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The effects of harmonics, interharmonics, and subharmonics on low-voltage distribution networks, leading to a deterioration in electrical power quality, have become more evident in recent years. The main harmonic sources are power electronic devices due to their implicit nonlinearity. Interharmonic and subharmonic components are mainly caused by a lack of synchronization between the grid frequency and the switching frequency of the power converters. This can be caused by asynchronous modulated devices, or more commonly by fluctuations in the fundamental grid frequency. Interharmonic currents cause interharmonic voltage distortions that affect grid-synchronized or frequency-dependent systems. The IEC-61000-4-7 proposes a general guide on harmonics, interharmonic measurements, and instrumentation in current supply systems. However, the techniques proposed in the standard are intended for measurement and do not enable a precise identification of the interharmonic components in a signal. This work proposes new definitions for the spectral energy aggrupation to improve signal component detection for the IEC standard. Furthermore, an adaptive Kalman filter algorithm is developed that enables the exact identification in real time of the frequency, amplitude, and phase of these components. The proposed system will become the basis for the implementation of a new range of measurement systems that provide improved accuracy and real-time operation. The work is supported by simulated results analysing various scenarios (including transients after changes in harmonic content in the grid voltage) that demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The nonlinear resonance between the saturated inductance of a transformer and capacitance of the switching device in a substation induces overvoltages and overcurrents. The voltage transformer experience 2–4 pu overvoltages due to the different modes of nonlinear resonance. Though many overvoltage suppression circuits are being proposed, the transformer does not have a single suppression circuit against all modes. A memristor-based suppression circuit has been proposed already for the fundamental (periodic) mode of ferroresonance. In this paper, an aperiodic mode of ferroresonance has been addressed with same memristive circuit along with meminductive circuit. A subharmonic mode of ferroresonance overvoltage of 3.13 pu has been induced in a (400 kV/ √ 3 )/(110 V/ √ 3 ) CVT model according to IEC 61869 -5 standards. The primary current got increased from 23.3 mA to 1.56 A and has subharmonic frequency components. A meminductor circuit is proposed as a suppression circuit against ferroresonance for a Substation CVT. A gas discharge lamp T8 Philips 18 W with low-frequency magnetic ballast emulated peculiar pinched hysteretic characteristics of a memristor. The relation between charge and flux termed as memristance of the memristor circuit is used to mitigate the nonlinear resonance oscillations. A mutator circuit for mitigation requirement has been connected to the lamp model to emulate meminductor characteristics. The mitigation performance shows that the meminductor circuit dominantly recovers the secondary voltage of CVT in 0.188 s with a reduction of 1/3rd, 1/5th, and 1/7th harmonic components by 35.4%, 78.15%, and 90.41%, respectively. [ABSTRACT FROM AUTHOR]

Various power quality disturbances commonly occur in a power system, including voltage fluctuations. These can be analysed as simultaneous occurrences of voltage subharmonics and interharmonics of various frequencies – components of frequency less than the fundamental one or not being its integer multiple. This work deals with the impact of voltage fluctuations on currents of a single-phase induction motor. The results of the research on currents are presented for rectangular amplitude modulation and are compared with the investigation results under sinusoidal modulation and the appearance of a single voltage subharmonic.

Cyclic voltage fluctuations can be considered as a superposition of the fundamental voltage component, subharmonic and interharmonic components – that is the components of frequency less than the fundamental one or not being its integer multiple. A commonly occurring case of voltage fluctuations is square voltage modulation. This paper deals with the effect of square voltage modulation on the rotational speed of an induction motor. The results of the FEM computations are presented for a cage induction motor with a rated power 3 kW and various parameters describing the voltage modulation.

