Discrete Vibrations Research Articles

Separation of the Structure Signal by the Maximal Overlap Discrete Wavelet Transform and Fast Fourier Transform

Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.

Continuous supplementary tactile feedback can be applied (and then removed) to enhance precision manipulation

BackgroundHuman sensorimotor control of dexterous manipulation relies on afferent sensory signals. Explicit tactile feedback is generally not available to prosthetic hand users, who have to rely on incidental information sources to partly close the control loop, resulting in suboptimal performance and manipulation difficulty. Recent studies on non-invasive supplementary sensory feedback indicated that time-discrete vibrational feedback delivered upon relevant mechanical events outperforms continuous tactile feedback. However, we hypothesize that continuous tactile feedback can be more effective in non-routine manipulation tasks (i.e., tasks where the grip force is modified reactively in response to the sensory feedback due to the unpredictable behavior of the manipulated object, such as picking and holding a virtual fragile object) if delivered to highly sensitive areas. We further hypothesize that this continuous tactile feedback is not necessary during all the duration of the manipulation task, since adaptation occurs.MethodsWe investigated the effectiveness of continuous tactile feedback in precision manipulation, together with a new sensory feedback policy, where the continuous tactile feedback is gradually removed when the grasp reaches a steady state (namely, transient tactile feedback). We carried out an experiment in a virtual-reality setting with custom tactile feedback devices, which can apply continuous pressure and vibrations, attached to the thumb and index finger. We enrolled 24 healthy participants and instructed them to pick and hold a fragile virtual cube without breaking it. We compared their manipulation performance when using four different sensory feedback methods, i.e., no tactile feedback, discrete vibrations, continuous tactile feedback, and transient tactile feedback. The latter consisted of gradually removing the continuous feedback in the static phase of the grasp.ResultsContinuous tactile feedback leads to a significantly larger number of successful trials than discrete vibrational cues and no feedback conditions, yet the gradual removal of the continuous feedback yields to comparable outcomes. Moreover, the participants preferred the continuous stimuli over the vibrational cues and the removal in the static phase did not significantly impact their appreciation of the continuous tactile feedback.ConclusionsThese results advocate for the use of continuous supplementary tactile feedback for fine manipulation control and indicate that it can seamlessly be removed in the static phase of the grasp, possibly due to the mechanism of sensory adaptation. This encourages the development of energy-efficient supplementary feedback devices for prosthetic and telemanipulation applications, where encumbrance and power consumption are burdensome constraints.

Effect of vibration characteristics and vibror arrangement on the tactile perception of the upper arm in healthy subjects and upper limb amputees

BackgroundVibrotactile stimulation is a promising venue in the field of prosthetics to retrain sensory feedback deficits following amputation. Discrimination is well established at the forearm level but not at the upper arm level. Moreover, the effects of combining vibration characteristics such as duration and intensity has never been investigated.MethodWe conducted experiments on spatial discrimination (experiment 1) and tactile intensity perception (experiment 2), using 9 combinations of 3 intensities and 3 durations of vibror stimulations device. Those combinations were tested under 4 arrangements with an array of 6 vibrors. In both experiments, linear orientation aligned with the upper arm longitudinal axis were compared to circular orientation on the upper arm circumference. For both orientations, vibrors were placed either with 3cm space between the center of 2 vibrors or proportionally to the length or the circumference of the subject upper arm. Eleven heathy subjects underwent the 2 experiments and 7 amputees (humeral level) participated in the spatial discrimination task with the best arrangement found.ResultsExperiment 1 revealed that circular arrangements elicited better scores than the linear ones. Arrangements with vibrors spaced proportionally elicited better scores (up to 75% correct) than those with 3 cm spacing. Experiment 2, showed that the perceived intensity of the vibration increases with the intensity of the vibrors’ activation, but also with their duration of activation. The 7 patients obtained high scores (up to 91.67% correct) with the circular proportional (CP) arrangement.DiscussionThese results highlight that discrete and short vibrations can be well discriminated by healthy subjects and people with an upper limb amputation. These new characteristics of vibrations have great potential for future sensory substitution application in closed-loop prosthetic control.

Discrete atomic vibrations localized on defects in linear chains of atoms adsorbed by carbon nanobundles

The conditions of the existence and the main characteristics (frequencies, intensities, and attenuation parameters) of discrete vibrational levels caused by structural defects of linear chains of inert gas atoms adsorbed on the surface of nanotubes aggregated in nanobundles, are calculated and analyzed. Discrete vibrational levels lying both above and below the band of the quasi-continuous spectrum of the chain are considered. Analytical expressions obtained for the frequencies of these discrete levels make it possible to determine with high precision the defect parameters (difference in the interaction with the substrate and with the atoms of the chain) basing on optical measurements.

