Beat Phenomenon Research Articles

Brain Responses to a 6-Hz Binaural Beat: Effects on General Theta Rhythm and Frontal Midline Theta Activity.

A binaural beat is a beat phenomenon that is generated by the dichotic presentation of two almost equivalent pure tones but with slightly different frequencies. The brain responses to binaural beats remain controversial; therefore, the aim of this study was to investigate theta activity responses to a binaural beat by controlling factors affecting localization, including beat frequency, carrier tone frequency, exposure duration, and recording procedure. Exposure to a 6-Hz binaural beat on a 250 Hz carrier tone for 30 min was utilized in this study. Quantitative electroencephalography (QEEG) was utilized as the recording modality. Twenty-eight participants were divided into experimental and control groups. Emotional states were evaluated by Brunel Mood Scale (BRMUS) before and after exposing to the stimulus. The results showed that theta activity was induced in the entire cortex within 10 min of exposure to the stimulus in the experimental group. Compared to the control group, theta activity was also induced at the frontal and parietal-central regions, which included the Fz position, and left hemisphere dominance was presented for other exposure durations. The pattern recorded for 10 min of exposure appeared to be brain functions of a meditative state. Moreover, tension factor of BRUMS was decreased in experimental group compared to control group which resembled the meditation effect. Thus, a 6-Hz binaural beat on a 250 Hz carrier tone was suggested as a stimulus for inducing a meditative state.

Single-Photon Interference due to Motion in an Atomic Collective Excitation.

We experimentally demonstrate the heralded generation of bichromatic single photons from an atomic collective spin excitation (CSE). The photon arrival times display collective quantum beats, a novel interference effect resulting from the relative motion of atoms in the CSE. A combination of velocity-selective excitation with strong laser dressing and the addition of a magnetic field allows for exquisite control of this collective beat phenomenon. The present experiment uses a diamond scheme with near-IR photons that can be extended to include telecommunications wavelengths or modified to allow storage and retrieval in an inverted-Y scheme.

Ringing response of offshore triceratops

Triceratops is a new generation offshore platform, proposed for oil and gas exploration in ultra-deep waters. Deck is supported by buoyant legs, but isolated from each other by ball joints. Buoyant legs are taut-moored to the seabed using tethers with high initial pretension. The presence of ball joints makes the platform less sensitive to the encountered environmental loads. The present study investigates transient response of triceratops under distinctly high sea waves through numerical studies. Spectral analysis is carried out to estimate the ringing response, which is highly nonlinear. While ringing waves are simulated with parametric variation, JONSWAP spectrum is used to simulate the time series of large irregular waves causing ringing response on triceratops. Based on the numerical studies carried out, a gradual decay is seen in the response of buoyant legs looking similar to that of a beat phenomenon. Deck response shows a significant reduction in rotational degrees-of-freedom than that of the buoyant legs due to the presence of ball joints, which aids the platform to remain operational even under high sea states. Statistical analyses on tether tension variation show that ringing caused by strong asymmetric waves is responsible for causing impact load on the platform.

Dynamic analysis of a pulley–belt system with spring supports

In this paper, a new dynamic model for a pulley–belt system is proposed, in which the system considers not only the deflection of a belt but also the rigid-body motion of pulleys. This paper focuses on the effects of the rigid-body motion, which determines the dynamic characteristics of the pulley–belt system with spring supports. To this end, by using Hamilton’s principle, four linear governing equations of motion and eight boundary conditions are derived. The Galerkin method is used to discretize the equations of motion. The eigenvalue problems are solved to analyze the natural frequencies and mode shapes that are affected by the rigid-body motion of the system. The natural frequency loci veering and mode exchange are investigated for different moving velocities of the belt and various values of the spring constant. In addition, the beat phenomena in the upper and lower belts are also analyzed. Based on these analyses, we show that the natural frequency veering and beat phenomena are caused by a coupling effect between the rigid-body motion and belt deflection in the pulley–belt system.

