Showing papers on "Fundamental frequency published in 2011"
TL;DR: A new multiresonant frequency-adaptive synchronization method for grid-connected power converters that allows estimating not only the positive- and negative-sequence components of the power signal at the fundamental frequency but also other sequence components at other harmonic frequencies is presented.
Abstract: This paper presents a new multiresonant frequency-adaptive synchronization method for grid-connected power converters that allows estimating not only the positive- and negative-sequence components of the power signal at the fundamental frequency but also other sequence components at other harmonic frequencies. The proposed system is called MSOGI-FLL since it is based on both a harmonic decoupling network consisting of multiple second-order generalized integrators (MSOGIs) and a frequency-locked loop (FLL), which makes the system frequency adaptive. In this paper, the MSOGI-FLL is analyzed for single- and three-phase applications, deducing some key expressions regarding its stability and tuning. Moreover, the performance of the MSOGI-FLL is evaluated by both simulations and experiments to show its capability for detecting different harmonic components in a highly polluted grid scenario.
950 citations
Proceedings Article•
28 Aug 2011TL;DR: In this article, a method using harmonic information in the residual signal is presented for pitch tracking in noisy conditions, which is used both for pitch estimation, as well as for determining the voicing segments of speech.
Abstract: This paper focuses on the problem of pitch tracking in noisy conditions. A method using harmonic information in the residual signal is presented. The proposed criterion is used both for pitch estimation, as well as for determining the voicing segments of speech. In the experiments, the method is compared to six state-of-the-art pitch trackers on the Keele and CSTR databases. The proposed technique is shown to be particularly robust to additive noise, leading to a significant improvement in adverse conditions. Index Terms: fundamental frequency, pitch tracking, pitch estimation, voicing decisions
248 citations
TL;DR: In this paper, the Galerkin method was used to reduce the nonlinear forced vibrations of FGM doubly curved shallow shells with a rectangular base to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities.
137 citations
TL;DR: The population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics is studied and implications for trapped matter-wave interferometers are discussed.
Abstract: We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.
127 citations
TL;DR: A novel PLL scheme based on a real-time implementation of the discrete Fourier transform (DFT) is presented in this paper and can be considered to be a PLL in which phase detection is performed via a DFT-based algorithm.
Abstract: Phase-locked loop (PLL) algorithms are commonly used to track sinusoidal components in currents and voltage signals in three-phase power systems. Despite the simplicity of those algorithms, problems arise when signals have variable frequency or amplitude, or are polluted with harmonic content and measurement noise, as can be found in aircraft ac power systems where the fundamental frequency can vary in the range 360-900 Hz. To improve the quality of phase and frequency estimates in such power systems, a novel PLL scheme based on a real-time implementation of the discrete Fourier transform (DFT) is presented in this paper. The DFT algorithm calculates the amplitudes of three consecutive components in the frequency domain. These components are used to determine an error signal which is minimized by a proportional-integral loop filter in order to estimate the fundamental frequency. The integral of the estimated frequency is the estimated phase of the fundamental component, and this is fed back to the DFT algorithm. The proposed algorithm can therefore be considered to be a PLL in which phase detection is performed via a DFT-based algorithm. A comparison has been made of the performances of a standard PLL and the proposed DFT-PLL using computer simulations and through experiments.
99 citations
Proceedings Article•
01 Aug 2011TL;DR: PEFAC is presented, a fundamental frequency estimation algorithm that is able to identify the pitch of voiced frames reliably even at negative signal to noise ratios, and performs exceptionally well in both high and low levels of additive noise.
Abstract: We present PEFAC, a fundamental frequency estimation algorithm that is able to identify the pitch of voiced frames reliably even at negative signal to noise ratios. The algorithm combines non-linear amplitude compression, to attenuate narrow-band noise components, with a comb-filter applied in the log-frequency power spectral domain, whose impulse response is chosen to attenuate smoothly varying noise components. We compare the performance of our algorithm with that of other widely used algorithms on a subset of the TIMIT database and demonstrate that it performs exceptionally well in both high and low levels of additive noise.
89 citations
TL;DR: In this article, the authors examined the differential effects of voice auditory feedback perturbation direction and magnitude on voice fundamental frequency (F0) responses and event-related potentials (ERPs) from EEG electrodes on the scalp.
