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This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in JOURNAL OF APPLIED PHYSICS. 101(3):034319 (2007) and may be found at https://doi.org/10.1063/1.2432025 ., Article, JOURNAL OF APPLIED PHYSICS. 101(3):034319 (2007)

Graphene sheets (GSs) are two-dimensional material with extremely favorable mass sensor properties. In the study, we examined the potential of nanoscale mass sensor based on simply supported double-layered graphene sheets (DLGSs) attached nanoparticles. Using the continuum elasticity theory, the influences of the attached mass and position of the nanoparticles on the frequency shifts of DLGSs are investigated in detail. The result shows that the frequency shift in DLGSs is much higher than that of the single-layered graphene sheets (SLGSs). The DLGSs based nanomechanical resonator could provide higher sensitivity than SLGSs.

Graphene sheet (GS) is a two-dimensional material with extremely favorable mass sensor properties. In this work, the potential of a nanoscale mass sensor based on individual single layer GS is examined. An atomic-resolution nanomechanical mass sensor is modeled by a fixed supported circular monolayer GS with attached nanoparticles, based on a continuum elastic model and Rayleigh's energy method. We analyze the vibrational properties of the GS used as a mass sensor in detail, and the relationship between the attached mass and the vibrational frequency (frequency shift) of the GS is simulated and discussed using the two models. The sensitivity of vibrational frequency (frequency shift) to both aspect ratio and vibration mode is demonstrated, and comparison of the two models proves their accuracy and that of the simulation of the monolayer GS mass sensor.

This paper presents a study on the natural vibration of circular double-layer graphene sheets (DLGSs) using circular plate theory. The circular DLGSs are assumed to be coupled together through the carbon–carbon van der Waals (vdW) force between their two layers. An analytical solution of coupled governing equations is proposed to predict the natural frequencies of circular DLGSs. The vibration behaviors in circular DLGSs are found to have an in-phase mode (IPM) associated with the classical natural frequency, and an anti-phase mode (APM) owing to the influence of the vdW interaction. The natural frequencies of the IPM are independent of vdW interactions between adjacent layers, while those of the APM depend on the vdW interaction, and are larger. Based on the exact solution, the influences of wavenumbers (m, n) on the natural frequencies of simply supported circular DLGSs are also investigated in detail.

Graphene nanoribbons (GNRs) are potential nanomaterial electromechanical oscillators because of their outstanding mechanical and electronic properties. Double-layer GNRs (DLGNRs), which are two-layer finite-wide counterparts of crystalline graphene sheets coupled to each other via van der Waals interaction forces, present two kinds of vibrational modes in flexural wave propagation. These two modes are defined as the in-phase mode and anti-phase mode. In this study, based on the nonlocal Timoshenko beam theory and Winkler spring model, the wave propagation characteristics of DLGNRs embedded in an elastic matrix are investigated by dividing the vibrational mode into the in-phase mode and anti-phase mode. This will provide more accurate guidance for the application of DLGNRs. When the nonlocal effects and elastic matrix are considered, three critical frequencies are found. These are defined as the cutoff, escape, and low-cutoff frequencies. Moreover, the results show that the wave propagation characteristics...

An elastic continuum mechanics model is presented to study the elastic buckling of single- and double-walled carbon nanotubes (CNTs) subjected to hydrostatic pressure. It is shown that a pressure-induced instability can occur in CNTs when a circle cross-section of the CNTs is destroyed. In this paper, we investigate the effects of deformation modes and dimension of CNTs on their mechanical stability. The results show that the critical pressure depends largely on the buckling mode, the diameter and aspect ratio of CNTs. The critical pressure of the single-walled CNTs (SWCNTs) with a diameter 1.3 nm is about 1.6 GPa, which is in excellent agreement the results reported in the relative literatures. The critical pressure of the double-walled nanotubes (DWCNTs) with a diameter of 2.2 nm will increase by 26%, compared with that of an identical diameter SWCNT.

Vibration characteristics of double-walled carbon nanotubes (DWCNTs) with conveying fluid are analyzed based on the Euler–Bernoulli beam theory and using the wave propagation approach. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The influences of internal moving fluids, such as flow velocity and mass density of fluids, on the vibration frequency of DWCNTs and the DWCNTs embedded in an elastic matrix are investigated in detail. The effect of matrix surrounding carbon nanotubes is considered as a spring element defined by the Winkler model. In this paper, we consider the double-walled nanotubes with an inner diameter of 2.2 nm and an outer diameter of 3.0 nm. According to this analysis, the numerical results indicate that the vibration frequency for the first mode (mode 1) reduces to zero at a critical flow velocity in the case of higher flow velocity, which coincides with the previous study based on a single beam model. The critical flow velocity is largely affected by the fluid properties and the vibration modes.

Carbon nanotubes may hold scientific promise in nanotechnology as nanopipes conveying fluid. In this paper, the wave propagation in double-walled carbon nanotubes (DWCNTs) conveying fluid is studied based on the Euler–Bernoulli beam theory. The influences of internal moving fluids, such as flow velocity and mass density of fluids, on the sound wave propagation of DWCNTs or the DWCNTs embedded in an elastic matrix are investigated in detail. The DWCNTs are considered as a two-shell model coupled together through the van der Waals interaction between two adjacent nanotubes. According to the proposed theoretical approach, the results indicate that fluid flow through carbon nanotubes affects the wave speed and the critical frequency in the carbon nanotubes. The amplitude ratios of the inner to outer nanotubes are largely affected by the fluid velocity and density when the vibrational frequency in nanotubes is larger than 1.5 Hz. The theoretical investigation may give a useful reference for potential applicati...

We present an approach for efficient, accurate calculations of the elastic wave properties of three-dimensional periodic solid-solid media with cubic lattice structures based on the principle that the elastic wave should be uniform when averaged over length scales much larger than the size of the scatterers. Utilizing the fact that the media has the same pure mode properties as natural crystal with the corresponding lattice structure, we derive formulas for effective velocities propagating along and normal to the lattice axis, from which three independent effective elastic moduli are calculated, respectively. Effective velocities propagating along any directions can be calculated with this method, which captures the multiple scattering and the structure of the periodic medium. The results agree well with those calculated directly from the slope of the corresponding bands near the Γ point of the first Brillouin zone and are in good agreement with previous isotropic theory at high-symmetry directions.