In-phase Motion Research Articles

Snap-through dynamics of buckled flexible filaments in a side-by-side configuration

The flow-induced snap-through dynamics of side-by-side buckled flexible filaments in a uniform flow were investigated using the penalty immersed boundary method. We systematically examined the effects of gap distance and bending rigidity on the filament's motion and energy harvesting performance. Four distinct modes were observed as we varied the aforementioned parameters: the dual equilibrium mode, the dual streamwise oscillation mode, the single snap-through oscillation (STO) mode, and the dual STO mode. We analyzed the corresponding wake patterns associated with each of these modes. A phase transition from out-of-phase to in-phase motion was observed at low gap distances and bending rigidities. At lower gap distances, the interaction between two filaments was pronounced, leading to a co-motion of the filaments and enhanced elastic energy. This interaction decreased as the gap distance increased. Filaments in the 2STO mode exhibited significantly higher strain energy compared to the other modes. The elastic energy was concentrated at the rear part of the filaments and increased with higher gap distances and bending rigidities. Considering both energy harvesting efficiency and space utilization rate, a gap distance equal to 1 exhibited the best performance.

Study of Tracker Software-assisted Spring Coupled Pendulum Oscillation

Oscillatory motions are an essential part of our physical world. These motions need to be studied and learned by students. However, complicated oscillatory motions, e.g.: spring coupled pendulum, are rarely taught to students because their analytical solutions (if they exist) are complicated Here, we use the Tracker software to bridge between the actual coupled pendulum oscillation and its analytical solution. This study aimed to determine the period and frequency of Tracker software-assisted spring coupled pendulum oscillations. The displacement of the pendulum is divided into in-phase and out-of-phase motions. Data collection was carried out by recording the oscillatory motions up to 10 oscillations. The data were obtained from the pendulum position with respect to time. The data analysis techniques in this study used two methods, namely: i) Tracker software and ii) analytical calculations. The results showed that the period and frequency obtained via the Tracker software were in accordance with the analytical calculations. The periods of the in-phase motion and analytical calculation were 1.42 s and 1.54 s, respectively. The periods of the out-of-phase motions and analytical calculation were 0.7 s and 0.55 s, respectively. The frequencies of the in-phase motion and analytical calculation were 0.70 Hz and 0.65 Hz, respectively. The frequencies of the out-of-phase motions and analytical calculation were 1.50 Hz and 1.83 Hz, respectively. The uncertainty values of the results were 7% to 22%. Hence, the spring coupled pendulum oscillations became tractable and can be compared to the analytical solution.

Lower extremity coordination strategies to mitigate dynamic knee valgus during landing in males and females

Frontal and sagittal plane landing biomechanics differ between sexes but reported values don’t account for simultaneous segment or joint motion necessary for a coordinated landing. Frontal and sagittal plane coordination patterns, angles, and moments were compared between 28 males and 28 females throughout the landing phase of a drop vertical jump. Females landed with less isolated thigh abduction (p = 0.018), more in-phase motion (p < 0.001), and more isolated shank adduction (p = 0.028) between the thigh and shank in the frontal plane compared with males. Females landed with less in-phase (p = 0.012) and more anti-phase motion (p = 0.019) between the thigh and shank in the sagittal plane compared with males. Females landed with less isolated knee flexion (p = 0.001) and more anti-phase motion (p < 0.001) between the sagittal and frontal plane knee coupling compared with males. Waveform and discrete metric analyses revealed females land with less thigh abduction from 20 % to 100 % and more shank abduction from 0 to 100 % of landing, smaller knee adduction at initial contact (p = 0.002), greater peak knee abduction angles (p = 0.015), smaller knee flexion angles at initial contact (p = 0.035) and peak (p = 0.034), greater peak knee abduction moments (p = 0.024), greater knee abduction angles from 0 to 13 % and 19 to 30 %, greater knee abduction moments from 19 to 25 %, and smaller knee flexion moments from 3 to 5 % of landing compared with males. Females utilize greater frontal plane motion compared with males, which may be due to different inter-segmental joint coordination and smaller sagittal plane angles. Larger knee abduction angles and greater knee adduction motion in females are due to aberrant shank abduction rather than thigh adduction.

