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.

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.

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.

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.

Nonlocal Flügge Shell Model for Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
R. Ansari ◽  
B. Arash
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Scale Effects ◽  
Elastic Shell ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the vibrational behavior of double-walled carbon nanotubes (DWCNTs) is studied by a nonlocal elastic shell model. The nonlocal continuum model accounting for the small scale effects encompasses its classical continuum counterpart as a particular case. Based upon the constitutive equations of nonlocal elasticity, the displacement field equations coupled by van der Waals forces are derived. The set of governing equations of motion are then numerically solved by a novel method emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. The influences of small scale factor, layerwise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are fully investigated. Explicit expressions for the nonlocal frequencies of DWCNTs with all edges simply supported are also analytically obtained by a nonlocal elastic beam model. Some new intertube resonant frequencies and the corresponding noncoaxial vibrational modes are identified due to incorporating circumferential modes into the shell model. A shift in noncoaxial mode numbers, not predictable by the beam model, is also observed when the radius of DWCNTs is varied. The results generated also provide valuable information concerning the applicability of the beam model and new noncoaxial modes affecting the physical properties of nested nanotubes.

scholarly journals Rayleigh-Ritz Vibrational Analysis of Multiwalled Carbon Nanotubes Based on the Nonlocal Flügge Shell Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
H. Rouhi ◽  
M. Bazdid-Vahdati ◽  
R. Ansari
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Multiwalled Carbon Nanotubes ◽  
Shell Theory ◽  
Scale Effects ◽  
Ritz Method ◽  
Elastic Shell ◽  
Small Scale ◽  
Multiwalled Carbon

A nonlocal elastic shell model considering the small scale effects is developed to study the free vibrations of multiwalled carbon nanotubes subject to different types of boundary conditions. Based on the nonlocal elasticity and the Flügge shell theory, the governing equations are derived which include the interaction of van der Waals forces between adjacent and nonadjacent layers. To analytically solve the problem, the Rayleigh-Ritz method is employed. In the present analysis, different combinations of layerwise boundary conditions are taken into account. Some new intertube resonant frequencies and the associated noncoaxial vibrational modes are identified owing to incorporating circumferential modes into the shell model.

scholarly journals Differential Quadrature and Differential Transformation Methods in Buckling Analysis of Nanobeams

2019 ◽  
Vol 6 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Transformation Method ◽  
Nonlocal Theory ◽  
Buckling Analysis ◽  
Differential Quadrature ◽  
Load Parameter ◽  
Computationally Efficient ◽  
Differential Transformation

AbstractIn this paper, two computationally efficient techniques viz. Differential Quadrature Method (DQM) and Differential Transformation Method (DTM) have been used for buckling analysis of Euler-Bernoulli nanobeam incorporation with the nonlocal theory of Eringen. Complete procedures of both the methods along with their mathematical formulations are discussed, and MATLAB codes have been developed for both the methods to handle the boundary conditions. Various classical boundary conditions such as SS, CS, and CC have been considered for investigation. A comparative study for the convergence of DQM and DTM approaches are carried out, and the obtained results are also illustrated to demonstrate the effects of the nonlocal parameter, aspect ratio (L/h) and the boundary condition on the critical buckling load parameter.

scholarly journals Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 87
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Scale Effects ◽  
Nonlocal Theory ◽  
Elastic Plates ◽  
Critical Temperatures ◽  
Buckling Behavior ◽  
Linear Vibrations ◽  
Nonlocal Strain Gradient ◽  
Plate Kinematics

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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