Sondipon Adhikari

Effective elastic mechanical properties of single layer graphene sheets.

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Youngs modulus, the shear modulus and Poissons ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

Piezoelectric energy harvesting from broadband random vibrations

Energy harvesting for the purpose of powering low power electronic sensor systems has received explosive attention in the last few years. Most works using deterministic approaches focusing on using the piezoelectric effect to harvest ambient vibration energy have concentrated on cantilever beams at resonance using harmonic excitation. Here, using a stochastic approach, we focus on using a stack configuration and harvesting broadband vibration energy, a more practically available ambient source. It is assumed that the ambient base excitation is stationary Gaussian white noise, which has a constant power-spectral density across the frequency range considered. The mean power acquired from a piezoelectric vibration-based energy harvester subjected to random base excitation is derived using the theory of random vibrations. Two cases, namely the harvesting circuit with and without an inductor, have been considered. Exact closed-form expressions involving non-dimensional parameters of the electromechanical system have been given and illustrated using numerical examples.

Magnetopiezoelastic energy harvesting driven by random excitations

This letter considers a nonlinear piezomagnetoelastic energy harvester driven by stationary Gaussian white noise. The increase in the energy generated by this device has been demonstrated for harmonic excitation with slowly varying frequency in simulation and validated by experiment. This paper considers the simulated response of this validated model to random base excitation and shows that the system exhibits a stochastic resonance. If the variance of the excitation were known then the device may be optimized to maximize the power harvested, even under random excitation.

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low natural frequency, non-buckled beam; and a buckled beam. The most practical configuration seems to be the pre-buckled case, where the proposed system has a low natural frequency, a high level of harvested power and an increased bandwidth over a linear harvester.

Effective mechanical properties of hexagonal boron nitride nanosheets

We propose an analytical formulation to extract from energy equivalence principles the equivalent thickness and in-plane mechanical properties (tensile and shear rigidity, and Poissons 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.

Nonlocal transverse vibration of double-nanobeam-systems

Vibration analysis of double-nanobeam-systems is considered. Double-nanobeam-systems are important in nano-optomechanical systems and sensor applications. Expressions for free bending-vibration of double-nanobeam-system are established within the framework of Eringen’s nonlocal elasticity theory. An analytical method is developed for determining the natural frequencies of the nonlocal double-nanobeam-system. Explicit closed-form expressions for natural frequencies are derived for the case when all four ends are simply-supported. The study highlights that the small-scale effects considerably influence the transverse vibration of double-nanobeam-systems. The nonlocal natural frequencies of double-nanobeam-system are smaller when compared to the corresponding local frequency values. The small-scale effects in the vibrating system are higher with increasing values of nonlocal parameter for the case of in-phase modes of vibration than in the out-of-phase modes of vibration. The increase in the stiffness of the...

The bending of single layer graphene sheets: the lattice versus continuum approach

The out-of-plane bending behaviour of single layer graphene sheets (SLGSs) is investigated using a special equivalent atomistic-continuum model, where the C-C bonds are represented by deep shear bending and axial stretching beams and the graphene properties by a homogenization approach. SLGS models represented by circular and rectangular plates are subjected to linear and nonlinear geometric point loading, similar to what is induced by an atomic force microscope (AFM) tip. The graphene models are developed using both a lattice and a continuum finite element discretization of the partial differential equations describing the mechanics of the graphene. The minimization of the potential energy allows us to identify the thickness, elastic parameters and force/displacement histories of the plates, in good agreement with other molecular dynamic (MD) and experimental results. We note a substantial equivalence of the linear elastic mechanical properties exhibited by circular and rectangular sheets, while some differences in the nonlinear geometric elastic regime for the two geometrical configurations are observed. Enhanced flexibility of SLGSs is observed by comparing the nondimensional force versus displacement relations derived in this work and the analogous ones related to equivalent plates with conventional isotropic materials.

DYNAMIC ANALYSIS OF FRAMED STRUCTURES WITH STATISTICAL UNCERTAINTIES

The forced harmonic vibration analysis of portal frames consisting of viscously damped beams with spatial stochastic variation of mass and stiffness properties is considered. The analysis is based on the assembly of element stochastic dynamic stiffness matrices. The solution involves inversion of the global dynamic stiffness matrix, which, in this case, turns out to be a complex-valued symmetric random matrix. Three alternative approximate procedures, namely, random eigenfunction expansion method, complex Neumann expansion method and combined analytical and simulation method are used to invert the matrix. The performance of these approximate procedures is evaluated using Monte Carlo simulation results.

Rates of change of eigenvalues and eigenvectors in damped dynamic system

Rates of change of eigenvalues and eigenvectors of a damped linear discrete dynamic system with respect to the system parameters are presented. A nonproportional viscous damping model is assumed. Because of the nonproportional nature of the damping, the mode shapes and natural frequencies become complex, and as a consequence the sensitivities of eigenvalues and elgenvectors are also complex. The results are presented in terms of the complex modes and frequencies of the second-order system, and the use of rather undesirable state-space representation is avoided. The usefulness of the derived expressions is demonstrated by considering an example of a nonproportionally damped two-degree-of-freedom system.

A mechanical equivalence for Poisson's ratio and thickness of C–C bonds in single wall carbon nanotubes

A formulation for the equivalent mechanical properties (Youngs modulus, shear modulus and Poissons ratio) of the C–C bond of CNTs under tensile and bending small deformations is derived. The C–C bonds behave like structural elements with negligible lateral deformation when stretched. The results from the model have been applied to structural mechanics truss assemblies representing single wall nanotube and nanoropes, providing good comparison with existing numerical and experimental results available.