Gradient elasticity and flexural wave dispersion in carbon nanotubes

2009 ◽  
Vol 80 (19) ◽  
Author(s):  
Harm Askes ◽  
Elias C. Aifantis
Keyword(s):  
Carbon Nanotubes ◽  
Gradient Elasticity ◽  
Wave Dispersion ◽  
Flexural Wave

Flexural waves of carbon nanotubes based on generalized gradient elasticity

2011 ◽  
Vol 249 (1) ◽  
pp. 50-57 ◽  
Author(s):  
J. Shen ◽  
J.-X. Wu ◽  
J. Song ◽  
X.-F. Li ◽  
K.Y. Lee
Keyword(s):  
Carbon Nanotubes ◽  
Gradient Elasticity ◽  
Flexural Waves ◽  
Generalized Gradient

scholarly journals Study of Abnormal Group Velocities in Flexural Metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hong Woo Park ◽  
Joo Hwan Oh
Keyword(s):  
Group Velocity ◽  
Periodic Structure ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Abnormal Behavior ◽  
Flexural Wave ◽  
Negative Group ◽  
One Dimensional ◽  
Optical Branch ◽  
Negative Group Velocity

Abstract Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media

2017 ◽  
Vol 84 (3) ◽  
Author(s):  
Ruize Hu ◽  
Caglar Oskay
Keyword(s):  
Heterogeneous Media ◽  
Spatial Scales ◽  
Gradient Elasticity ◽  
Layered Media ◽  
Wave Dispersion ◽  
Momentum Balance ◽  
Eighth Order ◽  
Homogenization Model ◽  
Dispersion And Attenuation ◽  
Periodic Layered Media

This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.

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.

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