Ground-state properties of the one-dimensional unconstrained pseudo-anyon Hubbard model

We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle $\theta\approx\pi$, we observe a wealth of exotic properties including {a first order transition} between different superfluid phases and a {two-component} partially paired phase for large fillings without need of an additional three-body hardcore constraint.In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid {ground states} for vanishing or even small attractive on-site interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single particle correlation functions.We show how some features of various ground state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame.

Dynamic responses of an engine front-end accessory belt drive system with pulley eccentricities via two spatial discretization methods

In this study, a generic mathematical model for calculating the natural frequencies and the dynamic responses of a typical front-end accessory drive system with any number of pulleys and arbitrary configurations of the tensioner and pulleys is established. The belt bending stiffness and the pulley eccentricities are considered in this model, and their influences on the natural frequency and the dynamic responses of the front-end accessory drive system are examined. A generic spatial discretization method and a Galerkin discretization method, which uses Lagrange multipliers to enhance the boundary conditions, are presented to discretize the continuous belt spans and to transform the governing partial differential equations into ordinary differential equations. The accuracies of the generic spatial discretization method and the Galerkin discretization method are validated by modal tests, and the advantages of the generic spatial discretization method with respect to the efficiency and the convenience of implementation are assessed by comparing the generic spatial discretization method with the Galerkin discretization method and the two-layer iteration approach. The dynamic responses of the typical front-end accessory drive system at different operational velocities are calculated from the governing ordinary differential equations derived from these two methods. It is shown that large vibration amplitudes occur in certain belt spans owing to the resonance conditions or the beat phenomena in certain operational conditions and that the belt bending stiffness has a negligible influence on the vibrations of the belt drive system because its value is small.

Influence of beat phenomenon on direction of arrival estimation based on a single vector hydrophone

The vector hydrophone can measure sound pressure and orthogonal components of particle velocity co-locately in space and simultaneously in time. DOA (direction of arrival) estimation based on a single vector hydrophone has attracted extensive attention. Beat phenomenon can cause confusion in the DOA estimation results. In this paper, the impact mechanism of beat phenomenon to DOA estimation by cross spectrum method and average acoustic intensity method is explored through theoretical study and simulation. The result shows that beat phenomenon causes the change of sound pressure and vibration velocity amplitude with time and leads to DOA estimation results of these two methods are instability eventually. First, DOA is estimated by the average sound intensity method, if the temporal resolution is smaller than the minimum envelope period, the DOA estimation will change over time; Second, DOA is estimated by the cross spectral method, if the FFT frequency resolution is greater than frequency difference, it is unable to distinguish the frequency of these two signals. Subsequent operations will also be confused by two signal energy, causing error estimates. In the end, the solutions and application examples are proposed. The conclusion could be applied to improve the DOA estimation performance of a single vector hydrophone.

Dynamic characteristics of immersed plate-type fuel assemblies under seismic excitation

The present paper deals with the investigation of plate type fuel assemblies immersed in still water under simulated seismic load. In a typical high flux reactor, plate type fuel assemblies are closely arranged to achieve the high neutron flux. The coolant filled gaps between the fuel assemblies play a significant role in determining and altering its dynamic characteristics. To account the added mass and damping effects posed by the fluid film present in these gaps, a number of experimental and numerical case studies are conducted for a specific range of fluid film thickness for single and double plate systems (SPS and DPS) and square channels. A coupling beat phenomenon has been observed in DPS for a certain range of fluid film thickness. To investigate the beating phenomenon further, wavelet analysis is performed to identify the frequencies in the vibration of submerged plates. It is observed that added mass coefficient (cm) follows a linear relation while the damping coefficient (cv) follows a cubic relation with fluid film thickness. It is also found that maximum displacement of the fuel assembly is significantly small than the fluid film gap, as per the present correlations under the seismic load.