88 citations
TL;DR: The results indicate that the neural responses reflected in the FFR preserve monaural temporal information that may be important for pitch, but provide no evidence for any additional processing over and above that already present in the auditory periphery.
Abstract: The frequency following response (FFR), a scalp-recorded measure of phase-locked brainstem activity, is often assumed to reflect the pitch of sounds as perceived by humans. In two experiments, we investigated the characteristics of the FFR evoked by complex tones. FFR waveforms to alternating-polarity stimuli were averaged for each polarity and added, to enhance envelope, or subtracted, to enhance temporal fine structure information. In experiment 1, frequency-shifted complex tones, with all harmonics shifted by the same amount in Hertz, were presented diotically. Only the autocorrelation functions (ACFs) of the subtraction-FFR waveforms showed a peak at a delay shifted in the direction of the expected pitch shifts. This expected pitch shift was also present in the ACFs of the output of an auditory nerve model. In experiment 2, the components of a harmonic complex with harmonic numbers 2, 3, and 4 were presented either to the same ear (“mono”) or the third harmonic was presented contralaterally to the ear receiving the even harmonics (“dichotic”). In the latter case, a pitch corresponding to the missing fundamental was still perceived. Monaural control conditions presenting only the even harmonics (“2 + 4”) or only the third harmonic (“3”) were also tested. Both the subtraction and the addition waveforms showed that (1) the FFR magnitude spectra for “dichotic” were similar to the sum of the spectra for the two monaural control conditions and lacked peaks at the fundamental frequency and other distortion products visible for “mono” and (2) ACFs for “dichotic” were similar to those for “2 + 4” and dissimilar to those for “mono.” The results indicate that the neural responses reflected in the FFR preserve monaural temporal information that may be important for pitch, but provide no evidence for any additional processing over and above that already present in the auditory periphery, and do not directly represent the pitch of dichotic stimuli.
77 citations
TL;DR: In this paper, a fast and accurate method to estimate the fundamental frequency of an electric power system is presented, based on an algebraic method, which is able to calculate the frequency of a pure sinusoidal signal using three samples.
Abstract: The continuous monitoring of voltage characteristics in electric power systems, such as in microgrids, is required for power quality assessment, grid control, and protection purposes. Due to the presence of disturbances in the grid voltage, such as harmonics, imbalances, noise, and offsets introduced by the instrumentation, among others, the frequency-estimation process has to be robust against all these disturbances to obtain an accurate estimation of the frequency value. This paper presents a fast and accurate method to estimate the fundamental frequency of an electric power system. The estimation method works properly in balanced and imbalanced three-phase systems, and even in single-phase systems. The proposed solution is based on an algebraic method, which is able to calculate the frequency of a pure sinusoidal signal using three samples. A filtering stage is used to increase the robustness of the algorithm against disturbances in a wide frequency range. Simulation and experimental results show the good performance of the method for single- and three-phase systems with a high level of harmonic distortion, even in the presence of amplitude, phase, and frequency changes.
60 citations
21 Jun 2011
TL;DR: Fluctuations of the frictional force arising from the stroke of a finger against flat and sinusoidal surfaces are studied and are consistent with the existence of a multiplicity of simultaneous and rapid stick-slip relaxation oscillations.
Abstract: Fluctuations of the frictional force arising from the stroke of a finger against flat and sinusoidal surfaces are studied A custom-made high-resolution friction force sensor, able to resolve milli-newton forces, was used to record those fluctuations as well as the net, low-frequency components of the interaction force Measurements show that the fluctuations of the sliding force are highly non-stationary Despite their randomness, force spectra averages reveal regularities With a smooth, flat, but not mirror-finish, surface the background noise follows a 1/f trend Recordings made with pure-tone sinusoidal gratings reveal complexities in the interaction between a finger and a surface The fundamental frequency is driven by the periodicity of the gratings and harmonics follow a non-integer power-law decay that suggests strong nonlinearities in the fingertip interaction The results are consistent with the existence of a multiplicity of simultaneous and rapid stick-slip relaxation oscillations Results have implications for high fidelity haptic rendering and biotribology
59 citations
TL;DR: In this paper, a finite element program is developed to analyze vibration of locally anisotropic composite plates, and the fundamental frequency is taken as an object function to be maximized.
