WAVE PROPAGATION IN RECTANGULAR NANOPLATES BASED ON STRAIN GRADIENT THEORY WITH ONE GRADIENT PARAMETER WITH CONSIDERING INITIAL STRESS

2014 ◽  
Vol 28 (03) ◽  
pp. 1450021 ◽  
Author(s):  
MOHAMMAD RAHIM NAMI ◽  
MAZIAR JANGHORBAN
Keyword(s):  
Wave Propagation ◽  
Initial Stress ◽  
Governing Equation ◽  
Gradient Elasticity ◽  
Initial Stresses ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Gradient Parameter ◽  
Gradient Elasticity Theory ◽  
Parameter Wave

In this paper, on the basis of gradient elasticity theory with one gradient parameter, wave propagation in rectangular nanoplates is studied. In the governing equation, the influences of initial stresses and elastic foundation are also considered. An analytical approach is used to solve the governing equation. The effects of different parameters such as gradient parameter on the circular and cut-off frequencies are presented. One can see that the initial stress and gradient parameter play an important role in investigating the wave propagation in nanoplates.

scholarly journals Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

2017 ◽  
Vol 24 (3) ◽  
pp. 489-507 ◽  
Author(s):  
Hamid M. Sedighi ◽  
Hassen M. Ouakad ◽  
Moosa Khooran
Keyword(s):  
Surface Energy ◽  
Strain Gradient ◽  
Dynamic Instability ◽  
Research Work ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Free Standing ◽  
Gradient Elasticity Theory ◽  
Casimir Attraction

AbstractSize-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, theproximity force approximation(PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires – based on the Gurtin-Murdoch model – and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

scholarly journals Exponential stability in Mindlin’s Form II gradient thermoelasticity with microtemperatures of type III

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200459
Author(s):  
M. Aouadi ◽  
F. Passarella ◽  
V. Tibullo
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Elastic Behaviour ◽  
Gradient Theory ◽  
Inertia Effects ◽  
Type Iii ◽  
Frictional Damping ◽  
Gradient Elasticity Theory

In this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account micro-inertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin’s Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures. The work is motivated by increasing use of materials having microstructure at both mechanical and thermal levels. The equations of the linear theory are also obtained. Then, we use the semigroup theory to prove the well-posedness of the obtained problem. Because of the coupling between high-order derivatives and microtemperatures, the obtained equations do not have exponential decay. A frictional damping for the elastic component, whose form depends on the micro-inertia, is shown to lead to exponential stability for the type III model.

Pull-In Instability of Electrostatically Actuated Nano-Beams Using the Nonlocal-Gradient Elasticity Theory

2014 ◽  
Vol 488-489 ◽  
pp. 1256-1259
Author(s):  
Jian She Peng ◽  
Liu Yang
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Gradient Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Beam Model ◽  
Electrostatically Actuated ◽  
Gradient Elasticity Theory

A nonlocal-gradient elasticity beam model with two independent gradient coefficients based on the classical nonlocal elasticity theory and strain gradient theory is used to study the pull-in instability of electrostatically actuated nanobeams. The numerical results show that the pull-in voltage of nanobeams are affected by the small scale. And the two independent gradient coefficients play the different roles in it. This paper broadens the way of studying scale effect.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

2020 ◽  
pp. 095440622096561
Author(s):  
Amir-Reza Asghari Ardalani ◽  
Ahad Amiri ◽  
Roohollah Talebitooti ◽  
Mir Saeed Safizadeh
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Surface Elasticity ◽  
Shear Deformation Theory ◽  
Wave Dispersion ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Specific Domain ◽  
Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

Calculation of the Additional Constants for fcc Materials in Second Strain Gradient Elasticity: Behavior of a Nano-Size Bernoulli-Euler Beam With Surface Effects

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
H. M. Shodja ◽  
F. Ahmadpoor ◽  
A. Tehranchi
Keyword(s):  
Strain Gradient ◽  
Gradient Elasticity ◽  
Surface Effects ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Strain Gradient Elasticity ◽  
Euler Beam ◽  
Concentrated Load ◽  
Material Constants ◽  
Nano Size

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework, sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fee metals are given in terms of the parameters of Sutton-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a nano-size Bernoulli-Euler beam in second strain gradient elasticity is provided; the appearance of the additional constants in the corresponding formulations, through the governing equation and boundary conditions, can serve to delineate the true behavior of the material in ultra small elastic structures, having very large surface-to-volume ratio. Now that the values of the material constants are available, a nanoscopic study of the Kelvin problem in second strain gradient theory is performed, and the result is compared quantitatively with those of the first strain gradient and traditional theories.

Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes

2018 ◽  
Vol 32 (24) ◽  
pp. 1850291
Author(s):  
Yugang Tang ◽  
Ying Liu
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Strain Gradient Theory ◽  
Flexural Wave ◽  
Gradient Theory ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the influence of van der Waals force on the wave propagation in viscoelastic double-walled carbon nanotubes (DWCNTs) is investigated. The governing equations of wave motion are derived based on the nonlocal strain gradient theory and double-walled Timoshenko beam model. The effects of viscosity, van der Waals force, as well as size effects on the wave propagation in DWCNTs are clarified. The results show that effects of van der Waals force on waves in inner and outer layers of DWCNTs are different. Flexural wave (FW) in outer layer and shear wave (SW) in inner layer are sensitive to van der Waals force, and display new phenomena. This new finding may provide some useful guidance in the acoustic design of nanostructures with DWCNTs as basic elements.

scholarly journals 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY

2016 ◽  
Vol 7 ◽  
pp. 33-37 ◽  
Author(s):  
Christian Liebold ◽  
Wolfgang H. Müller
Keyword(s):  
Finite Element ◽  
Size Effect ◽  
Numerical Solution ◽  
Stiffness Matrix ◽  
Gradient Elasticity ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Additional Material ◽  
Hermite Finite Elements

We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution.

Sign in / Sign up

Export Citation Format

Share Document