水平浅瀬域の固有振動と入射波のビート現象について

It is considered that proper oscillations with several minute periods are driven in shallow water by swells which invade the shallow water, and the proper oscillations cause the swells to beat with the same periods as the proper oscillation periods. Furthermore, it is considered that these phenomena cause ship's dragging anchor and waves to invade over breakwater. The proper oscillations in shallow water and the beat phenomena of swells due to the proper oscillations were investigated by wave generating experiments, in order to prevent the wave disasters.

Fatigue failure analysis of high speed train gearbox housings

Abstract The present work addresses the formation of fatigue cracks in gearbox housings of high speed trains. Systematic studies of fracture analysis, finite element analysis, and field tests under actual stress and acceleration conditions are employed. Time domain, frequency domain, and time-frequency domain analyses indicate that the first two natural vibration modes are excited by out-of-round wheels and rail-track irregularities, and the superposition of these vibration modes results in the occurrence of the beat phenomenon, where the amplitude of the vibration modulates periodically, which increases the likelihood of exceeding fatigue limits, and produces greater structural damage. Analyses reveal that the fatigue strength of the failure region is reduced by the casting process, which eventually leads to the formation of fatigue cracks. Our findings suggest that the gearbox housing casting process should be improved to reduce casting porosity, and the housing structure must be redesigned to avoid the resonance frequencies associated with wheel-rail excitation at operational speeds.

Dynamic response of a front end accessory drive system and parameter optimization for vibration reduction via a genetic algorithm

A typical engine front end accessory drive system (FEADS) is mathematically modeled through Hamilton’s principle and Newton’s second law. In this model, the belt’s flexural rigidity and pulley’s eccentricity are considered. Eccentricities of the pulleys are introduced into governing motion equations of the belt spans through the boundary conditions and then transformed to external forces acting on the belt spans. Vibration modes and natural frequencies of the FEADS are calculated by the state-space technique of the complex mode theory. Dynamic responses of the FEADS at different rotational rates of the crankshaft are calculated by solving the spatially discretized governing equations obtained by Galerkin method. The modeling and solution methods are formulated and programmed in a general purposed code. The study shows that the typical resonance and beat phenomenon happen in a certain portion of the belt spans at a certain rotational rate by the excitations of the pulley’s eccentricity. According to the modal analysis and dynamic response analysis, an optimization method based on a genetic algorithm is proposed. By comparing the vibration amplitudes of belt spans before and after optimization at different rotational rates, this optimization method is verified to be effective in reducing transverse vibrations of the belt spans.

Beat vibration of hybrid boron nitride-carbon nanotubes – A new avenue to atomic-scale mass sensing

In this paper a beat phenomenon is reported in molecular dynamics simulations for vibrating boron nitride-carbon nanotubes (BN-CNTs) and then analysed based on a continuum mechanics theory. It was shown that the distinctive dynamic behaviour is a result of the superposition of two orthogonal transverse vibrations whose frequencies are slightly different due to the oval cross-section of the hybrid nanotubes. In particular, the interaction between the two vibrations in BN-CNTs will facilitate to resolve the fundamental issue in developing mass nanosensors for atomic-scale mass measuring. To reach this goal, efforts should be made to maintain high quality factor of the BN-CNT oscillating system by minimising the damping effect of its surrounding environment. This issue turns out to be essential for the beat mode-based nanosensors as large damping will reduce the hybrid nanotubes to conventional resonators with only one transverse vibration same as that reported for homogeneous nanotubes.