TL;DR: This paper investigates the extraction of acoustic signatures from small boats using a passive sonar system and shows the HEAT algorithms ability to extract these signatures.
Abstract: This paper investigates the extraction of acoustic signatures from small boats using a passive sonar system. Noise radiated from a small boats consists of broadband noise and harmonically related tones that correspond to engine and propeller specifications. A signal processing method to automatically extract the harmonic structure of noise radiated from small boats is developed. The Harmonic Extraction and Analysis Tool (HEAT) estimates the instantaneous fundamental frequency of the harmonic tones, refines the fundamental frequency estimate using a Kalman filter, and automatically extracts the amplitudes of the harmonic tonals to generate a harmonic signature for the boat. Results are presented that show the HEAT algorithms ability to extract these signatures.
TL;DR: In this paper, the authors quantified and modeled the relative frequency drop affecting low-rise modern masonry buildings and discussed the damping variations based on two experimental data sets: Pseudo-dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL.
Abstract: The knowledge of fundamental frequency and damping ratio of structures is of uppermost importance in earthquake engineering, especially to estimate the seismic demand. However, elastic and plastic frequency drops and damping variations make their estimation complex. This study quantifies and models the relative frequency drop affecting low-rise modern masonry buildings and discusses the damping variations based on two experimental data sets: Pseudo-dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL. The relative structural frequency drop is shown to depend mainly on shaking amplitude, whereas the damping ratio variations could not be explained by the shaking amplitude only. Therefore, the absolute frequency value depends mostly on the frequency at low amplitude level, the amplitude of shaking and the construction material. The decrease in shape does not vary significantly with increasing damage. Hence, this study makes a link between structural dynamic properties, either under ambient vibrations or under strong motions, for low-rise modern masonry buildings. A value of 2/3 of the ambient vibration frequency is found to be relevant for the earthquake engineering assessment for this building type. However, the effect of soil–structure interaction that is shown to also affect these parameters has to be taken into account. Therefore, an analytical methodology is proposed to derive first the fixed-base frequency before using these results. Copyright © 2010 John Wiley & Sons, Ltd.
TL;DR: In this paper, the longitudinal frequency of a cracked nanobeam with clamped-clamped and clamped free boundary conditions is derived based on the nonlocal elasticity theory.
TL;DR: The nonlinear vibrational properties of single layer graphene sheets (SLGSs) are investigated using a membrane model and it is concluded that the nonlinear fundamental frequency of SLGSs increases by increasing the pretension and initial velocity.
Abstract: The nonlinear vibrational properties of single layer graphene sheets (SLGSs) are investigated using a membrane model. The nonlinear equation of motion is considered for the SLGSs by including the effects of stretching due to large amplitudes. The equation of motion is numerically solved utilizing the finite difference method for SLGSs with different initial and boundary conditions, sizes and pretensions. It is concluded that the nonlinear fundamental frequency of SLGSs increases by increasing the pretension and initial velocity. In addition, it is observed that an increase in the pretension weakens the effects of the initial velocity on the fundamental frequency, such that the fundamental frequency approximately becomes independent of the initial velocity. This is an important feature of the vibrating systems consisting of SLGSs which are used in the nano-electromechanical systems (NEMS), where resonators with a specific fundamental frequency and independent of the initial velocity are of interest.
TL;DR: In this paper, a switchable tunable and switchable bandpass fllter was designed by using the centrally-loaded slot-line resonator, which can give a 30.9% frequency tuning range with acceptable insertion loss when a varactor is used as the loading element.
Abstract: In this paper, novel uniplanar tunable and switchable bandpass fllters are designed by using the centrally-loaded slot-line resonator. From the voltage-wave distribution along the resonator, the appropriate location for the loading element is determined to be the center of the slot-line resonator, where the voltages of the fundamental signal and second harmonic are maximum and zero, respectively. As a result, the fundamental frequency can be tuned while the second harmonic remains almost unchanged. For the flrst time, the properties of the centrally-loaded slot-line resonator are analyzed by using the even- and odd-mode method, and their respective resonant frequencies are derived. The demonstrated tunable bandpass fllter can give a 30.9% frequency tuning range with acceptable insertion loss when a varactor is used as the loading element. By replacing the loading varactors with PIN diodes, a switchable bandpass fllter is realized in which the attenuation in the fundamental passband can be controlled. In experiments, the switchable bandpass fllter exhibits a 2.13dB insertion loss in the fundamental passband when the PIN diodes are ofi and more than 49dB isolation across the passband when the PIN diodes are on.