The effects of harmonics, interharmonics, and subharmonics on low-voltage distribution networks, leading to a deterioration in electrical power quality, have become more evident in recent years. The main harmonic sources are power electronic devices due to their implicit nonlinearity. Interharmonic and subharmonic components are mainly caused by a lack of synchronization between the grid frequency and the switching frequency of the power converters. This can be caused by asynchronous modulated devices, or more commonly by fluctuations in the fundamental grid frequency. Interharmonic currents cause interharmonic voltage distortions that affect grid-synchronized or frequency-dependent systems. The IEC-61000-4-7 proposes a general guide on harmonics, interharmonic measurements, and instrumentation in current supply systems. However, the techniques proposed in the standard are intended for measurement and do not enable a precise identification of the interharmonic components in a signal. This work proposes new definitions for the spectral energy aggrupation to improve signal component detection for the IEC standard. Furthermore, an adaptive Kalman filter algorithm is developed that enables the exact identification in real time of the frequency, amplitude, and phase of these components. The proposed system will become the basis for the implementation of a new range of measurement systems that provide improved accuracy and real-time operation. The work is supported by simulated results analysing various scenarios (including transients after changes in harmonic content in the grid voltage) that demonstrate the effectiveness of the proposed method.

In some power systems, the voltage waveform contains frequency components less than fundamental, called subharmonics or subsynchronous interharmonics. Voltage subharmonics can be both positive- and negative-sequence, independent of their frequency (order). Subharmonics exert harmful effects on sundry electrical equipment, especially on rotating machinery; they cause various noxious phenomena, such as a local saturation of the magnetic circuit, increases in power losses and windings temperature, and torque pulsations leading to vibration of unacceptable severity. Notably, previous works reported excessive vibration of rotating machinery only under no-load, while under full load, rather moderate vibration occurred. This study deals with vibration analysis of a line-start permanent magnet synchronous motor (LSPMSM) supplied with the voltage containing negative-sentence subharmonics. Experimental investigations were conducted for a 3 kW, four-pole production LSPMSM for subharmonics of various values and frequencies. Voltage subharmonics of values significantly less than reported in real power systems were found to cause unacceptable vibration, especially under full load. [ABSTRACT FROM AUTHOR]

The article considers the dynamics of a nonlinear mechanical system under the action of a kinematic perturbation on it. The object's vibration isolation system is described by a rigid cubic power characteristic and is based on compensation of external perturbations — the introduction of an additional elastic element with negative stiffness into the suspension. Numerical modeling of the system is performed, the results of which are analyzed by the method of spectral analysis, based on the representation of the correlation function on a small time interval by a square polynomial. As a result of the analysis, it is found that in the pre-resonant and resonant regions, the general solution should consist of three components: a subharmonic of the order of 1/3, the fundamental harmonic, and the third harmonic. It is noted that only the subharmonic of the order of 1/3 and the fundamental harmonic are important in the resonant zone. It is also noted that even simple nonlinear mechanical systems in the study of dynamics should use approximate analytical and numerical methods in combination with spectral analysis, since traditional methods of nonlinear mechanics are not adapted to solving problems taking into account a relatively large number of harmonic components that appear due to nonlinearity.

Oscillatory processes in nonlinear multiphase electro ferromagnetic circuits (EFMC) have an exceptional variety and complexity, and therefore their research is also associated with solving complex physical problems. Theoretical analysis, in order to identify the main patterns of excitation of subharmonic oscillations of various orders, and the development of engineering calculation methods are of particular importance in designing and creating various switching-type converter devices. On the other hand, two-phase self-oscillating circuits are physical models of power transmission lines (power lines). Consequently, the study of the excitation of the existence of subharmonic oscillations in two-phase systems allows us to establish some patterns of overvoltage with power lines with capacitive compensation caused by harmonic oscillations, and, if possible, take measures to prevent these abnormal modes or mitigate their negative consequences. This article discusses the process of excitation of subharmonic oscillations ω/2 in two-phase EFMC. Using the method of energy relations, the areas of existence and critical values of the circuit parameters are determined.