Dynamic modeling and analysis of a spinning Rayleigh beam under deployment

In this paper we propose a new model for a spinning beam under deployment and present analyses of the beam's dynamic responses and characteristics. The proposed model is established in an inertial reference frame by using the Rayleigh beam theory to consider the rotary inertia effect. This model is an advanced version of a model that we previously reported; that model was based on the Euler–Bernoulli beam theory, described in a rotating reference frame. We compare the dynamic responses and natural frequencies of a spinning beam under deployment between the proposed Rayleigh beam model and the previous Euler–Bernoulli beam model. In addition, we analyze the beat phenomena of a spinning Rayleigh beam under deployment in an inertial reference frame. Furthermore, we investigate the effects of the choice between the two reference frames (inertial and rotating reference frames) upon the analytical results for dynamic responses and natural frequencies. We show that the proposed model yields more accurate and reliable results for dynamic responses than the previous model, for the case in which a spinning beam is deployed.

Period-control and chaos-anti-control of a semiconductor laser using the twisted fiber

A novel semiconductor laser system is presented based on a twisted fiber. To study the period-control and chaos-anti-control of the laser system, we design a type of optic path as a control setup using the combination of the twisted fiber and the polarization controller while we present a physical dynamics model of the delayed dual-feedback laser containing the twisted fiber effect. We give an analysis of the effect of the twisted fiber on the laser. We use the effects of the delayed phase and the rotation angle of the twisted fiber and the characteristics of the system to achieve control of the laser. The laser is deduced to a stable state, a double-periodic state, a period-6 state, a period-8 state, a period-9 state, a multi-period state, beat phenomenon, and so on. The periodic laser can be anti-controlled to chaos. Some chaos-anti-control area is found. The laser system is very useful for the study of chaos-control of the laser setup and the applications of some physics effects.

Influences on water-hammer wave shape: an experimental study

Water-hammer phenomena are of strong interest in a number of different industrial fields, amongst which the space industry. Here the priming of feedlines during start-up of an engine as well as the rapid closing of valves upon shutdown may lead to pressure peaks symptomatic of a water-hammer wave. Test benches used to conduct tests on future as well as current engines are also sensitive to water-hammer waves traveling along their feedlines. To enhance the understanding of water-hammer, we investigated different configurations and their influence on the wave shape in the frequency domain. The configurations feature a coiled pipe setup with a support structure and without a support structure. Two other phenomena will be presented. We found a beat phenomenon which is likely to be the so called Poisson-coupling beat. Finally we will show that the second water-hammer peak can reach pressures a lot higher than the first peak by additive interference of the primary and secondary water-hammer wave.

Experimental and simulation study of wave motion upon railway overhead wire systems

To study the railway overhead wire's flexural wave motion that significantly affects the quality of current collection between pantograph and catenary, dynamic responses of a real catenary excited by different excitations are measured and analyzed by using a set of noncontact photogrammetric devices together with the finite-element simulation. Based on the measured and simulated results, the wave motion along the contact wire is investigated and some findings have been obtained. First, it is the first two dominant modal components in the catenary displacement responses that induce a beat phenomenon, and this beat phenomenon is increasingly obvious near the registration arm. Moreover, with the simulated displacement contour, catenary local vibration characteristics affected by the travelling wave can be clearly interpreted. Furthermore, the wave group velocity of contact wire in catenary is determined and verified to be approximately 139.18 m/s; in addition, treating the contact wire in the overhead wire system as an ideal string or a tensioned Euler beam will overestimate the corresponding group velocity with a relative error by about 13.21%.

Optically-detected nonlinear oscillations of single crystal silicon MEMS accelerometers

