On the mechanics of monofilaments used in touch sensory perception

The buckling of a slender monofilament is a standard clinical method used to assess touch sensory perception, with specific applications to somatosensory impairment in patients after a stroke, detecting carpal tunnel syndrome, and as a prognosis tool for diabetic peripheral neuropathy. The basis of this approach is the Semmes-Weinstein monofilament, which comprises a calibrated set of thin, polycarbonate rods with different diameters. Application of a monofilament onto the surface of the skin with increasing pressure causes the rod to buckle. That is, at a specific force of pushing down on the far end, the monofilament suddenly bows out sidewards - the buckling load. The ability of a patient to detect increasingly finer monofilament buckling (pressure threshold) is then used to assess sensory deterioration. This paper addresses the underlying mechanics of the buckling process. Despite the accuracy and repeatability problems that have been reported in the literature, and the necessarily subjective aspects of sensory physiology, the mathematical modeling of the monofilament buckling is unambiguous and provides some fundamental insight into the parameters that underlie this approach.

3D-printing and cylinder buckling: challenges and opportunities

Cylinder buckling is notoriously sensitive to small geometric imperfections. This is an underlying motivation for the use of knock-down factors in the design process, especially in circumstances in which minimum weight is a key design goal, an approach well-established at NASA, for example. Not only does this provide challenges in the practical design of this commonly occurring structural load-bearing configuration, but also in the carefully controlled laboratory setting. The recent development of 3D-printing (additive manufacturing) provides an appealing experimental platform for conducting relatively high-fidelity experiments on the buckling of cylinders. However, in addition to geometric precision, there are a number of shortcomings with this approach, and this article seeks to describe the challenges and opportunities associated with the use of 3D-printing in cylinder buckling in general, and probing the robustness of equilibrium configurations in particular. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Experimental study of isolas in nonlinear systems featuring modal interactions

The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas.

On the experimental identification of unstable static equilibria

This paper shows how the presence of unstable equilibrium configurations of elastic continua is reflected in the behaviour of transients induced by large perturbations. A beam that is axially loaded beyond its critical state typically exhibits two buckled stable equilibrium configurations, separated by one or more unstable equilibria. If the beam is then loaded laterally (effectively like a shallow arch) it may snap-through between these states, including the case in which the loading is applied dynamically and of short duration, i.e. an impact. Such impacts, if applied at random locations and of random strength, will generate an ensemble of transient trajectories that explore the phase space. Given sufficient variety, some of these trajectories will possess initial energy that is close to (just less than or just greater than) the energy required to cause snap-through and will have a tendency to slowdown as they pass close to an unstable configuration: a saddle point in a potential energy surface, for example. Although this close-encounter is relatively straightforward in a system characterized by a single degree of freedom, it is more challenging to identify in a higher order or continuous system, especially in a (necessarily) noisy experimental system. This paper will show how the identification of unstable equilibrium configurations can be achieved using transient dynamics.

On damping in the vicinity of critical points

The effect of damping on the behaviour of oscillations in the vicinity of bifurcations of nonlinear dynamical systems is investigated. Here, our primary focus is single degree-of-freedom conservative systems to which a small linear viscous energy dissipation has been added. Oscillators with saddle-node, pitchfork and transcritical bifurcations are shown analytically to exhibit several interesting characteristics in the free decay response near a bifurcation. A simple mechanical oscillator with a transcritical bifurcation is used to experimentally verify the analytical results. A transcritical bifurcation was selected because it may be used to represent generic bifurcation behaviour. It is shown that the damping ratio can be used to predict a change in the stability with respect to changing system parameters.

A heuristic method for identifying chaos from frequency content

The sign of the largest Lyapunov exponent is the fundamental indicator of chaos in a dynamical system. However, although the extraction of Lyapunov exponents can be accomplished with (necessarily noisy) the experimental data, this is still a relatively data-intensive and sensitive endeavor. This paper presents an alternative pragmatic approach to identifying chaos using response frequency characteristics and extending the concept of the spectrogram. The method is shown to work well on both experimental and simulated time series.

