mass is attached. The aim is to model a tapping mode atomic force microscope (TM-AFM), which can be utilized in imaging and the manufacture of Nano-scale structures. A TM-AFM uses high frequency oscillations to remove material, shape structures or scan the topology of a Nano-scale structure. The nonlocal theory is effective at modelling Nano-scale structures, as it takes small scale effects into account. Torsional elastic restraints can model clamped and pinned boundary conditions, as their stiffness values change between zero and infinity. The effects of the stiffness of the elastic restraints, tip mass and the small-scale parameter on the fundamental frequency are investigated numerically.

scholarly journals Nonlocal Torsional Vibration of Elliptical Nanorods with Different Boundary Conditions

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 189-203 ◽  
Author(s):  
Farshad Khosravi ◽  
Seyyed Amirhosein Hosseini ◽  
Babak Alizadeh Hamidi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Torsional Vibration ◽  
Scale Effects ◽  
Nonlocal Theory ◽  
Equation Of Motion ◽  
Small Scale ◽  
Different Boundary Conditions ◽  
Design And Optimization ◽  
Preliminary Validation ◽  
Aerospace Systems

This work aims at investigating the free torsional vibration of one-directional nanostructures with an elliptical shape, under different boundary conditions. The equation of motion is derived from Hamilton’s principle, where Eringen’s nonlocal theory is applied to analyze the small-scale effects. The analytical Galerkin method is employed to rewrite the equation of motion as an ordinary differential equation (ODE). After a preliminary validation check of the proposed formulation, a systematic study investigates the influence of the nonlocal parameters, boundary conditions, geometrical and mechanical parameters on the natural frequency of nanorods; the objective is to provide useful findings for design and optimization purposes of many nanotechnology applications, such as, nanodevices, actuators, sensors, rods, nanocables, and nanostructured aerospace systems.

Analytical Treatment of the Free Vibration of Single-Walled Carbon Nanotubes Based on the Nonlocal Flugge Shell Theory

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Scale Effects ◽  
Elastic Shell ◽  
Nonlocal Parameter ◽  
Single Walled Carbon Nanotubes ◽  
Small Scale ◽  
Resonant Frequencies ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

In the current work, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) under different boundary conditions are investigated. A nonlocal elastic shell model is utilized, which accounts for the small scale effects and encompasses its classical continuum counterpart as a particular case. The variational form of the Flugge type equations is constructed to which the analytical Rayleigh–Ritz method is applied. Comprehensive results are attained for the resonant frequencies of vibrating SWCNTs. The significance of the small size effects on the resonant frequencies of SWCNTs is shown to be dependent on the geometric parameters of nanotubes. The effectiveness of the present analytical solution is assessed by the molecular dynamics simulations as a benchmark of good accuracy. It is found that, in contrast to the chirality, the boundary conditions have a significant effect on the appropriate values of nonlocal parameter.

Nonlocal Modeling and Behavior of Carbon Nanotube-Based Sensors in Thermal Environment

2018 ◽  
Author(s):  
Seyedeh Sepideh Ghaffari ◽  
Samantha Ceballes ◽  
Abdessattar Abdelkefi
Keyword(s):  
Carbon Nanotube ◽  
Thermal Effects ◽  
Thermal Environment ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Mass Sensor ◽  
Buckling Behavior ◽  
Mass Detector ◽  
And Behavior

An exact solution that investigates the pre-buckling characteristics of nonlocal carbon nanotube (CNT)-based mass sensor subjected to thermal load under clamped-clamped boundary condition is determined. The uniform temperature rise is utilized to study thermal effects on the sensitivity of the mechanical resonator in pre-buckling configuration. Using Eringen’s nonlocal theory, along with the Hamilton’s principle, the governing equations considering small scale and geometric nonlinearity are derived. The influences of important parameters including nonlocal parameter, temperature change, length, and diameter of the CNT on the pre-buckling behavior and frequency shift of the CNT-based mass detector are also studied. Results show that these parameters have significant impact on the dynamic characteristics of the CNT-mass sensor.