In modern power systems, interharmonics have emerged as noninteger frequency components that appear in current or voltage signals. Double-stage AC-DC-AC converters have been identified as a primary source of interharmonics. Previous studies have highlighted modulation techniques, filters, passive components, unbalanced conditions and DC link effects as relevant factors. However, the interaction between these factors and the inertial properties of induction motors has not been explored. This study assesses various types of AC drives, including variable frequency drives (VFDs) and soft starters (AC choppers), to investigate their interaction with machine inertial properties in interharmonic generation. The employed technique for time-frequency spectral analysis is the wavelet synchrosqueezed transform combined with a clustering method. This paper demonstrates that the interaction of the inertial properties of low-power induction motors with the variations of the switching frequencies of the VFDs, the filters used in the DC link and a soft start indirectly contribute to harmonic generation and potentially to interharmonics in the electrical grid and the outputs of the inverter. [ABSTRACT FROM AUTHOR]

The presented study examines the effect of voltage subharmonics, which relates to components of the frequency less than the fundamental voltage harmonic, and the currents and vibration of the line start permanent magnet synchronous motor. The obtained experimental results corresponded to a production motor with a rated power of 3 kW and a rated speed of 1500 rpm. The main purpose of our study was to highlight that the subharmonic value had a non-linear effect on the vibration level of the considered motor. It was found that for subharmonic values up to approx. 0.5% of the vibration level could be considered acceptable for long-term operation, whereas vibration caused by voltage subharmonics of values greater than approx. 0.8% might promote machine damage. [ABSTRACT FROM AUTHOR]

This article presents the results of research on the influence of the distorted induction motor supply voltage on two selected indicators (phase trajectories and Poincare maps) of chaotic behavior observed in the stator current of an induction motor. The tests were carried out with the use of the proprietary engine model realized in the ANSYS Electronics Desktop environment. [ABSTRACT FROM AUTHOR]

In some power systems, the voltage waveform contains frequency components less than fundamental, called subharmonics or subsynchronous interharmonics. Voltage subharmonics can be both positive- and negative-sequence, independent of their frequency (order). Subharmonics exert harmful effects on sundry electrical equipment, especially on rotating machinery; they cause various noxious phenomena, such as a local saturation of the magnetic circuit, increases in power losses and windings temperature, and torque pulsations leading to vibration of unacceptable severity. Notably, previous works reported excessive vibration of rotating machinery only under no-load, while under full load, rather moderate vibration occurred. This study deals with vibration analysis of a line-start permanent magnet synchronous motor (LSPMSM) supplied with the voltage containing negative-sentence subharmonics. Experimental investigations were conducted for a 3 kW, four-pole production LSPMSM for subharmonics of various values and frequencies. Voltage subharmonics of values significantly less than reported in real power systems were found to cause unacceptable vibration, especially under full load.

As-prepared mesoporous silicon nanoparticles, which were synthesized by electrochemical etching of crystalline silicon wafers followed by high-energy milling in water, were explored as a sonosensitizer in aqueous media under irradiation with low-intensity ultrasound at 0.88 MHz. Due to the mixed oxide-hydride coating of the nanoparticles' surfaces, they showed both acceptable colloidal stability and sonosensitization of the acoustic cavitation. The latter was directly measured and quantified as a cavitation energy index, i.e., time integral of the magnitude of ultrasound subharmonics. The index turned out to be several times greater for nanoparticle suspensions as compared to pure water, and it depended nonmonotonically on nanoparticle concentration. In vitro tests with Lactobacillus casei revealed a dramatic drop of the bacterial viability and damage of the cells after ultrasonic irradiation with intensity of about 1 W/cm2 in the presence of nanoparticles, which themselves are almost non-toxic at the studied concentrations of about 1 mg/mL. The experimental results prove that nanoparticle-sensitized cavitation bubbles nearby bacteria can cause bacterial lysis and death. The sonosensitizing properties of freshly prepared mesoporous silicon nanoparticles are beneficial for their application in mild antibacterial therapy and treatment of liquid media. [ABSTRACT FROM AUTHOR]

In some power systems, voltage waveforms contain, apart from harmonics, interharmonics and subharmonics that are components of frequency less than or not an integer multiple of the fundamental frequency. Voltage subharmonics and interharmonics may be of both a positive and negative sequence, independently of their frequency. Previous papers on induction motors under subharmonics have been generally limited to the components of a positive sequence. This study deals with the effect of negative sequence subharmonics on the work of induction motors. Investigations were performed using the 2D finite element method and an experimental method. Differences between the impact of positive and negative sequence subharmonics are discussed. It was found that negative sequence voltage subharmonics can result in significant current subharmonics, torque pulsations and vibration. Further, because of possible resonance, motors that are comparatively resistant to positive sequence subharmonics might be especially sensitive to negative sequence subharmonics of the same frequency and vice versa. [ABSTRACT FROM AUTHOR]

