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 Young's modulus, the shear modulus and Poisson's 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.

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.

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.

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.

This paper examines and contrasts the feasibility of joint state and parameter estimation of noisedriven chaotic systems using the extended Kalman filter (EKF), ensemble Kalman filter (EnKF), and particle filter (PF). In particular, we consider the chaotic vibration of a noisy Duffing oscillator perturbed by combined harmonic and random inputs ensuing a transition probability density function (pdf) of motion which displays strongly non-Gaussian features. This system offers computational simplicity while exhibiting a kaleidoscope of dynamical behavior with a slight change of input and system parameters. An extensive numerical study is undertaken to contrast the performance of various nonlinear filtering algorithms with respect to sparsity of observational data and strength of model and measurement noise. In general, the performance of EnKF is better than PF for smaller ensemble size, while for larger ensembles PF outperforms EnKF. For moderate measurement noise and frequent measurement data, EKF is able to correctly track the dynamics of the system. However, EKF performance is unsatisfactory in the presence of sparse observational data or strong measurement noise.

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.

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved.

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