Acoustic signature of impermeable barriers in porous media

SUMMARY Impermeable barriers are abundant in rock formations and their delineation via seismic reflections are of prime importance. However, such barriers have received little attention in the poroelasticity literature. For this reason, we revisit the reflection–transmission problem for two porous half-spaces which are in welded contact and across which no fluid exchange is possible. We carry out this analysis in the poroelastic theory initiated by de la Cruz and Spanos (1985), which describes four waves: the fast P, fast S-, slow P and slow S waves. The fast P and S waves account for the in-phase motion in compression and shear nature, whereas the slow P and S waves are the out-of-phase motion. We find that the often times suggested notion of effective elastic scattering is not quite correct because of the generation of slow waves at the impermeable contact. The energy flux the slow waves carry is negligibly small at low frequencies when the fluid is viscously coupled to the solid frame. In contrast, slow waves carry substantial energy flux at high frequencies when the fluid is viscously decoupled. Moreover, the reflection–transmission behaviour at an impermeable contact is distinctively different when compared to that of a permeable contact, which means that, in principle, amplitudes of scattered waves can be used to identify the kind of contact. A seemingly unnoted but important result is the strong conversion scattering from a fast S wave into the slow P wave at high frequencies, which may be an alternative way to observe slow P waves in the laboratory as well as a means to characterize impermeable contacts.

Vector coding reveals the underlying balance control strategies used by humans during translational perturbation

Postural control research has focused on standing balance experiments on platforms moving with relatively large amplitudes (0.1–0.2 m). This study investigated balance strategies while standing on a platform moving 4 mm in anterior-posterior direction with frequency scaled linearly from 0.4 to 6 Hz. Platform motion and kinematic and kinetic information for nine healthy participants were recorded using motion capture and force plate systems. Coordination between hip, knee and ankle joint torque, and centre of mass (COM) and centre of pressure (COP) motion was quantified by vector coding. Significant main effect of platform frequency for knee-ankle and COP-COM phase relationship was observed (p = 0.023, p = 0.016). At frequencies below 2.11 and 2.34 Hz, ankle strategy was recruited. With ankle strategy, in-phase COP-COM motion with COP dominancy occurred at frequencies below 2.19 and 2.23 Hz during scaling up and down, respectively. As platform frequency passed these values, COM dominated over COP which was followed by anti-phase knee-ankle torque, called a knee strategy, and anti-phase motion between the COP and COM that allowed COP to regain dominance over COM. Collectively, we reveal knee strategy as a new and relevant strategy in real-life settings, and transition between ankle and knee strategies that underpinned transition between COP-COM relative motion.

Sound generated by flow over two traveling wavy foils in a side-by-side arrangement

Numerical simulations are employed to investigate the sound generated by flow over two traveling wavy foils in a side-by-side arrangement by an immersed-boundary-method-based hybrid approach. The effects of Strouhal number (St), phase difference, and lateral spacing (S) between the foils on the flow performance and the sound pressure field are examined. The results imply that the sound produced by a single foil is dominated by the lift dipole, and that the low-amplitude–high-frequency foil can achieve higher thrust and higher sound pressure compared to the high-amplitude–low-frequency foil. For the two side-by-side foils (i.e., an in-phase and anti-phase foil system), the sound pressure fields exhibit distinct features. Specifically, a dipole-like pattern appears during in-phase motion, whereas a monopole-like pattern exists during anti-phase motion. Moreover, the magnitude of the sound pressure increases slightly with increasing S in the in-phase case. However, the sound pressure decreases rapidly when S &amp;lt; 0.7L (foil length) and then remains nearly unchanged when S &amp;gt; 0.7L in the anti-phase case. Furthermore, the anti-phase foil system could improve thrust by increasing power consumption and could generate lower sound pressure compared to the in-phase one due to the distinct differences in wake patterns. The present work is expected to improve the understanding of sound-generation mechanisms of fish-like locomotion and collective motion for relevant biomimetic underwater vehicles.

Interface instabilities in Faraday waves of two-layer liquids with free surface

For a fluid system with an interface between two-layer liquids and a free surface, there exist two series of natural frequencies. Under vertical excitations, the interface and the free surface can be excited separately or simultaneously. Laboratory experiments were conducted to excite the first- and second-mode Faraday waves on the free surface, which forced the in-phase motion of the interface. The experimental data were used to validate the extended numerical model NEWTANK. The secondary surface instability in the form of period tripling breaking occurred on the free surface when second-mode surface resonant response was large. Further numerical investigations were conducted to study the resonance of interface and in addition to the primary Faraday instability, the secondary interface instability occurred due to Rayleigh–Taylor (RT) instability. The analysis revealed that this was due to the contribution from the combined effects of vertical fluid acceleration and external excitation, which made the upper layer liquid essentially ‘heavier’ than the lower layer at certain instances, even when the amplitude of acceleration of the external excitation was lower than that of gravity at all times. A dimensionless parameter ‘normalised effective gravitational acceleration’ (NEGA) was proposed to quantify the occurrence criterion of RT instability in a dynamic fluid system. Furthermore, simultaneous resonances at both the interface and the free surface were studied and reverse flows could be formed across the interface as the upper Faraday waves and lower Faraday waves moved in opposite directions, which generated the secondary interface instability of Kelvin–Helmholtz (KH) type. When KH instability took place, more energy was transferred to higher frequency modes as time evolved.