A specific case of voltage fluctuations is sinusoidal voltage modulation, which is a superposition of the fundamental voltage component and the subharmonic and interharmonic components - that is components of frequency less than the fundamental one or not being an integer multiple of it. Depending on the phase angles of the subharmonic and interharmonic components, various cases of voltage modulation can be distinguished, like amplitude, phase and intermediate modulations. This paper deals with the effect of phase angles of the subharmonic and interharmonic components on speed variation. The results of FEM computations are presented for a cage induction motor with a rated power of 3 kW. [ABSTRACT FROM AUTHOR]

One unique feature of nonlinear dynamical systems is the existence of superharmonic and subharmonic resonances in addition to primary resonances. In this study, an effective vibration testing methodology is introduced for the experimental identification of these secondary resonances. The proposed method relies on phase-locked loop control combined with adaptive filters for online Fourier decomposition. To this end, the monotonic evolution of the phase lag around secondary resonances is exploited for their identification. The method is demonstrated using two systems featuring cubic nonlinearities, namely a numerical Duffing oscillator and a physical experiment comprising a clamped–clamped thin beam. The obtained results highlight that the control scheme can accurately characterize secondary resonances as well as track their backbone curves. A particularly salient feature of the developed algorithm is that, starting from the rest position, it facilitates an automatic and smooth dynamic state transfer toward one point of a subharmonic isolated branch, hence, inducing branch switching experimentally. • Develop a novel control-based method for secondary resonances identification. • Integrate PLL control with adaptive filters to enable real-time Fourier decomposition. • Effectively characterize folded superharmonic responses and subharmonic isolas. • Validate the proposed method using numerical and experimental demonstration. • Demonstrate an automatic dynamic state transfer process inducing branch switching. [ABSTRACT FROM AUTHOR]

• Enhancing Ultrasonic Imaging of Microvascular Perfusion: This study explores the use of quantitative ultrasound (QUS) parameters to enhance the visualization of microvascular perfusion using ultrasound contrast agents (UCAs). • Novel Insights into Harmonic Signal Analysis: The research delves into the statistical properties of nonlinear harmonic signals emitted by UCAs, providing a comprehensive understanding of their behavior under varying conditions. • Innovative WMC Nakagami Ratio Parameter: The study introduces a new QUS parameter, the Weighted Median-Clipped (WMC) Nakagami ratio, which offers robust and accurate measurements of UCAs, with potential applications in detecting small tumor neovascularization and improving clinical diagnostics. Assessing microvascular perfusion using medical modalities is crucial for diagnosing various diseases accurately. To enhance ultrasound image contrast and improve visualization of vascular distribution, nonlinear harmonic signals of ultrasound contrast agents (UCAs) are widely employed. However, there is a lack of comprehensive discussion on the statistical properties of the nonlinear harmonic signals emitted by UCAs, necessitating further elucidation of quantitative ultrasound (QUS) parameters derived from ultrasonic backscattered signals. To address these issues, two-dimensional computer simulations were conducted to investigate the impact of UCAs' harmonic emission on estimating QUS parameters like integrated backscatter (IB), Nakagami parameters, and Gray-level Co-occurrence Matrix (GLCM) parameters. The simulation studies assessed the performance of QUS parameters estimated from ultrasonic nonlinear harmonic backscattered signals under varying levels of sub- and second harmonic levels and UCAs concentrations. The results unveiled a consistent upward trend in QUS parameters derived from the Nakagami statistical model, aligning with the escalation of sub-harmonic and second harmonic levels. Conversely, as these levels approached 0.4, GLCM parameters exhibited a pivotal turning point, indicative of substantial alterations. This progression delineates that the elevation of sub- and second-harmonic levels to 0.4 accentuates local dynamic changes in B-mode images, instigating a transformative shift in parameter growth attributed to an augmented proportion of harmonic signals. In contrast, QUS parameters derived from the Nakagami model exhibited a persistent increase with ascending harmonic signals, showcasing a notable resilience to fluctuations in local image intensity. This study explored the feasibility of using QUS parameters to evaluate the harmonic emission of UCAs. Both the Nakagami statistical model and the GLCM statistical method exhibited the capability to describe the sub- and second harmonic emission characteristics of UCAs. Notably, the newly developed WMC Nakagami ratio parameter demonstrated more robust measurements of UCAs compared to other QUS parameters. [ABSTRACT FROM AUTHOR]