TL;DR: In this paper, the authors investigated the power absorbed by the electrons Pe as a function of θ and time experimentally, by a particle in cell simulation, and an analytical model.
Abstract: The symmetry of capacitive radio frequency discharges can be controlled via the electrical asymmetry effect by driving one electrode with a fundamental frequency and its second harmonic. In such electrically asymmetric discharges, the mean ion energies at both electrodes are controlled separately from the ion flux by tuning the phase angle θ between the harmonics at fixed voltage amplitudes. Here, the question why the ion flux is nearly independent of θ is answered by investigating the power absorbed by the electrons Pe as a function of θ and time experimentally, by a particle in cell simulation, and an analytical model. The dynamics of Pe is understood by the model and is found to be strongly affected by the choice of θ. However, on time average, Pe is nearly constant, independently of θ. Thus, the ion flux remains approximately constant. In addition, it is shown that the absolute value of the individual voltages across the powered and grounded electrode sheath vary linearly with the dc self-bias. Howeve...
TL;DR: In this paper, the application of compact non-uniform transmission line transformers (NTLTs) in suppressing and controlling the odd harmonics of the fundamental frequency is presented.
Abstract: In this paper, the application of compact non-uniform transmission line transformers (NTLTs) in suppressing and controlling the odd harmonics of the fundamental frequency is presented. A design example showing the complete suppression of the odd harmonics of the fundamental frequency is given. In addition, several compact NTLTs are designed showing the possibility of controlling the existence of a fundamental frequency's odd harmonics. Moreover, multi-band operation using NTLTs is investigated. Speciflcally, a design example of a miniaturized triple-frequency NTLT is introduced. Based on these compact NTLTs, a 3-way triple-frequency modifled Bagley power divider (BPD) with a size reduction of 50%, and a 5-way modifled BPD with harmonics suppression and size reduction of 34%, are designed. For veriflcation purposes, both dividers are simulated using the two full-wave simulators IE3D and HFSS. Moreover, the modifled 5-way BPD with harmonics suppression is fabricated and measured. Both the simulation and measurement results validate the design approach.
TL;DR: In this paper, an analysis of ideal power amplifier (PA) efficiency maximization subject to a finite set of arbitrary complex harmonic terminations, extending previous results where only reactive harmonic termination(s) were treated.
Abstract: This paper presents an analysis of ideal power amplifier (PA) efficiency maximization subject to a finite set of arbitrary complex harmonic terminations, extending previous results where only purely reactive harmonic terminations were treated. Maximum efficiency and corresponding fundamental output power and load impedance are analyzed as a function of harmonic termination(s). For a PA restricted to second harmonic drain waveform shaping, maximum efficiency as a function of second harmonic termination is treated for cases of both purely real and complex fundamental frequency impedances. For the case of a PA restricted to second and third harmonic drain waveform shaping, peak efficiency as a function of third harmonic impedance with an ideal second harmonic termination is analyzed. Additionally, the sensitivity of PA efficiency with respect to the magnitude and phase of the second and third harmonic load reflection coefficients is examined. The analysis is extended to include device and package parasitics. The paper concludes with a discussion of how the presented general analysis method provides useful insights to the PA designer.
TL;DR: It is shown that the excitation of localized surface plasmon polaritons in these structures can remarkably modify the nonlinear response of the system by enhancing surface and/or bulk contributions, creating regimes where bulk nonlinear terms dominate over surface linear terms and vice versa.
