lateral vibrations of single-layered graphene sheets using doublet mechanics

Authors

a fatahi-vajari

department of mechanical and aerospace engineering, science and research branch, islamic azad university, tehran, iran a. imam

department of mechanical and aerospace engineering, science and research branch, islamic azad university, tehran, iran

abstract

this paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. after a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. using doublet mechanics, the relation between natural frequency and length scale parameter is obtained in the lateral mode of vibration for single-layered graphene. it is shown that length scale parameter plays a significant role in the lateral vibration behavior of single-layered graphene sheets. such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. however with increasing the length of the plate, the effect of scale parameter on the natural frequency decreases. for validating the results of this method, the results obtained herein are compared with the existing nonlocal and molecular dynamics results and good agreement with the latter is observed.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Lateral Vibrations of Single-Layered Graphene Sheets Using Doublet Mechanics

This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. Using doublet mechanics, the relation between natural f...

full text

Stress Concentration Factor of Single-Layered Graphene Sheets Containing Elliptical Vacancies

In the present study, potential of finite element based molecular structural mechanics (MSM) for evaluating stress concentration factor of single-layered graphene sheets (SLGSs) with elliptical vacancies is successfully addressed. The MSM approach mimics the interatomic forces of the nanostructure by defining an equivalent frame structure containing beam elements. To obtain the mechanical and c...

full text

Nonlinear Mechanics of Single-atomic-layer Graphene Sheets

The unique lattice structure and properties of graphene have drawn tremendous interests recently. By combining continuum and atomistic approaches, this paper investigates the mechanical properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear continuum mechanics is developed for graphene under both in-plane and bending deformation. Atomistic simulations are carrie...

full text

Elastic Properties and Frequencies of Free Vibrations of Single-Layer Graphene Sheets

We determine the basal plane stiffness and Poisson’s ratio of single layer graphene sheets (SLGSs) in armchair and zigzag directions by using molecular mechanics simulations of their uniaxial tensile deformations with the MM3 potential, and of their axial and bending vibrations. Both approaches give the basal plane stiffness equal to ∼340 N/m which agrees well with that reported in the literatu...

full text

Coupled Axial-Radial Vibration of Single-Walled Carbon Nanotubes Via Doublet Mechanics

This paper investigates the coupled axial-radial (CAR) vibration of single-walled carbon nanotubes (SWCNTs) based on doublet mechanics (DM) with a scale parameter. Two coupled forth order partial differential equations that govern the CAR vibration of SWCNTs are derived. It is the first time that DM is used to model the CAR vibration of SWCNTs. To obtain the natural frequency and dynamic respon...

full text

Bending Analysis of Multi-Layered Graphene Sheets Under Combined Non-Uniform Shear and Normal Tractions

Bending analysis of multilayer graphene sheets (MLGSs) subjected to non-uniform shear and normal tractions is presented. The constitutive relations are considered to be non-classical based on nonlocal theory of elasticity. Based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. The effects of nano scale parameter, radius of c...

full text

My Resources

Save resource for easier access later


Journal title:
journal of solid mechanics

جلد ۸، شماره ۴، صفحات ۸۷۵-۸۹۴

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023