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Some of the most common power quality disturbances are voltage fluctuations. They are interconnected with the presence of voltage subharmonics and interharmonics. Voltage fluctuations, subharmonics and interharmonics exert a negative effect on various elements of a power system, including cage induction motors. This work is devoted to the impact of voltage fluctuations on the current of a one-phase induction motor. The results of empirical investigations are presented for sinusoidal amplitude modulations of various frequencies and are compared with the effects of voltage subharmonics occurring as a single power quality disturbance. [ABSTRACT FROM AUTHOR]

In modern power systems, interharmonics have emerged as noninteger frequency components that appear in current or voltage signals. Double-stage AC-DC-AC converters have been identified as a primary source of interharmonics. Previous studies have highlighted modulation techniques, filters, passive components, unbalanced conditions and DC link effects as relevant factors. However, the interaction between these factors and the inertial properties of induction motors has not been explored. This study assesses various types of AC drives, including variable frequency drives (VFDs) and soft starters (AC choppers), to investigate their interaction with machine inertial properties in interharmonic generation. The employed technique for time-frequency spectral analysis is the wavelet synchrosqueezed transform combined with a clustering method. This paper demonstrates that the interaction of the inertial properties of low-power induction motors with the variations of the switching frequencies of the VFDs, the filters used in the DC link and a soft start indirectly contribute to harmonic generation and potentially to interharmonics in the electrical grid and the outputs of the inverter.

We establish the necessary conditions for the existence and multiplicity of periodic and subharmonic solutions to a second-order nonlinear ordinary differential equation (ODE). This ODE describes the motion of a bead on a rotating circular hoop subjected to a constant angular velocity ω and a T -periodic forcing. Our approach involves estimating bounds for the angular velocity and period using upper and lower solution methods. [ABSTRACT FROM AUTHOR]

In this paper we study the generation and behavior of subharmonics in a bubbly liquid confined in an acoustic resonator, through numerical simulations carried out at finite-amplitude acoustic pressure. Several configurations in terms of resonator length and driving frequency are considered here. Our results show that these frequency components, created from a higher-frequency signal at the source (ultrasound), are due to the nonlinearity of the medium at high acoustic-pressure amplitude and to the configuration of the resonator (geometry and boundaries). We also show that they have an amplitude-threshold dependence, which is in concordance with the literature. The response of these subharmonics to different sequences of pressure amplitudes also reveals the hysteretic nature of the bubbly liquid.

Elastic compliance of the blood vessels contributes high-frequency components in the peripheral pulse, which are analyzed with the help of the power spectral density of the signal. The frequency corresponding to heart rate in a subject is called his fundamental harmonic or first harmonic, frequency twice the heart rate is called second harmonic, and so on. The contribution of these harmonics is assessed by performing Fourier transform on the peripheral blood volume or flow pulse signal for sufficient duration, which yields power spectral density of the peripheral pulse. Dedicated software, known as pulse harmonic analyzer, has also been developed for performing harmonic analysis of the peripheral signal. It not only yields a contribution of higher harmonics in the pulse but also subharmonics (frequencies smaller than the heart rate of the subject). Researchers have observed suppression of second harmonics in subjects aging more than 30 years, suppression of high-frequency components in the power spectral density of the pulse in the coronary artery disease and enhancement of the first harmonic in hypertensives and subjects susceptible to diabetes during the past four decades. Subharmonic components are observed to be related to variability in heart rate, pulse volume, and pulse morphology, which has the potential to become a method of choice for continuous real-time variability monitoring in intensive care units. These observations are reviewed in this paper briefly.

