Abstract: Graphene is a material system of increasing technological importance with excellent mechanical and electrical properties. Depending on the edge configuration, graphene may be electrically conducting, semiconducting, or insulating, so deformation is believed to have strong effects on electrical properties. In this letter, ab initio approach is used to demonstrate the effect of torsional and strain induced deformation on the electrical conductance characteristics. These nanostructures are described using a single-band tight-binding Hamiltonian. Important observations on the connection between mechanical and electrical behavior are made based on the transport calculations. In particular, the conductance behavior shows interesting features on deformed graphene.
Abstract: We develop the mathematical framework for using single layer graphene sheet as nanoscale label-free mass sensors. Graphene resonators are assumed to be in the cantilevered configuration. Four types of mass loadings are considered and closed-form equations are derived for the frequency shift due to the added mass. Using the potential and kinetic energy of the mass loaded graphene sheets, generalised non-dimensional calibration constants are proposed for an explicit relationship between the added mass and the frequency shift. These equations in turn are used for sensing the added mass. Numerical results illustrate that the sensitivity of graphene sensors is in the order of gigahertz/zeptogram. We show that the performance of the sensor depends on the spatial distribution of the attached mass on the graphene sheet.
Abstract: Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the alpha cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with Fuzzy variables. The method is then integrated with a commercial Finite Element software (ADINA). Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of Finite Element function calls can be reduced without significantly compromising the accuracy.
Abstract: Bilayergraphenesheets (BLGSs) are currently receiving increasing attention. In this paper, the vibration characteristics of BLGSs are investigated using analytical and atomistic finite element approaches. Various possible scenarios, namely different geometrical configuration (armchair and zigzag), boundary conditions, and aspect ratio are considered in the present study. The dynamic characteristics of BLGS studied have shown dependence on aspect ratio and the boundary conditions. The unique vibrational properties and large stiffness of BLGS identified in the present work make them suitable candidates for manufacturing nanosensors; electromechanical resonators also will aid the nanomaterials research community to design nanodevices.
Abstract: This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The graphene is modelled at the atomistic scale, and the matrix deformation is analysed by the continuum finite element method. Inter-connectivity between graphene and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The impact of geometrical configuration (armchair and zigzag), boundary conditions and length on the overall stiffness of the graphene reinforced plastics (GRP) is studied. The natural frequency and vibrational mode shapes of GRP studied have displayed dependence on the length and also the boundary conditions. The exceptional vibrational behaviour and large stiffness displayed by GRP makes them a potential replacement for conventional composite fibres such as carbon and glass fibres.
Abstract: We investigate the vibrational properties of zigzag and armchair single-layer graphene sheets (SLGSs) using the molecular mechanics (MM) approach. The natural frequencies of vibration and their associated intrinsic vibration modes are obtained. Vibrational analysis is performed with different chirality and boundary conditions. The simulations are carried out for three types of zigzag and armchair SLGS. The universal force field potential is used for the MM approach. The first four natural frequencies are obtained for increasing lengths. The results indicate that the natural frequencies decrease as the length increases. The results follow similar trends with results of previous studies for SLGS using a continuum structural mechanics approach. These results have shown the applicability of SLGSs as electromechanical resonators.
Abstract: We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs) of the type (8,0) and (0,8) using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length). We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.
Abstract: We introduce the ab-initio framework for zigzag-edged graphene fragment based single-electron transistor (SET) operating in the Coulomb blockade regime. Graphene is modeled using the density-functional theory and the environment is described by a continuum model. The interaction between graphene and the SET environment is treated self-consistently through the Poisson equation. We calculate the charging energy as a function of an external gate potential, and from this we obtain the charge stability diagram. Specifically, the importance of including re-normalization of the charge states due to the polarization of the environment has been demonstrated.
Abstract: This paper investigates the effects of spatially uncertain material properties on the aeroelastic response predictions (e.g., rotating frequencies, vibratory loads etc.) of composite helicopter rotor. Initially, the spatial uncertainty is modeled as discrete random variables along the blade span and uncertainty analysis is performed with direct Monte Carlo simulations (MCS). Uncertainty effects on the rotating frequencies vary with the higher order modes in a non-linear way. Each modal frequency is found to be more sensitive to the uncertainty at certain sections of the rotor blade than uncertainty at other sections. Uncertainty effects on the vibratory hub load predictions are studied in the next stage. To reduce the computational expense of stochastic aeroelastic analysis, a high dimensional model representation (HDMR) method is developed to approximate the aeroelastic response as functions of blade stiffness properties which are modeled as random fields. Karhunen-Loeve expansion and a lower order expansion are used to represent the input and outputs, respectively, in the HDMR formulation which is similar to the spectral stochastic finite element method. The proposed method involves the approximation of the system response with lower dimensional HDMR, the response surface generation of HDMR component functions, and Monte Carlo simulation. The proposed approach decouples the computationally expensive aeroelastic simulations and uncertainty analysis. MCS, performed with computationally less expensive HDMR models, shows that spatial uncertainty has considerable influence on the vibratory hub load predictions.
Abstract: We propose an analytical formulation to extract from energy equivalence principles the equivalent thickness and in-plane mechanical properties (tensile and shear rigidity, and Poisson's ratio) of hexagonal boron nitride (h-BN) nanosheets. The model developed provides not only very good agreement with existing data available in the open literature from experimental, density functional theory (DFT) and molecular dynamics (MD) simulations, but also highlights the specific deformation mechanisms existing in boron nitride sheets, and their difference with carbon-based graphitic systems.