Abstract: We numerically study second harmonic generation from dipole gold nanoantennas by analyzing the different contributions of bulk and surface nonlinear terms. We focus our attention to the properties of the emitted field related to the different functional expressions of the two terms. The second harmonic field exhibits different far and near field patterns if both nonlinear contributions are taken into account or if only one of them is considered. This effect persists despite of the model used to estimate the parameters of the nonlinear sources and it is strictly related to the resonant behavior of the plasmonic nanostructure at the fundamental frequency field and to its linear properties at the second harmonic frequency. We show that the excitation of localized surface plasmon polaritons in these structures can remarkably modify the nonlinear response of the system by enhancing surface and/or bulk contributions, creating regimes where bulk nonlinear terms dominate over surface linear terms and vice versa. Finally, the results of our calculations suggest a method that could be implemented to experimentally extract information on the relevance of bulk and surface contributions by measuring and analyzing the generated far field second harmonic patterns in metal nanoantennas and, more in general, in plasmonic nanostructures.
TL;DR: In this paper, a detailed multipolar tensor analysis of second-harmonic (SH) generation from arrays of L-shaped gold nanoparticles is presented, which includes electric dipoles only (A eee ) and lowest order magnetic (and quadrupole) effects at the fundamental and the SH (A mee ) frequency.
Abstract: We present a detailed multipolar tensor analysis of second-harmonic (SH) generation from arrays of L-shaped gold nanoparticles. We define three effective nonlinear tensors, which include electric dipoles only (A eee ) and lowest- order magnetic (and quadrupole) effects at the fundamental (A eem ) and the SH (A mee ) frequency. The components of the various tensors are distinguished through their different transformations as the experimental geometry is varied. The response is dominated by electric-dipole effects. However, the higher multipoles also play a significant role and are more important at the fundamental frequency than at the SH frequency. The results correlate well with the particles' plasmonic resonances and symmetry rules.
TL;DR: With both simulated and experimental data of broken rotor bars, it shows that the proposed algorithm can extract more detailed fault signature frequency components and realize the incipient fault detection of induction motors.
Abstract: Faults, such as broken rotor bars, in induction motors may be detected by estimating the spectral signature of the stator currents, particularly the sidebands around the supply line frequency. However, the amplitude of the fundamental frequency (50 Hz) is considerably greater than the sideband amplitude. How to demodulate the signature frequency components under the heavy background of fundamental frequency, or how to remove the fundamental frequency, is becoming a key problem in motor current signature analysis. This paper puts forward a novel transform demodulation algorithm to solve the problem. The three-phase currents are transformed to a magnetic-torque (M-T) coordinate using this algorithm. It is found that the signature frequency components are demodulated in the magnetizing and torque-producing currents obtained by the transformation. Thus, the two demodulated M-T currents can be used to extract the enhanced signature frequency components of faults, and the incipient fault detection of induction motors is easy to realize. With both simulated and experimental data of broken rotor bars, it shows that the proposed algorithm can extract more detailed fault signature frequency components and realize the incipient fault detection of induction motors.
TL;DR: A sound-coding strategy for users of cochlear implants, named enhanced-envelope-encoded tone (eTone), was developed to improve coding of fundamental frequency (F0) in the temporal envelopes of the electrical stimulus signals and was designed to provide an accurate estimate of F0 with minimal processing lag and robustness to the effects of competing noise.
Abstract: A sound-coding strategy for users of cochlear implants, named enhanced-envelope-encoded tone (eTone), was developed to improve coding of fundamental frequency (F0) in the temporal envelopes of the electrical stimulus signals. It is based on the advanced combinational encoder (ACE) strategy and includes additional processing that explicitly applies F0 modulation to channel envelope signals that contain harmonics of prominent complex tones. Channels that contain only inharmonic signals retain envelopes normally produced by ACE. The strategy incorporates an F0 estimator to determine the frequency of modulation and a harmonic probability estimator to control the amount of modulation enhancement applied to each channel. The F0 estimator was designed to provide an accurate estimate of F0 with minimal processing lag and robustness to the effects of competing noise. Error rates for the F0 estimator and accuracy of the harmonic probability estimator were compared with previous approaches and outcomes demonstrated that the strategy operates effectively across a range of signals and conditions that are relevant to cochlear implant users.
10 Jun 2011
TL;DR: In this article, a piezoelectric cantilevered-type bimorph harvester is considered and it is shown that by tilting the axis of the beam through a proper angle with respect to the direction of excitation, a parametric pump can enhance the output power at the fundamental frequency.