Wave Propagation Analysis of Piezoelectric Nanoplates Based on the Nonlocal Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850060 ◽  
Author(s):  
Li-Hong Ma ◽  
Liao-Liang Ke ◽  
Yi-Ze Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Wave Propagation ◽  
Electric Potential ◽  
Mechanical Load ◽  
Tensile Force ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Wave Number ◽  
Small Scale ◽  
Axial Tensile ◽  
Propagation Analysis

Based on the nonlocal theory, this paper develops the Kirchhoff nanoplate and Mindlin nanoplate models for the wave propagation analysis of piezoelectric nanoplates. The effects of small scale parameter and thermo-electro-mechanical loads are incorporated in the nanoplate models. The Hamilton’s principle is employed to derive the governing equations of the nanoplate, which are solved analytically to obtain the dispersion relation for piezoelectric nanoplates. The results show that the nonlocal parameter, temperature change, mechanical load and external electric potential have significant influence on the wave propagation characteristics of the piezoelectric nanoplates. The cut-off wave number is observed to exist for piezoelectric nanoplates subjected to positive electric potential, axial tensile force and temperature rise.

scholarly journals Nonlocal Analysis of the Flexural–Torsional Stability for FG Tapered Thin-Walled Beam-Columns

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1936
Author(s):  
Masoumeh Soltani ◽  
Farzaneh Atoufi ◽  
Foudil Mohri ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Power Law ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Small Scale ◽  
Torsional Buckling ◽  
Beam Columns ◽  
Thin Walled ◽  
Torsional Stability ◽  
Flexural Torsional Buckling

This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems.

scholarly journals Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

2018 ◽  
Vol 38 (1) ◽  
pp. 122-142 ◽  
Author(s):  
Mohammad Arefi ◽  
Mahmoud Pourjamshidian ◽  
Ali Ghorbanpour Arani ◽  
Timon Rabczuk
Keyword(s):  
Nonlinear Vibration ◽  
Elasticity Theory ◽  
Strain Gradient ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Numerical Results ◽  
Small Scale ◽  
Beam Model ◽  
Surface Stresses

This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.

Differential quadrature solutions for the nonconservative instability of a class of single-walled carbon nanotubes

2018 ◽  
Vol 35 (1) ◽  
pp. 251-267 ◽  
Author(s):  
Maria Anna De Rosa ◽  
Maria Lippiello ◽  
Stefania Tomasiello
Keyword(s):  
Free Vibration ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Added Mass ◽  
Differential Quadrature ◽  
Small Scale ◽  
Numerical Schemes ◽  
Content Type ◽  
Single Walled Carbon ◽  
Integration Schemes

Purpose The purpose of the present paper is to investigate the nonconservative instability of a single-walled carbon nanotube (SWCNT) with an added mass through nonlocal theories. The governing equations are discretized by means of the differential quadrature (DQ) rules, as introduced by Bellman and Casti. DQ rules have been largely used in engineering and applied sciences. Recently, they were applied to enhance some numerical schemes, such as step-by-step integration schemes and Picard-like numerical schemes. Design/methodology/approach In the present paper, the DQ rules are used to investigate the nonconservative instability of a SWCNT through nonlocal theories. Findings To show the sensitivity of the SWCNT to the values of added mass and the influence of nonlocal parameter on the fundamental frequencies values, some numerical examples have been performed and discussed. Yet, the effect of the different boundary conditions on the instability behaviour has been investigated. The validity of the present model has been confirmed by comparing some results against the ones available in literature. Originality/value Applying the nonlocal elasticity theory, this paper presents a re-formulation of Hamilton’s principle for the free vibration analysis of a uniform Euler–Bernoulli nanobeam. The main purpose of this paper is to investigate the free vibration response of an SWCNT with attached mass and for various values of small scale effects.

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