Nonlinear modal interactions in clamped-clamped mechanical resonators

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. Experimentally observed complex nonlinear dynamics of the coupled modes are quantitatively captured by a model which couples the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams.Comment: 5 pages, 3 figure

Parametric resonances in electrostatically interacting carbon nanotube arrays

We study, numerically and analytically, a model of a one-dimensional array of carbon nanotube resonators in a two-terminal configuration. The system is brought into resonance upon application of an AC-signal superimposed on a DC-bias voltage. When the tubes in the array are close to each other, electrostatic interactions between tubes become important for the array dynamics. We show that both transverse and longitudinal parametric resonances can be excited in addition to primary resonances. The intertube electrostatic interactions couple modes in orthogonal directions and affect the mode stability.Comment: 11 pages, 12 figures, RevTeX

Noise-enabled precision measurements of a Duffing nanomechanical resonator

We report quantitative experimental measurements of the nonlinear response of a radiofrequency mechanical resonator, with very high quality factor, driven by a large swept-frequency force. We directly measure the noise-free transition dynamics between the two basins of attraction that appear in the nonlinear regime, and find good agreement with those predicted by the one-dimensional Duffing equation of motion. We then measure the response of the transition rates to controlled levels of white noise, and extract the activation energy from each basin. The measurements of the noise-induced transitions allow us to obtain precise values for the critical frequencies, the natural resonance frequency, and the cubic nonlinear parameter in the Duffing oscillator, with direct applications to high sensitivity parametric sensors based on these resonators.Comment: 5 pages, 5 figure

Quantum Effects in the Mechanical Properties of Suspended Nanomechanical Systems

We explore the quantum aspects of an elastic bar supported at both ends and subject to compression. If strain rather than stress is held fixed, the system remains stable beyond the buckling instability, supporting two potential minima. The classical equilibrium transverse displacement is analogous to a Ginsburg-Landau order parameter, with strain playing the role of temperature. We calculate the quantum fluctuations about the classical value as a function of strain. Excitation energies and quantum fluctuation amplitudes are compared for silicon beams and carbon nanotubes.Comment: RevTeX4. 5 pages, 3 eps figures. Submitted to Physical Review Letter

Dissipation in graphene and nanotube resonators

Different damping mechanisms in graphene nanoresonators are studied: charges in the substrate, ohmic losses in the substrate and the graphene sheet, breaking and healing of surface bonds (Velcro effect), two level systems, attachment losses, and thermoelastic losses. We find that, for realistic structures and contrary to semiconductor resonators, dissipation is dominated by ohmic losses in the graphene layer and metallic gate. An extension of this study to carbon nanotube-based resonators is presented.Comment: Published version with updated reference

The Effect of Mechanical Resonance on Josephson Dynamics

We study theoretically dynamics in a Josephson junction coupled to a mechanical resonator looking at the signatures of the resonance in d.c. electrical response of the junction. Such a system can be realized experimentally as a suspended ultra-clean carbon nanotube brought in contact with two superconducting leads. A nearby gate electrode can be used to tune the junction parameters and to excite mechanical motion. We augment theoretical estimations with the values of setup parameters measured in the samples fabricated. We show that charging effects in the junction give rise to a mechanical force that depends on the superconducting phase difference. The force can excite the resonant mode provided the superconducting current in the junction has oscillating components with a frequency matching the resonant frequency of the mechanical resonator. We develop a model that encompasses the coupling of electrical and mechanical dynamics. We compute the mechanical response (the effect of mechanical motion) in the regime of phase bias and d.c. voltage bias. We thoroughly investigate the regime of combined a.c. and d.c. bias where Shapiro steps are developed and reveal several distinct regimes characteristic for this effect. Our results can be immediately applied in the context of experimental detection of the mechanical motion in realistic superconducting nano-mechanical devices.Comment: 18 pages, 11 figure

Telemonitoring after discharge from hospital with heart failure: cost-effectiveness modelling of alternative service designs.

Objectives To estimate the cost-effectiveness of remote monitoring strategies versus usual care for adults recently discharged after a heart failure (HF) exacerbation. Design Decision analysis modelling of cost-effectiveness using secondary data sources. Setting Acute hospitals in the UK. Patients Patients recently discharged (within 28 days) after a HF exacerbation. Interventions Structured telephone support (STS) via human to machine (STS HM) interface, (2) STS via human to human (STS HH) contact and (3) home telemonitoring (TM), compared with (4) usual care. Main outcome measures The incremental cost per quality-adjusted life year (QALY) gained by each strategy compared to the next most effective alternative and the probability of each strategy being cost-effective at varying willingness to pay per QALY gained. Results TM was the most cost-effective strategy in the scenario using these base case costs. Compared with usual care, TM had an estimated incremental cost effectiveness ratio (ICER) of £11 873/QALY, whereas STS HH had an ICER of £228 035/QALY against TM. STS HM was dominated by usual care. Threshold analysis suggested that the monthly cost of TM has to be higher than £390 to have an ICER greater than £20 000/QALY against STS HH. Scenario analyses performed using higher costs of usual care, higher costs of STS HH and lower costs of TM do not substantially change the conclusions. Conclusions Cost-effectiveness analyses suggest that TM was an optimal strategy in most scenarios, but there is considerable uncertainty in relation to clear descriptions of the interventions and robust estimation of costs