Oscillators: Phenomenological mappings and analogies: Second part: Structural analogy and chains

New analytical and numerical results of dynamics for both linear and nonlinear system with two degrees of freedom are presented. For the mechanical chain system with two degrees of freedom, oscillations are investigated analytically and numerically with corresponding comparison between free and forced oscillatory dynamics of linear and nonlinear system. Using the Mihailo Petrovic's theory of elements of mathematical phenomenology, the phenomenological mappings in vibrations, signals, resonances and dynamical absorptions in models with two degrees of freedom-abstractions of different real system dynamics are identified, as well as in eigen time functions of multi-deformable coupled body system dynamics, and presented. Mathematical description of a chain mechanical system with two mass particles coupled by linear and nonlinear elastic springs and with two degree of freedom is given. By the analysis of corresponding solutions for free and forced vibrations, series of related two-frequency regimes and resonant states, as well as dynamical absorption states, are identified. Phenomenological mappings are used to explain dynamics in two deformable body (beams, plates or membranes) systems. In short, new analytical and numerical results of linear and non-linear dynamics of a system with two-degrees of freedom in analogy with eigen time functions oscillations of transversal vibrations of two body system dynamics are presented. Structural analogies are identified between eigen time functions of different multi-coupled deformable body transversal vibrations (plates, beams, belts or membranes). Mathematical phenomenology elements and phenomenological mappings are applied in the scientific results integration. Mathematical analogy and phenomenological mappings of linear and nonlinear singular phenomena in discrete and multi-body system vibrations (torsional system, multi-pendulum system, coupled electrical circuit and multi-deformable-body oscillations-beams, plates, membranes) are performed. Structural analogy is used to explain phenomenological mappings between displacements of the mass particles in discrete system and eigen time functions in one eigen amplitude mode of dynamics in two coupled deformable body (beams, plates or membranes) systems.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Early modality-specific somatosensory cortical regions are modulated by attended visual stimuli: interaction of vision, touch and behavioral intent.

Bimodal interactions between relevant visual and tactile inputs can facilitate attentional modulation at early stages in somatosensory cortices to achieve goal-oriented behaviors. However, the specific contribution of each sensory system during attentional processing and, importantly, how these interact with the required behavioral motor goals remains unclear. Here we used electroencephalography and event-related potentials (ERPs) to test the hypothesis that activity from modality-specific somatosensory cortical regions would be enhanced with task-relevant bimodal (visual-tactile) stimuli and that the degree of modulation would depend on the difficulty of the associated sensory-motor task demands. Tactile stimuli were discrete vibrations to the index finger and visual stimuli were horizontal bars on a computer screen, both with random amplitudes. Streams of unimodal (tactile) and crossmodal (visual and tactile) stimuli were randomly presented and participants were instructed to attend to one type of stimulus (unimodal or crossmodal) and responses involved either an indication of the presence of an attended stimulus (detect), or the integration and summation of two stimulus amplitudes using a pressure-sensitive ball (grade). Force-amplitude associations were learned in a training session, and no feedback was provided during the task. ERPs were time-locked to tactile stimuli and extracted for early modality-specific components (P50, P100, N140). The P50 was enhanced with bimodal (visual-tactile) stimuli that were attended to. This was maximal when the motor requirements involved integration of the two stimuli in the grade task and when the visual stimulus occurred before (100 ms) the tactile stimulus. These results suggest that visual information relevant for movement modulates somatosensory processing as early as the primary somatosensory cortex (S1) and that the motor behavioral context influences this likely through interaction of top-down attentional and motor preparatory systems with more bottom-up crossmodal influences.

Phonon lasing in an electromechanical resonator.

An electromechanical resonator harboring an atomlike spectrum of discrete mechanical vibrations, namely, phonon modes, has been developed. A purely mechanical three-mode system becomes available in the electromechanical atom in which the energy difference of the two higher modes is resonant with a long-lived lower mode. Our measurements reveal that even an incoherent input into the higher mode results in coherent emission in the lower mode that exhibits all the hallmarks of phonon lasing in a process that is reminiscent of Brillouin lasing.

Exciton-phonon scattering and photoexcitation dynamics inJ-aggregate microcavities

We have developed a model accounting for the photoexcitation dynamics and the photoluminescence of strongly coupled $J$-aggregate microcavities. Our model is based on a description of the $J$-aggregate film as a disordered Frenkel exciton system, in which relaxation occurs due to the presence of a thermal bath of molecular vibrations. In a strongly coupled microcavity exciton polaritons are formed, mixing super-radiant excitons and cavity photons. The calculation of the microcavity steady-state photoluminescence, following a cw nonresonant pumping, is carried out. The experimental photoluminescence intensity ratio between upper and lower polariton branches is accurately reproduced. In particular, both thermal activation of the photoluminescence intensity ratio and its Rabi splitting dependence are a consequence of the bottleneck in the relaxation, occurring at the bottom of the excitonic reservoir. The effects due to radiative channels of decay of excitons and to the presence of a particular set of discrete optical molecular vibrations active in relaxation processes are investigated.

