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The output frequency response of a nonlinear system. ... The restoring force of a bilinear oscillator. ... The output frequency response of a linear system. ... Bilinear oscillator... The polynomial approximation result for a bilinear oscillator ... Nonlinear output frequency response function... Bilinear oscillator model. ... In this paper, the new concept of nonlinear output frequency response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized frequency response functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial-type nonlinear oscillator, the NOFRFs are used to analyse the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.
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Dominant frequency... The first and the second dominant frequencies variation with the steam mass flux. ... The first and the second dominant frequencies variation with the water temperature. ... The dominant frequency regime map. ... Pressure oscillation... Frequency spectrums of pressure oscillation at different water temperatures and steam mass flux. ... Experimental investigations and analysis on the dominant frequency of pressure oscillation for sonic steam jet in subcooled water have been performed. It was found that sometimes there is only one dominant frequency for pressure oscillation, and sometimes there is a second dominant frequency for pressure oscillation. The first dominant frequency had been investigated by many scholars before, but the present study mainly investigated the characteristics of the second dominant frequency. The first dominant frequency is mainly caused by the periodical variation of the steam plume and the second dominant frequency is mainly caused by the generating and rupture of the large steam bubbles. A dominant frequency regime map related to the water temperature and steam mass flux is given. When the water temperature and the steam mass flux are low, there is only one dominant frequency of pressure oscillation. When the water temperature or the steam mass flux is high, the second dominant frequency appears for pressure oscillation. The second dominant frequency decreases with the increasing water temperature and steam mass flux. Meanwhile, the second dominant frequency at high steam mass flux and water temperature is lower than the first dominant frequency at low steam mass flux and water temperature. A dimensionless correlation is proposed to predict the second dominant frequency for sonic steam jet. The predictions agree well with the present experimental data, the discrepancies are within ±20%.... The dominant frequencies in different measurement points by Qiu et al. [14].
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Low-frequency oscillations... Undamped swing curve: one oscillation mode. ... Un-damped swing curve with two oscillation modes: f1=0.4, f2=0.5Hz and σ1=−0.025, σ2=+0.037s−1. ... Low-frequency oscillations in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-frequency oscillations in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the oscillation frequency. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method.
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Frequency spectra (a), (b) and (c) correspond to the frequency spectra of signals in Fig. 6 (a), (b) and (c), respectively. By construction, frequency spectrum in (a) is equal to the sum of the spectra in (b) and (c). ... Period and amplitude of oscillation versus average dilution rate (h−1) calculated by FFT analysis in intervals of 512 data points of the filtered data shown in Fig. 4. ... Frequency spectra of the exhaust CO2 signal shown in Fig. 1: (a) through (d) correspond to regions 1 through 4 of Fig. 1, respectively; (e) shows the frequency spectrum of the overall signal. ... Autonomous oscillations... Calculated periods of oscillations, in minutes, obtained by FFT analysis of various signals ... Measurements of state variables from oscillating chemostat cultures of Saccharomyces cerevisiae were analyzed by Fourier transformation. Of the signals tested, carbon dioxide and oxygen in the exit gas stream and dissolved oxygen in the medium, all gave identical results. Analysis of data from reactors operated at fixed conditions showed that after oscillations start, they pass through an extended transient lasting several days, before the oscillation period becomes constant. Under transient operating conditions, Fourier analysis revealed expected qualitative trends in the change of oscillation period with dilution rate.... Filtered CO2 signal of the ramp experiment shown in Fig. 3. The filtered signal was obtained by subtracting moving signal averages from the original signal and represents the oscillating part of the signal.
