Nano-mechanical sensing exploiting frequency shift of a cantilever beam to obtain the mass of an object is well
established. This paper is aimed at investigating the possibility of sensing mass as well as rotary inertia of an
attached object. The rotary inertia of an object gives additional insight into its shape, which is a key motivation
of this work. It is shown that by using two modes it is possible to formulate two coupled nonlinear equations,
which it turn can be solved to obtain mass and rotary inertia simultaneously from the frequency shifts of first
two vibration modes. Analytical results are validated using high fidelity molecular mechanics simulation.
This paper investigates the use of electrostatic forces for vibration control of MEMS devices. A micro beam subject to electrostatic loading is considered. The electrostatic forces cause softening nonlinearity and their amplitudes are proportional to the square of applied DC voltages. An optimization problem is set up to minimize the vibration level of the micro-beam at given excitation frequencies. A new method based on incrementing nonlinear control parameters of the system and Harmonic Balance is used to obtain the required DC voltages that suppress unwanted vibration of the micro-beam. The results are illustrated using numerical simulations
This paper develops an equivalent linear model for piezomagnetoelastic energy harvesters under broadband
random ambient excitations. Piezomagnetoelastic harvesters are used for powering low power electronic sensor
systems. Nonlinear behaviour arising due to the vibration in a magnetic field makes piezomagnetoelastic energy
harvesters different from the more classical piezoelastic energy harvesters. First numerical simulation of the
nonlinear model is presented and then an equivalent linearization based analytical approach is developed for the
analysis of harvested power. A cosed-form approximate expression for the ensemble average of the harvested
power is derived. The equivalent model is seen to capture the details of the nonlinear model and also provides
more details to the behaviour of the harvester to random excitation. Our results show that it is possible to
optimally design the system such that the mean harvested power is maximized for a given strength of the input
broadband random ambient excitation.
Graphene nanoribbons (GNRs) are novel interesting nanostructures for the electronics industry, whereas their state as metallic or semiconductor material depends on the chirality of the graphene. We model the natural frequencies and the wave propagation characteristics of GNRs 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 wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic structures. We demonstrate that the thickness and equilibrium lengths for the different dynamic cases are different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length), in particular when considering out-of-plane flexural deformations. These parameters have to be taken into account when nanoribbons are designed as nano-oscillators.
This paper considers the analysis of structures with nonlocal damping, where the reaction force at any point is obtained as a weighted average of state variables over a spatial domain. The model yields an integro-differential equation, and obtaining closed form solutions is only possible for a limited range of boundary conditions by the transfer function method. Approximate solutions using the Galerkin method for beams are presented for typical spatial kernel functions, for a nonlocal viscoelastic foundation model. This requires the approximation of the displacement to be defined over the whole domain. To treat more complicated problems with variable damping parameters, non-uniform section properties, intermediate supports or arbitrary boundary conditions, a finite element method for beams is developed. However, in nonlocal damping models, nodes remote from the element do have an effect on the energy expressions, and hence the damping matrix is no longer block diagonal. The expressions for these direct and cross damping matrices are obtained for separable spatial kernel functions. The approach is demonstrated on a range of examples.