Analytically obtained frequency-response curves defined by Eq. (35) of the oscillator governed by Eq. (1) for van der Pol damping, α=4/5, ε=0.2 and different values of F. Numerical results are depicted by dots. The lines and zones related to tr2−4det, tr and det are defined by Eqs. (39) and (40). A backbone curve is plotted as a dashed–dotted line. The mark ‘∗’ stands for the characteristics of free limit cycle oscillations.
... Frequency-response curves of the oscillator governed by Eq. (1) for van der Pol damping, α=3, ε=0.566 and two different values of F. Analytical results from  are depicted by a dashed–dotted line, analytical results from this paper by a solid and dotted line and numerical results by dots. The lines and zones related to tr and det are defined by Eqs. (39) and (40). The mark ‘∗’ stands for the characteristics of free limit cycle oscillations.
... Period of oscillations TexND given by Eq. (7).
... Frequency-response curves of the oscillator governed by Eq. (1) for linear viscous damping, F=ε=0.1 and for: (a) α=1/4; (b) α=4. Analytical results (49) are depicted by a solid line (stable) and by a dotted line (unstable); a shaded region (instability zone) is bounded by the curves defined by Eq. (53); a backbone curve (48) is shown as a dashed–dotted line; numerical results are depicted by dots.
... Frequency-response curve
Contributors:Farzad Rafieian, François Girardin, Zhaoheng Liu, Marc Thomas, Bruce Hazel
Detection of high-frequency repeating impacts in robotic grinding (detailed views). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
... Impact-cutting map from the speed signal based on the experiment with the bump showing (─) a major regime of 2 impacts/revolution and (…) minor oscillations. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
... Vibration and rotational frequency in single-pass grinding (overview). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
... Typical values of ω, ωmax and Δω during a cutting impact from measured rotational frequency in Test (3) at 4500rpm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
... Instantaneous angular frequency
Contributors:Grace Xiong, George V. Lauder
Center of mass displacement (green curve) and acceleration (blue curve) relative to tail position (red, shown for reference) in L. macrochirus swimming at 1.5BL/s. Surge acceleration shows a double peak oscillation at twice the frequency of the tail beat which is absent in the sway data.
... Comparison of COM oscillation magnitude for different animals. COM oscillation magnitude (peak-to-peak) in each direction was averaged across speeds for terrestrial species to give a single number generally representative of each species. Non-fish data were taken from the literature, and represent COM heave (vertical) motion only since this is the most commonly reported direction of COM oscillation, except for the sandfish point which represents sway motion. Fish data (green, red, and blue points) are from the present study and excursions are shown for all three different measured directions: heave, surge, and sway. The linear fit for data on terrestrial animals shown is 1.44x−6.07 (R2=0.88), indicating that COM displacement scales positively with mass, and that larger animals display a larger vertical oscillation than would be expected for their size. Fish have significantly lower heave COM oscillations than terrestrial animals. The orange point represents lizard sandfish moving in a granular medium and is derived from Ding et al. (2012).
... Two-way ANOVA table to show F-values for speed and species effects on each of the three dimensions of center of mass (COM) oscillation.
... Fast Fourier transforms of surge COM acceleration and displacement data for locomotion at 1.5BL/s in (A) L. macrochirus, (B) A. rostrata, and (C) N. chitala. The frequency components of the tail beat are shown for comparison in red. At this speed, L. macrochirus uses body and caudal fin undulation and so body undulations are comparable to those of the other species. Grey bars mark the tail beat and double tail beat frequencies. Both L. macrochirus and A. rostrata show COM acceleration frequency peaks at greater power for double the tail beat frequency than for the single beat frequency, and significant power for displacement at double the tail beat frequency. N. chitala, on the other hand, shows minimal power at double the tail beat frequency for acceleration, and negligible power for displacement.
... Speed vs. frequency for three species swimming in four swimming modes. Frequency had a significant positive relationship (pfrequency was substituted for tail beat frequency during labriform propulsion at 0.5BL/s as there was no body undulation at this speed.
Contributors:Nadav Cohen, Izhak Bucher
Bistable bilinear oscillator: (a) bilinear restoring force (solid curve) and (b) numerical solution of (1) for γt=0.118, ζt=0.071, and xs=0.0073 (solid curve).
