Unidirectional direct current in coupled nanomechanical resonators by tunable symmetry breaking

We investigate theoretically the non-linear dynamics of a coupled nanomechanical oscillator. Under a weak radio frequency excitation, the resonators can be parametrically tuned into a self-sustained oscillatory regime. The transfer of electrons from one contact to the other is then mechanically assisted, generating a rectified current. The direction of the rectified current is, in most unstable regions, determined by the phase shift between the mechanical oscillations and the signal. However, we locate intriguing parametrical regions of uni-directional rectified current, suggesting a practical scheme for the realization of a self-powered device in the nanoscale. In these regions, a dynamical symmetry breaking is induced by the non-linear coupling of the mechanical and electrical degrees of freedom. When operating within the Coulomb blockade limit, we locate bands of instability of enhanced gain.Comment: 5 pages, 4 figure

Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices

The squeeze effect in non-integrable Hamiltonian systems

In non-integrable Hamiltonian systems (represented by mappings of the plane) the stable island around an elliptic fixed point is generally squeezed into the fixed point by three saddle points, when the rotation number ρ of the motion at the fixed point approaches 1/3. At ρ=1/3 the island is reduced to one single point.\ud A detailed investigation of this squeeze effect, and some of its global implications, is presented by means of a typical two-dimensional area-preserving map. In particular, it turns out that the squeeze effect occurs in any mapping for which the Taylor expansion around the fixed point contains a quadratic term, whereas it does not occur if the first non-linear term is cubic. We illustrate this with two physical examples: a compass needle in an oscillating field, showing the squeeze effect, and a ball which bounces on a vibrating plane, for which the squeeze effect does not occur

Probing nonlinear mechanical effects through electronic currents: the case of a nanomechanical resonator acting as electronic transistor

We study a general model describing a self-detecting single electron transistor realized by a suspended carbon nanotube actuated by a nearby antenna. The main features of the device, recently observed in a number of experiments, are accurately reproduced. When the device is in a low current-carrying state, a peak in the current signals a mechanical resonance. On the contrary, a dip in the current is found in high current-carrying states. In the nonlinear vibration regime of the resonator, we are able to reproduce quantitatively the characteristic asymmetric shape of the current-frequency curves. We show that the nonlinear effects coming out at high values of the antenna amplitude are related to the effective nonlinear force induced by the electronic flow. The interplay between electronic and mechanical degrees of freedom is understood in terms of an unifying model including in an intrinsic way the nonlinear effects driven by the external probe.Comment: 7 pages, 3 figures, submitted to Physical Review

A Natural Seismic Isolating System: The Buried Mangrove Effects

The Belleplaine test site, located in the island of Guadeloupe (French Lesser Antilles) includes a three-accelerometer vertical array, designed for liquefac- tion studies. The seismic response of the soil column at the test site is computed using three methods: the spectral ratio method using the vertical array data, a numerical method using the geotechnical properties of the soil column, and an operative fre- quency domain decomposition (FDD) modal analysis method. The Belleplaine test site is characterized by a mangrove layer overlaid by a stiff sandy deposit. This con- figuration is widely found at the border coast of the Caribbean region, which is exposed to high seismic hazard. We show that the buried mangrove layer plays the role of an isolation system equivalent to those usually employed in earthquake engineering aimed at reducing the seismic shear forces by reducing the internal stress within the structure. In our case, the flexibility of the mangrove layer reduces the distortion and the stress in the sandy upper layer, and consequently reduces the potential of liquefaction of the site

Design considerations for micromechanical sensors using encapsulated built-in resonant strain gauges

This paper describes the various design aspects for micromechanical sensors consisting of a structure with encapsulated built-in resonant strain gauges. Analytical models are used to investigate the effect of device parameters on the behaviour of a pressure sensor and a force sensor. The analyses indicate that the sealing cap can have a strong degrading effect on the device performance if the thicknesses of the cap and of the supporting structure are of the same order of magnitude. A novel design, employing bossed structures, is described, which reduces the design complexity and virtually eliminates the influence of the cap on the sensitivity of the sensor

Aerodynamic behavior of the bridge of a capacitive RF MEMS switch

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The present paper proposes a coupled 3D multi-physics model and presents the results of its transient simulation, for a RF MEMS capacitive switch of bridge-type. The fluid structure interaction (FSI) simulation sustains time-varying viscous damping and modified time response of the bridge deflection compared to the actuation modulation above closing of the switch. Complex 3D geometries of the bridge were rarely taken into account in viscous damping assessment much less in the simulation of the full flow around the bridge of the switch. The final goal of the paper is to obtain the dependency of an equivalent damping coefficient with respect to time, to be used in subsequent reduced order models for the switch, that include the aerodynamic behaviour of the switch