Abstract: This Letter considers a molecular mechanics approach for the vibration spectra analysis of fullerenes. Sixteen different fullerenes starting from C20 to C720 are considered. The universal force field potential is used for the molecular mechanics approach. An analytical expression based on the elastic shell theory is suggested to explain the variation of the natural frequencies across the whole family. It is shown that any given frequency across the fullerene family varies proportional to the inverse square root of their mass.
Abstract: Reliability analysis of uncertain dynamical systems is considered. The excitations are modeled as non-stationary Gaussian processes, whereas parametric uncertainties due to structural randomness are modelled as non-Gaussian random variables. The structural responses are, therefore, non-Gaussian processes. The limit state is formulated in terms of the extreme value distribution of the response process. Developing these extreme value statistics analytically is not straight-forward, which makes failure probability estimations difficult. An alternative procedure is investigated for computing exceedance probabilities. Proposed approach involves generating a full functional operational model, which approximates the original limit surface. Once the approximate form of the original limit state is defined, the failure probability can be obtained by statistical simulation. Thus, the method can be integrated with commercial finite element software, which permits uncertainty analysis of large structures with complexities that include material and geometric nonlinear behavior.
Abstract: The thickness and in-plane mechanical properties (Young's, shear modulus, Poisson's ratios) of fully hydrogenated graphene (graphane) sheets are predicted using a molecular mechanics approach. The equilibrium lengths and bond angles distortions used for the graphane models are obtained from Density Functional Theory (DFT) simulations. Our models compare well with existing data on the uniaxial properties of graphane and graphene sheets from first principle and Molecular Dynamics (MD) simulations, highlight a special orthotropic mechanical behaviour for graphane, and identify thickness and shear stiffness values which are peculiar of hydrogenated graphene.
Abstract: In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the CâC bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.
Abstract: Boron Nitride Nanotubes are being increasingly used due to their superior bio compatibility. We develop sensor equations for using Boron Nitride Nanotubes (BNNTs) as possible mass sensors for nano-scale biological objects. Two approaches based on static and dynamic deflection shapes have been investigated. Two types of sensor configurations, namely cantilevered and bridged, have been studied. New sensor equations have been validated using molecular mechanics simulations. Our results show that BNNTs can be used as bio sensor with sensitivity reaching in the order of 0.1zg/GHz.
Abstract: The potential of graphene nanoribbons (GNRs) as molecular-scale sensors is investigated by calculating the electronic properties of the ribbon and the organic molecule ensemble. The organic molecule is assumed to be absorbed at the edge of a zigzag GNR. These nanostructures are described using a single-band tight-binding Hamiltonian. Their transport spectrum and density of states are calculated using the non-equilibrium Green's function formalism. The results show a significant suppression of the density of states (DOS), with a distinct response for the molecule. This may be promising for the prospect of GNR-based single-molecule sensors that might depend on the DOS, e.g., devices that respond to changes in either conductance or electroluminescence. Further, we have investigated the effect of doping on the transport properties of the system. The substitutional boron and nitrogen atoms are located at the center and edge of GNRs. These dopant elements have significant influence on the transport characteristics of the system, particularly doping at the GNR edge.
Abstract: We investigate the vibrational properties of two kinds of single-wall ZnO nanotubes. The simulations are carried out for three types of zigzag nanotubes (5,0), (8,0), (10,0) and armchair nanotubes (3,3), (4,4), (6,6). The natural frequencies are determined by means of the molecular mechanics approach with the universal force field potential. The first four natural frequencies are obtained for length/diameter ratio of about 5â20. The vibration modes associated with these frequencies have been computed. Closed-form analytical expressions have been derived using the continuum shell theory for the physical explanations of the simulations results. We observe that the natural frequencies decrease as the aspect ratios increase. The results follow similar trends with results of previous studies for carbon nanotubes (CNT). However, the magnitudes of the frequencies are lower from the corresponding CNT counterparts, indicating that ZnO nanotubes are comparatively less stiff.
Abstract: The potential of graphene nanoribbons (GNRs) as molecular-scale sensors is investigated by calculating the electronic properties of the ribbon and the organic molecule ensemble. The organic molecule is assumed to be absorbed at the edge of a zigzag GNR. These nanostructures are described using a single-band tight-binding Hamiltonian. Their transport spectrum and density of states are calculated using the non-equilibrium Green's function formalism. The results show a significant suppression of the density of states (DOS), with a distinct response for the molecule. This may be promising for the prospect of GNR-based single-molecule sensors that might depend on the DOS, e.g., devices that respond to changes in either conductance or electroluminescence. Further, we have investigated the effect of doping on the transport properties of the system. The substitutional boron and nitrogen atoms are located at the center and edge of GNRs. These dopant elements have significant influence on the transport characteristics of the system, particularly doping at the GNR edge.
Abstract: This paper presents a novel method for predicting the failure probability of structural or mechanical systems subjected to random loads and material properties involving multiple design points. The method involves Multicut High Dimensional Model Representation (Multicut-HDMR) technique in conjunction with moving least squares to approximate the original implicit limit state/performance function with an explicit function. Depending on the order chosen sometimes truncated Cut-HDMR expansion is unable to approximate the original implicit limit state/performance function when multiple design points exist on the limit state/performance function or when the problem domain is large. Multicut-HDMR addresses this problem by using multiple reference points to improve accuracy of the approximate limit state/performance function. Numerical examples show the accuracy and efficiency of the proposed approach in estimating the failure probability.