Abstract: Due to inherent system nonlinearities, many vibratory excitation sources possess a frequency spectrum which contains energy components at multiple integers of the fundamental frequency of the source. In this paper, we theoretically explore the prospect of enhancing the transduction of a vibratory energy harvester (VEH) by utilizing the parametric amplification phenomenon to channel energy from one of these superharmonics, namely the one at twice the fundamental frequency, to a purely resistive load. Towards that end, we consider a piezoelectric cantilevered-type bimorph harvester and show that by tilting the axis of the beam through a proper angle with respect to the direction of excitation, it is possible to utilize a parametric pump to enhance the output power at the fundamental frequency. Percentage improvement in the output power depends on the excitation’s parameters and the mechanical damping ratio. It is observed that when the mechanical damping ratio is small, significant enhancement in the output...
TL;DR: The multimode linear cavity laser is shown to be a suitable candidate for thermal-noise-limited, meter-long fiber laser strain sensors with a strain resolution of 14 fϵ/Hz(1/2) at 1 kHz.
Abstract: A multimode linear cavity and a single-mode unidirectional ring cavity fiber laser with meter-long cavity lengths are shown to exhibit frequency noise limited by fundamental thermodynamic noise from 100 Hz to 100 kHz. Their measured spectra agree closely with theoretically derived thermodynamic noise and the characteristic dependence of the frequency noise power spectrum on the inverse of the cavity length is observed. The unidirectional ring laser exhibits a frequency noise of 2 Hz/Hz1/2 at 1 kHz, one of the lowest published values to date from a free-running laser. The multimode linear cavity laser is shown to be a suitable candidate for thermal-noise-limited, meter-long fiber laser strain sensors with a strain resolution of 14 fϵ/Hz1/2 at 1 kHz.
TL;DR: In this article, the fundamental frequencies for CNTs range from 10 to 250GHz and 100 to 1000GHz for the cantilevered and bridged conditions, respectively, with an odd/even shape mode switch.
TL;DR: The spectral analysis of complex noisy signals containing several frequency components enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency, and is applicable to relatively short time series containing frequencies that are time variable.
Abstract: A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
TL;DR: The experimental results show only a weak dependence of the harmonic current ratio error and phase displacement on the amplitude and phase shift of the excitation harmonic of the Rogowski coil current transducer.
Abstract: This paper reports the results of an experimental study dealing with a commercial Rogowski coil current transducer (RCCT) in the presence of harmonic distortion The RCCT was observed under two conditions: 1) sinusoidal excitation with frequencies from 50 to 750 Hz and 2) nonsinusoidal excitation using fundamental frequency and one harmonic, with adjustable amplitude and phase shift The experimental results show only a weak dependence of the harmonic current ratio error and phase displacement on the amplitude and phase shift of the excitation harmonic The phase displacement is also independent of the conductor position within the Rogowski coil window An error compensation method, based on the frequency response, was implemented and tested with a distorted waveform The compensation method allows one to obtain an improvement of the RCCT accuracy class from 1% and 1°, in the case of a sinusoidal signal at mains frequency, to 005% and 005°, both for the fundamental and the distorted signal harmonics
TL;DR: In this paper, a genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells, where the objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial bearing load.
TL;DR: In this article, nonlinear free and forced vibrations of doubly curved isotropic shallow shells are investigated via multi-modal Galerkin discretization and the method of multiple scales.
Abstract: Non-linear free and forced vibrations of doubly curved isotropic shallow shells are investigated via multi-modal Galerkin discretization and the method of multiple scales. Donnell’s non-linear shallow shell theory is used and it is assumed that the shell is simply supported with movable edges. By deriving two different forms of the stress function, the equations of motion are reduced to a system of infinite non-linear ordinary differential equations with quadratic and cubic non-linearities. A quadratic relation between the excitation and the fundamental frequency is considered and it is shown that, although in case of hardening non-linearities the results resemble those found via numerical integration or continuation softwares, in case of softening non-linearity the solution breaks down as the amplitude becomes larger than the thickness. Results reveal that, expressing the relation between the excitation and fundamental frequency in this form, which was considered by many researchers as a useful tool in analyzing strong non-linear oscillators, yields in spurious results when the non-linearity becomes of softening type.