Multiplexing superparamagnetic beads driven by multi-frequency ratchets

Here, we explore the single particle dynamics of superparamagnetic beads exposed to multifrequency ratchets. Through a combination of theory, simulation, and experiment, we determine the important tuning parameters that can be used to implement multiplexed separation of polydisperse colloidal mixtures. In particular, our results demonstrate that the ratio of driving frequencies controls the transition between open and closed trajectories that allow particles to be transported across a substrate. We also demonstrate that the phase difference between the two frequencies controls not only the direction of motion but also which particles are allowed to move within a polydisperse mixture. These results represent a fundamentally different approach to colloidal separation than the previous methods which are based on controlling transitions between phase-locked and phase-slipping regimes, and have a higher degree of multiplexing capabilities that can benefit the fields of biological separation and sensing as well as provide crucial insights into general ratchet behavior.

Transport of superparamagnetic beads through a two-dimensional potential energy landscape

The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an external rotating field oriented at an angle θ relative to the magnetization direction of the substrate. The bead's motion was highly sensitive to the angle of the driving field near critical angles and to various system parameters, including bead size, rotation frequency, and substrate pole density. Our results suggest the possibility of using this behavior in a highly discriminative colloidal separation system, in which two different bead types can be tuned to move in orthogonal directions.

The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

We present theoretical, numerical, and experimental analyses on the non-linear dynamic behavior of superparamagnetic beads exposed to a periodic array of micro-magnets and an external rotating field. The agreement between theoretical and experimental results revealed that non-linear magnetic forcing dynamics are responsible for transitions between phase-locked orbits, sub-harmonic orbits, and closed orbits, representing different mobility regimes of colloidal beads. These results suggest that the non-linear behavior can be exploited to construct a novel colloidal separation device that can achieve effectively infinite separation resolution for different types of beads, by exploiting minor differences in their bead's properties. We also identify a unique set of initial conditions, which we denote the "devil's gate" which can be used to expeditiously identify the full range of mobility for a given bead type.

Nonlinear dynamics of superparamagnetic beads in a traveling magnetic-field wave

The nonlinear dynamic behavior of superparamagnetic beads exposed to a periodic array of micromagnets and an external rotating field is simulated as a function of the relative size of the bead with respect to the micromagnet size and the strength of the external field relative to the pole density of the substrate. For large bead sizes, it is confirmed that the motion of the beads corresponds to the dynamics of an overdamped nonlinear harmonic oscillator. For lower bead sizes, additional subharmonic locking effects are observed along with the emergence of bounded orbits. These results qualitatively support previous experimental investigations of traveling-wave magnetophoresis and provide guidelines for achieving nearly infinite separation resolution between differently sized beads.

Bragg grating-based fibre optic sensors in structural health monitoring

This work first considers a review of the dominant current methods for fibre Bragg grating wavelength interrogation. These methods include WDM interferometry, tunable filter (both Fabry-Perot and acousto-optic) demultiplexing, CCD/prism technique and a newer hybrid method utilizing Fabry-Perot and interferometric techniques. Two applications using these techniques are described: hull loads monitoring on an all-composite fast patrol boat and bolt pre-load loss monitoring in a composite beam in conjunction with a state-space modelling data analysis technique.

Use of chaotic excitation and attractor property analysis in structural health monitoring

This work explores the utility of attractor-based approaches in the field of vibration-based structural health monitoring. The technique utilizes the unique properties of chaotic signals by driving the structure directly with the output of a chaotic oscillator. Using the Kaplan-Yorke conjecture, the Lyapunov exponents of the driving signal may be tuned to the dominant eigenvalues of the structure, thus controlling the dimension of the structural response. Data are collected at various stages of structural degradation and a simple nonlinear model, constructed from the undamaged data, is used to make predictions for the damaged response data. Prediction error is then introduced as a "feature" for classifying the magnitude of the damage. Results are presented for an experimental cantilevered beam instrumented with fiber-optic strain sensors.