... NL bistable oscillator. (a) Bistable oscillator composed of a linear oscillator and a NL element. (b) The dimensionless restoring force of a bistable oscillator for different values of α (α=0, solid curve; α=0.1, dotted curve; α=0.3, dashed curve; α=1, dot-dashed curve) in the case of k˜NL=1 and β=1. (c) Typical response of bistable oscillator to harmonic excitation in a highly pre-resonance regime. The displacement (solid curve), potential (dashed curve) and restoring force (dot-dashed curve) are taken from the experimental setup, see Appendix.
... Bistable energy harvester prototype. (a) Close-up on coil and MP, (b) the prototype oscillator, and (c) excitation base comprised of a motorized lead screw base.
... (a) Power ratio of a bistable oscillator vs. linear oscillator as a function of (γ,ζ) for xs=±0.0073. Analytical results represented by 2-dimensional surface; numerical results represented by the contour plot at the bottom of the figure. (b) Power ratio numeric simulation of a wide barrier bistable oscillator. The restoring force used on the numerical simulation is extracted from the bistable prototype; (c) the extracted force. The excitation amplitude used is Y=50[mm]. For description of the prototype, see Appendix. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Contributors:Nadav Cohen, Izhak Bucher, Michael Feldman
Bi-stable oscillator... Frequency up-conversion... Velocity decomposition. (Right) Fast component shown in a 3D form: projections show the instantaneous frequency (IF) vs. time, the envelope vs. time and IF vs. envelope on the far projection. (Left) Velocity components: instantaneous amplitude vs. instantaneous frequency.
... Simulated response of a bi-stable energy harvester under constant frequency base excitation ω≈0.1ωn () ωn=7Hz, ζ=0.07. Right: nonlinear (bi-stable) potential (––) and force (–––) functions of the system taken from experimental system.
... Fine resolution spectrum of the bi-stable oscillator response to pure sine excitation.
Contributors:Seth H. Weinberg, Kelly C. Chang, Renjun Zhu, Harikrishna Tandri, Ronald D. Berger, Natalia A. Trayanova, Leslie Tung
Conduction block and ventricular fibrillation vulnerability. A: Percentage of trials (a) initiating and (b) terminating ventricular fibrillation (VF) as a function of field frequency and strength. (c) Mean defibrillation threshold (DFT; red line) and upper limit of vulnerability (ULV; black line) as functions of frequency. Lines at the bottom of the plot indicate pairwise statistical significance. B: (a) Average loss of conduction power (LCP) values and (b) average conduction block (CB) size as a function of field strength and frequency. LCP standard errors are given in Table S2. Correlation between (C) average LCP or (D) average CB size and (a) the percentage of trials initiating VF or (b) the percentage of trials terminating VF.
... Surface and subsurface conduction block and ventricular fibrillation termination. (A) Percentage of simulations terminating ventricular fibrillation (VF), (B) average (a) surface and (b) subsurface loss of conduction power (LCP) values, and (C) average (a) surface and (b) subsurface conduction block (CB) size as a function of field frequency and strength. Correlation between (D) average LCP or (E) CB size on the surface (red) or the subsurface (blue) myocardium and the percentage of simulations terminating ventricular fibrillation (VF).
... Conduction block on the surface and subsurface myocardium during high frequency alternating current (HFAC) fields. (A) Successful and (B) failed termination of ventricular fibrillation (VF), following 15-V/cm and 10-V/cm HFAC fields, respectively. Spatial maps of loss of conduction power (LCP) on (left) the epicardial surface and (middle) a short-axis slice. (Right) Transmembrane potential (Vm) traces at sites a–e, shown in the spatial maps in image A, with the corresponding LCP values. Gray bar indicates time of the HFAC field. The time windows used for LCP analysis before and during the HFAC field are shown in red and blue, respectively.
... Successful and failed defibrillation following partial conduction block. (A) Successful and (B) failed defibrillation, following 10.7-V/cm and 9.2-V/cm high frequency alternating current (HFAC) fields, respectively. Top: Time-space plot, along the dashed line in the first panel of Figure 1B. Red regions in the plots indicate fully depolarized cells; deep blue indicates fully repolarized cells at rest. Propagating activations are denoted by white arrows. Bottom: Spatial map of loss of conduction power (LCP).