Quantum-classical simulations of rhodopsin reveal excited-state population splitting and its effects on quantum efficiency.

The activation of rhodopsin, the light-sensitive G-protein coupled receptor responsible for dim-light vision in vertebrates, is driven by an ultrafast excited-state double-bond isomerization with a quantum efficiency of almost 70%. The origin of such light sensitivity is not understood and a key question is whether in-phase nuclear motion controls the quantum efficiency value. Here, we use hundreds of quantum-classical trajectories to show that, 15 femtoseconds after light absorption, a degeneracy between the reactive excited state and a neighboring state causes the splitting of the rhodopsin population into subpopulations. These subpopulations propagate with different velocities and lead to distinct contributions to the quantum efficiency. We also show that such splitting is modulated by protein electrostatics, thus linking amino-acid sequence variations to quantum efficiency modulation. Finally, we discuss how such a linkage that in principle could be exploited to achieve higher quantum efficiencies, would simultaneously increase the receptor thermal noise leading to a trade-off that may have played a role in rhodopsin evolution.

Changes in task-specific fear of movement and impaired trunk motor control by pain neuroscience education and exercise: A preliminary single-case study of a worker with low back pain

We report a case (a worker with low back pain) who was provided patient education and therapeutic exercise, and we performed a detailed kinematic analysis of his work-related activity over time. The subjects were one 28-year-old male worker with low back pain. In addition, to clearly identify impaired trunk movement during work-related activity in the low back pain subject, 20 age-matched healthy males (control group) were also included as a comparison subject. He received pain neurophysiology education and exercise instruction. We analyzed the subject’s trunk movement pattern during a lifting task examined by a three-dimensional–motion capture system. In addition, task-specific fear that occurred during the task was assessed by the numerical rating scale. The assessment was performed at the baseline phase (4 data points), the intervention phase (8 data points), and the follow-up phase (8 data points), and finally at 3 and 8 months after the follow-up phase. No intervention was performed in the control group; they underwent only one kinematic evaluation at baseline. As a result, compared to the control group, the low back pain subject had slower trunk movement velocity (peak trunk flexion velocity = 50.21 deg/s, extension velocity = −47.61 deg/s), and his upper-lower trunk segments indicated an in-phase motion pattern (mean absolute relative phase = 15.59 deg) at baseline. The interventions reduced his pain intensity, fear of movement, and low back pain–related disability; in addition, his trunk velocity was increased (peak trunk flexion velocity = 82.89 deg/s, extension velocity = −77.17 deg/s). However, the in-phase motion pattern of his trunk motor control remained unchanged (mean absolute relative phase = 16.00 deg). At 8 months after the end of the follow-up, the subject’s in-phase motion pattern remained (mean absolute relative phase = 13.34 deg) and his pain intensity had increased. This report suggests that if impaired trunk motor control remains unchanged after intervention, as in the course of the low back pain subject, it may eventually be related to a recurrence of low back pain symptoms.

Third party stabilization of unstable coordination in systems of coupled oscillators

The Haken-Kelso-Bunz (HKB) system of equations is a well-developed model for dyadic rhythmic coordination in biological systems. It captures ubiquitous empirical observations of bistability – the coexistence of in-phase and antiphase motion – in neural, behavioral, and social coordination. Recent work by Zhang and colleagues has generalized HKB to many oscillators to account for new empirical phenomena observed in multiagent interaction. Utilising this generalization, the present work examines how the coordination dynamics of a pair of oscillators can be augmented by virtue of their coupling to a third oscillator. We show that stable antiphase coordination emerges in pairs of oscillators even when their coupling parameters would have prohibited such coordination in their dyadic relation. We envision two lines of application for this theoretical work. In the social sciences, our model points toward the development of intervention strategies to support coordination behavior in heterogeneous groups (for instance in gerontology, when younger and older individuals interact). In neuroscience, our model will advance our understanding of how the direct functional connection of mesoscale or microscale neural ensembles might be switched by their changing coupling to other neural ensembles. Our findings illuminate a crucial property of complex systems: how the whole is different than the system’s parts.