Electron Collisions with Formic Acid Monomer and Dimer

Processes induced by the attachment of slow electrons to formic acid and its hydrogen-bonded dimer were studied. The elastic cross section and the cross section for the excitation of low quanta of discrete vibrations were found to be of a similar magnitude for both targets. A dramatic difference was found in the excitation of a vibrational quasicontinuum in the 1-2 eV range with the ejection of very slow electrons (E<0.1 eV), which was about 20x more intense in the dimer. The association of two formic acid molecules to form a dimer thus dramatically increases the power to quasithermalize electrons arriving with energies in the 1-2 eV energy range. Rapid electron-driven intracluster proton transfer is invoked to explain the observation.

Effect of external Gaussian random field on phonon spectrum of linear atomic chains

We present the theoretical study of the effect of external random field characterized by a Gaussian probability distribution function on the continuous phonon spectrum of one-dimensional (1D) chain, based on the Jacobian matrix method. The cumulative effect of the random field and simple isotopic defect is studied analytically and numerically. The Gaussian random field removes a square-root divergence appearing in the phonon spectrum of ideal 1D chain. The impurity phonon DOS shows strong dependence on the variance and the mean of the random field and exhibits very different behavior from the non-random case: the continuous spectrum is expanded and the δ-peak, describing discrete impurity vibrations in the non-random chain with the impurity, falls into a continuous zone.

Photoinduced quantum interference antiresonances in pi-conjugated polymers.

We observed photoinduced quantum interference antiresonances between several discrete infrared-active vibrations and the lower-polaron continuous absorption band in a series of pi-conjugated polymer films having superior planar orders, where the polaron transition energy is relatively small. The photoinduced Fano-type antiresonances are well explained by extending the amplitude mode model beyond the adiabatic limit. The agreement between the data and the model confirms the presence of a continuous electronic band above the polaron state. We show that high frequency modes are strongly coupled to electrons, with implications for superconductivity.

Méthode de Le Verrier–Souriau et équations différentielles linéaires

A crucial step of algorithms allowing the study of discrete mechanical system vibrations is the determination of eigenmodes and eigenvalues. The accuracy of the results is of great importance because the stability study of the system depends on them. Eigenvalues can be found with a very good precision, however the eigenmodes determination is awkward: their direction could present significant instabilities. We proposed a method which avoids the necessity of doing eigenmodes research and so the attendant instabilities. It is based on Le Verrier–Souriau algorithm usually reserved for the resolution of linear algebraic systems.

Size Segregation in Granular Beds Subject to Discrete and Continuous Vertical Oscillations

ABSTRACTSize segregation of particulates is of concern in a number of industries that handle materials such as chemicals, pharmaceuticals, fertilizers, and food products. Of particular interest in this paper is segregation resulting from externally applied vibration. In industrial applications this vibration may either be applied intentionally in devices such as vibrating conveyors or “live wall” hoppers, or unintentionally during material handling and transport. This paper investigates size segregation in granular beds subject to discrete “taps” and continuous, sinusoidal vertical vibration. The results from discrete element computer simulations indicate that the rise rate of a single impurity increases monotonically with amplitude for discrete vibrations but for continuous vibrations the rise rate increases, reaches a maximum value, then decreases as the oscillation amplitude increases.

A coarse-grained model for granular compaction and relaxation

We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the same collective structure. We rigourously construct the model from first principles and show that numerical solutions compare favourably with a range of experimental results. This includes the logarithmic relaxation towards a statistical steady state, the effect of varying the intensity of vibration resulting in a so-called ``annealing'' curve, and the power spectrum of density fluctuations in the steady state itself. A mean field version of the model is introduced which shares many features with the exact model and is open to quantitative analysis.

The Apprehension and Cognition of Music

When we listen to a piece of music, whether it be a fugue by Bach, a song by Schubert, or a symphony by Beethoven, the actual physical, objective, stimuli which reach our ears consist of incredibly complicated pulsations of air pressure. These produce equally complicated vibrations of the tympanum or ear-drum, and so set up successions of nervous impulses in the brain. But our subjective experience of the music, the thing that we actually hear, consists of a logical and meaningful sequence of harmoniously interrelated auditory impressions, possessing form and unity both as a whole and in detail. How then does this series of discrete air vibrations, which are produced by the musical instruments or voices of the performers, become transformed and organised into the mental thing that we call music? In other words, what is the psychological nature of our perception or cognition of music?