Purpose The purpose of this study is to address the nonlinear oscillations of single-crystal silicon micro-electromechanical systems (MEMS) accelerometers subjected to mechanical excitation. Methodology/approach The nonlinear behavior was detected and analyzed by using experimental, analytical and numerical approaches. Piezoelectric shaker as a source of mechanical excitation and differential laser Doppler vibrometer in combination with a micro system analyzer were used in the experimental effort. Two types of devices considered included nonencapsulated samples and samples encapsulated in nitrogen gas compressed between two glasses. Numerical and analytical investigations were conducted to analyze the nonlinear response. A novel method has been suggested to calculate the nonlinear parameters. The obtained experimental, numerical and analytical results are in good agreement. Findings It has been found that the nonlinearity leads to a shift in frequencies and generates higher harmonics, but, most importantly, reveals new phenomena, such as the jump and instability of the vibration amplitudes and phases. Originality/value It has been shown that under the constant excitation force, the MEMS device can work in both linear and nonlinear regions. The role of the beat phenomenon has been also addressed and discussed. It has been found that the attributes of the nonlinear response are strongly dependent on the level and duration of the excitation. It is concluded that the nonlinear response of the systems is strongly dependent on the level of the excitation energy. It has been also concluded that larger quality factors are able to enhance dramatically the nonlinear effects and vice versa.

Anisotropic density fluctuations, plasmons, and Friedel oscillations in nodal line semimetal

Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of the nodal line semimetal by computing the polarizability for both undoped and doped cases. The nodal line semimetal in the absence of doping is characterized by a ring-shape zero energy contour in momentum space, which may be considered as a collection of Dirac points. In the doped case, the Fermi surface has a torus shape and two independent processes of the momentum transfer contribute to the singular features of the polarizability even though we only have a single Fermi surface. In the static limit, there exist two independent singularities in the second derivative of the static polarizability. This results in the highly anisotropic Friedel oscillations which show the angle-dependent algebraic power law and the beat phenomena in the oscillatory electron density near a charged impurity. Furthermore, the dynamical polarizability has two singular lines along and , where η is the angle between the external momentum and the plane where the nodal ring lies. From the dynamical polarizability, we obtain the plasmon modes in the doped case, which show anisotropic dispersions and angle-dependent plasma frequencies. Qualitative differences between the low and high doping regimes are discussed in light of future experiments.

An Accurate Frequency Control Method and Atomic Clock Based on Coherent Population Beating Phenomenon

An accurate frequency control method and atomic clock based on the coherent population beating (CPB) phenomenon is implemented. In this scheme, the frequency difference of an rf and an atomic transition frequency can be digitally obtained by measuring the CPB oscillation frequency. The frequency measurement resolution of several milli-hertz can be achieved by using a 10 MHz oven controlled crystal oscillator as the reference. The expression of the Allan deviation of the CPB clock is theoretically deduced and it is revealed that the Allan deviation is inversely proportional to the signal-to-noise ratio and proportional to the line-width of coherent population trapping spectrum. We also approve that the CPB atomic clock has a large toleration of the drift of the local oscillator. In our CPB experimental system, a frequency instability of 3.0 × 10−12 at 1000s is observed. The important feature of high frequency measurement resolution of the CPB method may also be used in magnetometers, atomic spectroscopy, and other related research.

Two degree of freedom flow-induced vibration of cylindrical structures in marine environments: frequency ratio effects

The flow-induced vibration of a cylindrical structure is a very common problem in marine environments such as undersea pipelines, offshore risers, and cables. In this study, the vortex-induced vibration (VIV) of an elastically mounted cylinder at a low Reynolds number is simulated by a transient coupled fluid–structure interaction numerical model. Considering VIV with low damping ratio, the response, hydrodynamic forces, and vortex shedding modes of the cylinder is systematically analyzed and summed up the universal rule under different frequency ratios. On the basis of the analysis, we find that the frequency ratio α is a very important parameter. It decides the locked-in, beat, and phase-switch phenomena of the cylinder, meanwhile, it also influence the vortex mode of the cylinder. The trajectory of the two degrees of freedom (2 DOF) case at different natural frequency ratios is discussed, with most trajectories having a “figure of 8” shape and a few having a “crescent” shape. A fast Fourier transformation technique is used to obtain the frequency characteristics of the vibration of the cylindrical structure. Using the 2 DOF cylinder model in place of the 1 DOF model presents several advantages in simulating the nonlinear characteristics of cylindrical structures, including the capacity to model the crosswise vibration generated by in-line vibration.