Control synchronization of three eccentric rotors driven by motors in space considering adaptive fuzzy sliding mode control algorithm

In this paper, to obtain ideal dynamic behavior of vibration screen, control synchronization of three eccentric rotors (ERs) driven by motors in space vibration system is investigated by employing the adaptive fuzzy sliding mode control (AFSMC) algorithm. First, the dynamic model of the vibration system is established, and the motion equation of the electromechanical coupling system is derived via Lagrange equation. Then, the synchronization controllers of three ERs are systematically designed with the combination of AFSMC algorithm and master–slave control (MSC) structure, and the stability of the control system is verified by Lyapunov theory. Additionally, in comparison with the conventional sliding mode control (SMC) algorithm, the superiority and feasibility of the proposed AFSMC strategy are confirmed through numerical simulation in MATLAB/Simulink. Moreover, the robustness of the control system is demonstrated in the simulation via changing the motor velocities and structure parameters. The research result shows that the proposed adaptive strategy can effectively control the ERs to implement the desired in-phase synchronization motion, and the control method possesses commendable efficacy in reducing chattering, enhancing control accuracy, eliminating overshoot, and resisting parameter perturbation.

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes

It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase in the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of complexification-averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period-doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes), and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors’ knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.

Energetics of synchronization for model flagella and cilia.

Synchronization is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronize their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of coswimming spermatozoa was consistent with minimization of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella, (2) spheres orbiting above a no-slip surface to model interacting flexible cilia, and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimized in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics, (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres, and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronization in these setups.

Experimental Comparison of Field and Accelerated Random Vertical Vibration Levels of Stacked Packages for Small Parcel Delivery Shipments

In the last decade, there has been a significant increase in parcel delivery shipments all over the world due to online stores and consumer demand to receive the products in a shorter period of time. It is especially true when situations like COVID-19 limits personal purchases in shopping malls as well as grocery and pharmaceutical stores. This often means that courier operators try to deliver packages utilizing vehicles with racks or shelves, which during the COVID-19 epidemic are not there anymore. This study measured the vertical vibration levels that occur in stacked parcels during express delivery versus the simulation technique in the laboratory. The goal of this paper was to measure and compare the vibration levels between laboratory practice and field transportation. For the measurement a three-layer stacked unit was built to observe the vibration levels on different road conditions in a parcel delivery vehicle and ASTM vibration profile (ASTM International). Then the measured acceleration-time data were analyzed in terms of power spectral densities (PSD) and the presented statistical data provided an understanding of the variability of intensity in different levels in stacked unit. The results showed that the vibration level increases in the stacked load upwards and with worse road conditions, but even in the worst case it did not reach those vibration levels that the laboratory test showed. Moreover, the layers of the stacked unit are in out-of-phase motion in the field, while the stacked unit in the vibration simulation usually is in-phase motion. Results indicate that the proposed vibration simulation does not correlate well with typical field vibration. This is fundamentally true as during a forced vibration created by a single-axis shaker, do not account for additional inputs occurring simultaneously creating an off-balance to the loads and as a result are less severe than simulated conditions. These findings are limited to single axis vibration simulation and unsecured loads.

On the Efficiency of a Conical Underplatform Damper for Turbines

Abstract Underplatform dampers (UPDs) are commonly used in aircraft engines to limit the risk of high-cycle fatigue of turbine blades. The latter is located in a groove between two consecutive blades. The dry friction contact interface between the damper and the blades dissipates energy and so reduces the vibration amplitudes. Two common geometries of dampers are used nowadays, namely wedge and cylindrical dampers, but their efficiency is limited when the blades have an in-phase motion (or a motion close to it), since the damper tends to have a pure rolling motion. The objective of this study is to analyze a new damper geometry, based on a conical shape, which prevents from this pure rolling motion of the damper and ensures a high kinematic slip. The objective of this study is to demonstrate the damping efficiency of this geometry. Hence, in a first part, the kinematic slip is approximated with analytical considerations. Then, a nonlinear dynamic analysis is performed, and the damping efficiency of this new geometry is compared to the wedge and the cylindrical geometries. The results demonstrate that the conical damper has a high damping capacity and is more efficient and more robust than the two others.

Joint Coordination and Stiffness During Landing in Individuals With Chronic Ankle Instability.

The purpose of the present study was to examine the effect of chronic ankle instability (CAI) on lower-extremity joint coordination and stiffness during landing. A total of 21 female participants with CAI and 21 pair-matched healthy controls participated in the study. Lower-extremity joint kinematics were collected using a 7-camera motion capture system, and ground reaction forces were collected using 2 force plates during drop landings. Coupling angles were computed based on the vector coding method to assess joint coordination. Coupling angles were compared between the CAI and control groups using circular Watson-Williams tests. Joint stiffness was compared between the groups using independent t tests. Participants with CAI exhibited strategies involving altered joint coordination including a knee flexion dominant pattern during 30% and 70% of their landing phase and a more in-phase motion pattern between the knee and hip joints during 30% and 40% and 90% and 100% of the landing phase. In addition, increased ankle inversion and knee flexion stiffness were observed in the CAI group. These altered joint coordination and stiffness could be considered as a protective strategy utilized to effectively absorb energy, stabilize the body and ankle, and prevent excessive ankle inversion. However, this strategy could result in greater mechanical demands on the knee joint.

