A Review on the Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

Finite conductivity, surface energy and nonlocal effect can influence the electromechanical performance of micro/nano-electromechanical systems (MEMS/NEMS). However, these factors are yet ignored on stability analysis of MEMS/NEMS fabricated from functionally graded materials (FGM). In this paper, dynamic stability of double-sided NEMS fabricated from non-symmetric FGM is investigated incorporating finite conductivity, surface energy and nonlocal effect. The Gurtin–Murdoch model and Eringen's elasticity are employed to consider the surface energy and nonlocal effect, respectively. Effect of finite conductivity of FGM on electrostatic and Casimir attractions is incorporated via relative permittivity and plasma frequency of the material. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. Moreover, bifurcation analysis is conducted to investigate the stability of the fixed points of the nano-structure. The validity of the proposed model is examined by comparing the results of the present study with those reported in the literature. The impact of various parameters i.e. finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic instability of the NEMS are addressed.

Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect

Effects of nonlocal elasticity and slip condition on vibration and stability analysis of viscoelastic cantilever carbon nanotubes conveying fluid

Nonlinear mechanics of nanotubes conveying fluid

In this study, for the first time, the transverse vibrational model of a viscous-fluid-conveying single-walled carbon nanotube (SWCNT) embedded in biological soft tissue is developed. Nonlocal Euler–Bernoulli beam theory has been used to investigate fluid-induced vibration of the SWCNT while visco-elastic behaviour of the surrounding tissue is simulated by the Kelvin–Voigt model. The results indicate that the resonant frequencies and the critical flow velocity at which structural instability of nanotubes emerges are significantly dependent on the properties of the medium around the nanotube, the boundary conditions, the viscosity of the fluid and the nonlocal parameter. Detailed results are demonstrated for the dependence of damping and elastic properties of the medium on the resonant frequencies and the critical flow velocity. Three standard boundary conditions, namely clamped–clamped, clamped–pinned and pinned–pinned, are applied to study the effect of the supported end conditions. Furthermore, it is found that the visco-elastic foundation causes an obvious reduction in the critical velocity in comparison with the elastic foundation, in particular for a compliant medium, pinned–pinned boundary condition, high viscosity of the fluid and small values of the nonlocal coefficient.

/pdf/vibration-and-instability-of-a-viscous-fluid-conveying-1avxekd15i.pdf

Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium

The transverse vibration of a single-walled carbon nanotube (SWCNT) with light waviness along its axis is modeled by the nonlocal Euler-Bernoulli and Timoshenko beam theory. Unlike the Euler-Bernoulli beam model (EBM), the effects of transverse shear deformation and rotary inertia are considered within the framework of the Timoshenko beam model (TBM). The surrounding elastic medium is described as both Winkler-type and Pasternak-type foundation models. The governing equations are derived using Hamilton’s principle, and the Galerkin method is applied to solve these equations. According to this study, the results indicate that the frequency calculated by TBM is lower than that obtained by EBM. Detailed results show that the importance of transverse shear deformation and rotary inertia become more significant for stocky SWCNTs with clamped-clamped boundary conditions. Moreover, the influences of the amplitude of waviness, nonlocal parameter, medium constants, boundary conditions and aspect ratio are analyzed and discussed. It is shown that waviness in the curved SWCNT causes an obvious increase in the natural frequency in comparison with the straight SWCNT, especially for a compliant medium, pinned-pinned boundary condition, short SWCNT and large nonlocal coefficient.

/pdf/vibration-of-wavy-single-walled-carbon-nanotubes-based-on-58iemskgo1.pdf

Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models

Nonlinear and Quasi-Linear Behavior of a Curved Carbon Nanotube Vibrating in an Electric Force Field; An Analytical Approach

The present paper proposes a new equation utilizing the nonlocal Euler-Bernoulli beam model to investigate the linear transverse vibration of an embedded single-walled carbon nanotube (SWCNT) which incorporates an extra-added nanoparticle. The elastic behavior of the surrounding medium is simulated by the Pasternak-type foundation model. Hamilton’s principle is applied to derive the governing equation, and the natural frequencies are obtained by the Galerkin method. The numerical results are compared with the molecular dynamics (MD) simulation as well as with the local continuum approach in the previous literature, to validate the nonlocal continuum elastic model. Unlike the classical continuum model, the present new approach shows acceptable accuracy and good agreement to the MD approximation. The results indicate that the fundamental frequencies are significantly dependent on the attached mass and boundary conditions. To study the effects of supported end conditions, three typical boundary conditions, namely clamped-clamped, clamped-pinned and pinned-pinned, are simulated. It is found that an attached mass causes a noticeable reduction in natural frequencies, in particular, for the clamped-clamped boundary condition, a stiff medium, stocky SWCNT and a small nonlocal parameter. In addition, when the position of the added nanoparticle is closer to the middle point of SWCNT length, the mass sensitivity is increased. Detailed results demonstrate that the present equation-based nonlocal continuum theory can be utilized for SWCNT-based mass sensor, efficiently.

/pdf/an-efficient-continuum-model-for-cnts-based-bio-sensors-31h1cabhai.pdf

An efficient continuum model for CNTs-based bio-sensors

In this paper, nonlocal Euler-Bernoulli beam theory is applied to investigate the dynamical behavior of a single-walled carbon nanotube (SWCNT) with an extra added nanoparticle. The SWCNT is assumed to be embedded on a Winkler-type elastic foundation with cantilever boundary condition. This configuration can be used as a nano-mass sensor which works on the basis of the changing the natural frequencies. The results show that the added mass causes an obvious increase in sensitivity of SWCNT-based nano-mass sensor, especially for stiff mediums, small nonlocal parameters, and stocky SWCNTs.

/pdf/free-vibration-of-a-carbon-nanotube-based-mass-sensor-346neo80ka.pdf

M.M. Taherian

Papers

Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium

Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models

Nonlinear and Quasi-Linear Behavior of a Curved Carbon Nanotube Vibrating in an Electric Force Field; An Analytical Approach

An efficient continuum model for CNTs-based bio-sensors

Free Vibration of a Carbon Nanotube-Based Mass Sensor