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Diagram of the MNI detector. (A) baseline detector. (B) HFOs detection in channels with baseline. (C) HFOs detection in channels with continuous high frequency activity. If more than 5s/min of baselines are found, HFOs are detected with respect to the baseline segments (B). If less than 5s/min of baseline were detected, HFOs are detected with respect to the entire EEG segment in an iterative way (C). WE: wavelet entropy; Rxx: autocorrelation; th: Threshold. ... High frequency oscillations... Histogram of peak frequencies of FRs not occurring with ripples. Out of the 7994 PosAnd HFOs, 554 corresponded to FR that did not co-occur with a visually marked ripple. The peak frequencies of these events included not only the 250–500Hz band but also the 80–250Hz band. All these events were visually marked as FR using a high-pass filter at 250Hz. Two examples are presented. Top: FR with a peak frequency at 150Hz; Bottom: FR with a peak at 265Hz. The unfiltered EEG, the filtered EEG above 80Hz and the filtered EEG above 250Hz are shown. The oscillations become visible only when filtering above 250Hz. ... High frequency oscillations (HFOs) are a biomarker of epileptogenicity. Visual marking of HFOs is highly time-consuming and inevitably subjective, making automatic detection necessary. We compare four existing detectors on the same dataset.
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Cortical distributions of SEPs and high-frequency oscillations to median nerve stimulation in Patient 5. (A) Typical high-frequency oscillation potential recorded at electrode A5. (B) The location of recording electrodes. (C) Cortical distributions of the SEPs and high-frequency oscillations. P20/N20 are distributed diffusely around the primary hand sensorimotor area, while P25 is elicited in a restricted cortical area. Most oscillation potentials show a cortical distribution similar to that of P20/N20. Two later oscillations (n21 and p22) are elicited in a restricted cortical area similar to P25. ... Typical examples of high-frequency oscillations to median nerve stimulation recorded with a restricted bandpass filter of 500–2000 Hz compared with SEPs recorded with a wide bandpass filter of 30–2000 Hz. The SEPs and high-frequency oscillations were recorded at the same precentral electrodes (A1 in Patient 2 and A5 in Patient 5). Note the better isolated oscillation potentials on restricted filtering as a result of the attenuation of slower SEP components. Most of the oscillation potentials can be identified with both bandpass filters. p22 can only be seen on restricted bandpass filtering in Patient 2. The latencies of oscillations differed by 0.11 ms for the two different bandpass filters. ... Clinical and imaging characteristics of 8 patients for whom high-frequency oscillations were evaluateda ... Cortical distributions of SEPs and high-frequency oscillations to median nerve stimulation in Patient 7. (A) Typical high-frequency oscillation potential recorded at electrode C1. (B) The location of recording electrodes on the 3-dimensional MRI reconstruction. (C) Cortical distributions of the SEPs and high-frequency oscillations. Most oscillation potentials are distributed similar to or more diffusely than P20/N20. Three later oscillations (n18, p18 and n19) are elicited in a restricted cortical area similar to P25. ... High-frequency oscillation... Objective: To elucidate the generator sources of high-frequency oscillations of somatosensory evoked potentials (SEPs), we recorded somatosensory evoked high-frequency oscillations directly from the human cerebral cortex.... The locations of the subdural electrode array and functional brain mapping in each patient. SEPs and high-frequency oscillations were recorded from the electrodes enclosed by solid lines. Electrodes A7 and C4, and A4 were not used for recording because of disconnection of the wires in Patients 5 and 7, respectively. CS, central sulcus.
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Frequency spectra of pressure oscillations for cavity L4A90 without hydrogen injection. ... Frequency spectra of pressure oscillations for cavity L7A90. ... Oscillation... Pressure and flame oscillations in a scramjet combustor are investigated experimentally. In cold flows, cavity oscillations appear to be dominated by Rossiter mode, and cavities with larger aft angle seem to exhibit pressure oscillations of higher frequency and intensity. When combustion occurs, both the frequency and intensity of the pressure oscillations shift to higher levels (15–20kHz, >170dB), indicating the existence of high-frequency, strong flow and combustion oscillations. The cavity flameholder with larger aft angle tends to exhibit stronger flame oscillations as well as shorter ignition distances, indicating moderate oscillations may be beneficial to the ignition and combustion.... History and frequency spectra of flamefront oscillations for cavity L7A90, Pjet=1.2MPa. ... Frequency and intensity of pressure oscillations. ... Average location and rms of flamefront oscillations.