Theoretical and numerical investigations on resonant characteristics of two piezoelectric plates coupled with a finite fluid field

The vibration characteristics of two piezoelectric cantilevered plates in air and water are investigated in this study. The two-piezoelectric-plate system can provide different vibration characteristics compared to the previous studies in which only one cantilever plate is used because the anti-phase motion can be evoked in this newly designed system. First, the vibration characteristics of the plates coupled with a bounded compressible inviscid fluid are derived by theoretical analysis. The governing equation of the piezoelectric plate and the superposition method are used to analyze the vibration displacement of the piezoelectric plate, and the acoustic wave equation is used to derive the fluid equation. The frequency eigenfunction of the coupled system is derived by the boundary conditions of hydrostatic equilibrium. After solving the characteristics equation, the resonant frequencies and corresponding mode shapes for assumptions about both compressible and incompressible fluids and the velocity and pressure fields of the fluid can be obtained. Next, finite element analysis (FEA) is used to verify the theoretical results. It is shown from this study that the theoretical predictions of resonant frequencies and the corresponding mode shapes have a good agreement with those of the FEA for water and compressible fluid assumption of air. The unique high pressure value in the outer or middle layer in an air-coupled condition does not occur in water because water’s compressibility is relatively smaller than that of air. The influence of the depth and properties of the fluid on the behavior of the coupled solid–fluid is also investigated. For anti-phase motion, the frequency variation with change in the depth of the middle layer is similar to that of the outer layer for both air- and water-coupled conditions. For in-phase motion, the variation in frequency with the change in the depth of the middle layer is negligible. The particular modes in fluid compounded by modes in vacuum are analyzed on the distortion of mode shapes at higher resonant modes. These results can provide complete information on the vibration characteristics of a solid–fluid coupled system and will contribute to the evolution of hydroacoustic devices in which two piezoelectric plates are used.

Phase Control for the Dynamics of Connected Rotators

We study the dynamics of rotational motions in a system of two asymmetrically coupled pendulum-type systems, investigating the mechanisms of losing stability for in-phase rotational motion. We analyze the scenario where chaotic dynamics appears depending on the values of the control parameters.

Coral tentacle elasticity promotes an out-of-phase motion that improves mass transfer.

Corals rely almost exclusively on the ambient flow of water to support their respiration, photosynthesis, prey capture, heat exchange and reproduction. Coral tentacles extend to the flow, interact with it and oscillate under the influence of waves. Such oscillating motions of flexible appendages are considered adaptive for reducing the drag force on flexible animals in wave-swept environments, but their significance under slower flows is unclear. Using in situ and laboratory measurements of the motion of coral tentacles under wave-induced flow, we investigated the dynamics of the tentacle motion and its impact on mass transfer. We found that tentacle velocity preceded the water velocity by approximately one-quarter of a period. This out-of-phase behaviour enhanced mass transfer at the tentacle tip by up to 25% as compared with an in-phase motion. The enhancement was most pronounced under flows slower than 3.2 cm s-1, which are prevalent in many coral-reef environments. We found that the out-of-phase motion results from the tentacles' elasticity, which can presumably be modified by the animal. Our results suggest that the mechanical properties of coral tentacles may represent an adaptive advantage that improves mass transfer under the limiting conditions of slow ambient flows. Because the mechanism we describe operates by enhancing convective processes, it is expected to enhance other fitness-determining transport phenomena such as heat exchange and particle capture.

Influence of bimanual exercise on muscle activation in post-stroke patients

Brain damage due to stroke often leaves survivors with lateral functional motor deficits. Bimanual rehabilitation of the paretic arm is an active field of research aimed at restoring normal functionality by making use of the complex neural bindings that exist between the arms. In search of an effective rehabilitation method, we introduced a group of post-stroke rehabilitation patients to a set of bimanual motion tasks with inter-manual coupling and phasing. The surface EMG profiles of the patients were compared in order to understand the effect of the motion conditions. The paretic arms of the patients were more strongly affected by the task conditions compared with the non-paretic arms. These results suggest that in-phase motion may activate neural circuits that trigger recovery. Coupling also had an effect on behavior, but the response of patients was divided between those whom coupling helped or hindered.