In very low power drives, a single-phase induction motor is used. This motor, like the 3-phase induction squirrel-cage motor, requires a voltage supply with suitable parameters – of suitable quality, in practice. In energy systems, voltage quality distortions may occur in connection with the deviation of the RMS voltage and the occurrence of harmonics, subharmonics and interharmonics in its waveforms. Subharmonics and interharmonics in the voltage waveforms are particularly detrimental to induction motors. They cause, for example, additional power losses, electromagnetic torque pulsation and motor vibrations. It should be stressed that the existing publications on the impact of the considered distortions on the induction squirrel-cage motor are almost only applicable to 3-phase machines. The article presents the results of research on the influence of subharmonic and interharmonic voltage components on the single-phase induction squirrel-cage motor.

In some power systems, voltage waveforms contain, apart from harmonics, interharmonics and subharmonics that are components of frequency less than or not an integer multiple of the fundamental frequency. Voltage subharmonics and interharmonics may be of both a positive and negative sequence, independently of their frequency. Previous papers on induction motors under subharmonics have been generally limited to the components of a positive sequence. This study deals with the effect of negative sequence subharmonics on the work of induction motors. Investigations were performed using the 2D finite element method and an experimental method. Differences between the impact of positive and negative sequence subharmonics are discussed. It was found that negative sequence voltage subharmonics can result in significant current subharmonics, torque pulsations and vibration. Further, because of possible resonance, motors that are comparatively resistant to positive sequence subharmonics might be especially sensitive to negative sequence subharmonics of the same frequency and vice versa.

The measurement of harmonics is one of the key tasks in modern power systems, performed basically for power quality assessment, verification of planning levels compliance, immunity and compatibility purposes, and so on. Especially at medium voltage (MV) and high voltage (HV) levels, harmonics are always measured through voltage and current transformers (VTs and CTs), which very often are inductive. Recent articles show that inductive VTs and CTs, due to the intrinsic iron core nonlinearity, can introduce errors up to some percent in harmonic measurements. This article aims to investigate in-depth this phenomenon by analyzing how the accuracy of harmonic measurements performed through an inductive MV VT is affected by the presence subharmonics in its input voltage. Subharmonics are spectral components having frequencies lower than the power frequency, that is 50 Hz for European countries. Some theoretical considerations are carried out and the performances of two different inductive MV VTs are tested in various operating conditions. Experimental results show that subharmonics can worsen the harmonic measurements done through inductive VTs up to some tens of percent. [ABSTRACT FROM AUTHOR]

In very low power drives, a single-phase induction motor is used. This motor, like the 3-phase induction squirrel-cage motor, requires a voltage supply with suitable parameters - of suitable quality, in practice. In energy systems, voltage quality distortions may occur in connection with the deviation of the RMS voltage and the occurrence of harmonics, subharmonics and interharmonics in its waveforms. Subharmonics and interharmonics in the voltage waveforms are particularly detrimental to induction motors. They cause, for example, additional power losses, electromagnetic torque pulsation and motor vibrations. It should be stressed that the existing publications on the impact of the considered distortions on the induction squirrel-cage motor are almost only applicable to 3-phase machines. The article presents the results of research on the influence of subharmonic and interharmonic voltage components on the single-phase induction squirrel-cage motor. [ABSTRACT FROM AUTHOR]