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In this paper, a new method for computing the amplitude and frequency of differential ring oscillators (ROs) is proposed. The analysis is performed in two separate parts. In the first of these, equations are derived with the assumption of a sinusoidal waveform of outputs, while in the other, the outputs are assumed to be exponential. It is shown that the derived equations for frequency and amplitude are sufficiently exact. In addition, conditions in which sinusoidal and exponential output occur are thoroughly discussed. In the instances in which the results did not satisfy the necessary conditions for sinusoidal output, the output is assumed to be exponential. Moreover, the related analytical equations are written, and the new expressions for frequency and amplitude of ROs are derived. Analytical results are confirmed by simulation results, using the Taiwan Semiconductor Manufacturing Company 0.18µm technology model. The simulation results indicate the high level of accuracy of the proposed model.... Plot of oscillation frequency versus the number of stage for sinusoidal case. Vbias=0.7, Iss=[0.6_1mA], Wn/L=7/0.18, Wp/L=10/0.18. ... Plot of oscillation frequency versus resistor load for sinusoidal case. N=3, Wn/L=[4/0.18_10/0.18], Cl=[67.5fF_87fF], Iss=1mA. ... The chain of delay stages in (a) a single-ended ring oscillator and (b) a differential ring oscillator. ... Ring oscillators... Plot of oscillation frequency versus the number of stage for exponential case. Vbias=0.7, Iss=[0.6_1mA], Wn/L=15/0.18, Wp/L=10/0.18. ... Plot of oscillation frequency versus external capacitor for exponential case. N=3, Wn/L=15/0.18, RL=1.5k, Iss=1mA.
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Sinusoidal oscillator... In this paper, two new designs are proposed for sinusoidal oscillators based on a single differential voltage current conveyor transconductance amplifier (DVCCTA). Each of the proposed circuits comprises a DVCCTA combined with passive components that simultaneously provides both voltage and current outputs. The first circuit is a DVCCTA-based single-resistance-controlled oscillator (SRCO) that provides independent control of the oscillation condition and oscillation frequency by using distinct circuit parameters. The second circuit is a DVCCTA-based variable frequency oscillator (VFO) that can provide independent control of the oscillation frequency by adjusting the bias current of the DVCCTA. In this paper, the DVCCTA and relevant formulations of the proposed oscillator circuits are first introduced, followed by the non-ideal effects, sensitivity analyses, frequency stability discussions, and design considerations. After using the 0.35-μm CMOS technology of the Taiwan Semiconductor Manufacturing Company (TSMC), the HSPICE simulation results confirmed the feasibility of the proposed oscillator circuits.... Simulation results of the start-up oscillations of the variable frequency dual-mode sinusoidal oscillator (Fig. 4). ... Circuit diagram of the proposed DVCCTA-based variable frequency dual-mode sinusoidal oscillator. ... Variation of the oscillation frequency against R2 for the circuit (Fig. 3). ... Simulation results of the highest applicable oscillations of the variable frequency dual-mode sinusoidal oscillator (Fig. 4): (a) output waveform in the steady state; and (b) the start-up of the oscillations. ... Oscillation frequency against the bias current IB of the circuit shown in Fig. 4.
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Sectorial oscillation of acoustically levitated water drop: (a) δ and ε versus time, (b) fit of outline with Eq. (2). δ and ε are the instantaneous amplitude of the axisymmetric oscillation and sectorial oscillation respectively. ... Sectorial oscillation frequencies and the corresponding modulation frequencies of levitated drops for degree l=2. ... Liquid drops can be suspended in air with acoustic levitation method. When the sound pressure is periodically modulated, the levitated drop is usually forced into an axisymmetric oscillation. However, a transition from axisymmetric oscillation into sectorial oscillation occurs when the modulation frequency approaches some specific values. The frequency of the sectorial oscillation is almost exactly half of the modulation frequency. It is demonstrated that this transition is induced by the parametric resonance of levitated drop. The natural frequency of sectorial oscillation is found to decrease with the increase of drop distortion extent.... Sectorial oscillation frequency of acoustically levitated water drops: (a) the angular frequency ω versus the equatorial radius a, (b) the decrease of ω with the increase of distortion extent a/r0. r0 is the radius of drop when it takes a spherical shape. ... Forced axisymmetric oscillation of acoustically levitated water drop: (a) bottom view images of the drop, (b) the time evolution of the equatorial radius R. ... Drop oscillation
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