... Defibrillation by high frequency alternating current (HFAC) field. A: Anterior surface of the heart: left ventricle (LV), right ventricle (RV), and left anterior descending (LAD) artery. The optical mapped field of view is shown in the white box. B: Normalized transmembrane potential (Vm) maps before, during (gray backing), and after 200-Hz 300-ms HFAC field application. Red regions in the maps indicate fully depolarized cells; deep blue indicates fully repolarized cells at rest. C: Vm before, during, and after partial conduction block during the HFAC field. The time windows used for loss of conduction power (LCP) analysis before and during the HFAC field are shown in red and blue, respectively. Gray bar indicates the time of the HFAC field. D: Vm power spectrum before and during partial conduction block during the HFAC field. Sites a and c are close to the left and right field of view edges, respectively; site b is at the center of the field of the view, shown in image A. LCP values for each site are shown.
Contributors:Miklós Szakáll, Simon Kessler, Karoline Diehl, Subir K. Mitra, Stephan Borrmann
3D representation of the frequencies of the active oscillation modes for all phases of the recorded collisions. Top view represents the dependence of the frequencies of the transverse mode, while front view the dependence of the horizontal mode frequencies on the frequency of the axisymmetric mode.
... Temporal variation of the axis ratio: (a) the virtual canting angle, and (b) the projected drop size (c) of the largest drop during collision. The collision process is divided in four phases: I: pre-collision phase; IIa: transverse oscillation and/or rotation phase including also the very short transient phase instantaneously after collision; IIb: damping phase; and IIc: phase with quiescent drop characteristics. (Details about the definitions of the phases are given in Section 4 Results and Discussion.)
... Raindrop oscillation
The effects of an ultrasonic wave (20kHz) on the dendritic microstructure of Sn–13at%Bi alloys were studied using time-resolved in situ X-ray imaging. Sequential images clearly showed the secondary effects such as the ultrasonic streaming and the oscillation with much lower frequency comparing to the ultrasonic vibration frequency. The ultrasonic wave caused a circulating convection, whose domain size was almost the same as the specimen size, and simultaneously periodic convection (40Hz), which was identified from the longitudinal oscillation of the dendrites. The fragmentation of the primary and secondary dendrite arms in the columnar zone was significantly enhanced under the ultrasonic wave. The secondary effects of the ultrasonic wave play a significant role for modifying the solidification structure.
Contributors:Alexander Hoover, Laura Miller
The trajectories of the diameter oscillation during the free vibration study for different viscosities. Notice that the subsequent amplitudes of the free vibration oscillation decrease for higher viscosities until the oscillations present are negligible, as in μ=64μref.
... The oscillations of the diameter during the free vibration study as a function of time. The diameter is measured as the distance between two symmetric points at the widest cross-section of the bell.
... The inverted Strouhal number (St−1) vs. driving frequency for several choices of force magnitude. St−1 was calculated using the maximum amplitude and forward velocity information taken from the driving frequency simulations. Although the best performing frequency is the recorded frequency of free vibration for small applied forces, the frequency that produces the largest deformations is shifted to lower force magnitudes as the force magnitude is increased. The different values of P show how the swimming speeds change in time as steady state is approached.
... Comparing the maximum amplitude of diameter oscillation for each of the driving frequencies, f, at different force magnitudes, FMag, during the pulse cycle P=5,10,15,20,25. The recorded frequency of free vibration is highlighted with the dotted red line. Notice that the frequency with the largest maximum amplitude is found for the largest force magnitude when f=.75s−1, which is slightly below the measured frequency of vibration. The different values of P show how the maximum amplitudes change in time as steady state is approached. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
... A comparison of the 5th, 10th, and 15th propulsive cycles of the maximum amplitude of diameter oscillation during a driving force study with differing levels of μ. Notice that the peak frequency shifts lower frequencies as more fluid damping is added. Also note how the maximum amplitudes stay relatively fixed in more damped fluid environments.
Contributors:Fanghao Yang, Xianming Dai, Chih-Jung Kuo, Yoav Peles, Jamil Khan, Chen Li
High frequency... High frequency two-phase oscillations powered by bubble growth/collapse processes at a heat flux of 100W/cm2 for a mass flux of 400kg/m2s.
... Self-sustained two-phase oscillation