Subharmonics are an important class of voice signals, relevant for speech, pathological voice, singing, and animal bioacoustics. They arise from special cases of amplitude (AM) or frequency modulation (FM) of the time-domain signal. Surprisingly, to date there is only one open source subharmonics detector available to the scientific community: Sun's subharmonic-to-harmonic ratio (SHR). Here, this algorithm was subjected to a formal evaluation with two data sets of synthesized and empirical speech samples. Both data sets consisted of electroglottographic (EGG) signals, ie, a physiological correlate of vocal fold oscillation that bypasses vocal tract acoustics. Data Set I contained 2560 synthesized EGG signals with varying degrees of AM and FM, fundamental frequency (fo), periodicity, and signal-to-noise ratio (SNR). Data Set II was made up of 25 EGG samples extracted from the CMU Arctic speech data base. For a "ground truth" of subharmonicity, these samples were manually annotated by a group of five external experts. Analysis of the synthesized data suggested that the SHR metric is relatively robust as long as the subharmonic modulation extent is below 0.35 and 0.7 for the FM and AM scenarios, respectively. In the CMU Arctic speech data samples, the SHR analysis reached a maximum sensitivity of about 87% at a specificity of over 90%, but only for adaptive algorithm parameter settings. In contrast, the algorithm's default parameter settings could only successfully classify about 9% of all subharmonic instances. The SHR is a useful metric for assessing the degree of subharmonics contained in voice signals, but only at adaptive parameter settings. In particular, the frequency ceiling should be set to five times the highest fo, and the frame length to at least five times the largest fundamental period of the analyzed signal. For subharmonic classification a threshold of SHR ≥ 0.01 is recommended. [ABSTRACT FROM AUTHOR]

Nonlinear behavior of bubbles, and most importantly 1 2 -order subharmonics (SH), are used to increase the contrast-to-tissue ratio (CTR) in diagnostic ultrasound (US) and to monitor bubble-mediated therapeutic US. It is shown experimentally and numerically that when bubbles are sonicated with a frequency that is twice their resonance frequency ( f r ), SHs at half the excitation frequency are generated at the minimum excitation pressure. Thus, f = 2 f r is defined as the SH resonance frequency. SHs increase rapidly with pressure and reach an upper limit of the achievable SH signal strength. Numerous studies have investigated the pressure threshold of SH oscillations; however, conditions to enhance the saturation level of SHs have not been investigated. In this paper, nonlinear dynamics of bubbles excited at frequencies in the range of f r < f < 2 f r is studied for different sizes of bubbles (400 nm–8 μ m ). In agreement with previous studies, we show that the SH resonance frequency is pressure dependent and decreases as pressure increases. When a bubble is sonicated with its pressure-dependent SH resonance frequency, oscillations undergo a saddle node bifurcation from a P1 or P2 regime to a P2 oscillation regime with higher amplitude. The saddle node bifurcation is concomitant with over-saturation of the SH and UH amplitude and eventual enhancement of the upper limit of SH and UH strength (e.g., ≈ 7 dB in UH amplitude). This can increase the CTR and signal-to-noise ratio in applications. Here, we show that the highest non-destructive SH amplitude occurs when f ≊ 1.6 - 1.8 f r . In the case of interacting bubbles, f r and pressure threshold of SH emissions decrease with increasing concentration, and supersaturation amplitude decreases above an upper limit of concentration. [ABSTRACT FROM AUTHOR]

Power quality disturbances related to voltage waveform distortions and effective value deviation are common in power systems. Apart from higher harmonics, subharmonics and interharmonics may also appear in voltage waveforms. The presence of the above-mentioned disturbances causes additional power losses and an increase in thermal loads on induction motors. In this paper, the results of the study of the influence of subharmonics present in voltage waveform on the currents in the investigated induction motors of standard efficiency class – IE1 and high efficiency class – IE3, are presented.

Abstract To study synodic period and its subharmonics, we have utilized hourly average data of solar wind plasma field, geomagnetic index, and galactic cosmic ray intensity along with 5 min average data of selected solar wind field parameters during the recent minimum of Solar Cycle 24. Wavelet analyses of hourly average data reveal 28.1, 13.1, and 6.8 day of sigma in interplanetary magnetic field; 27.1, 13.1, and 9.0 day of plasma speed; 27.1, 13.6, 3.9, and 2.2 day of interplanetary electric field; 27.1, 13.6, 3.8, and 2.2 day of southward component of magnetic field; 26.2, 13.6, 8.6, and 3.0 day of geomagnetic Ap index; and 28.1, 11.0, 9.3, 7.0, and 1.6 day periods of galactic cosmic ray intensity. In addition to these prominent short‐term periods, we have significantly observed 6.6, 3.3, and 1.7 day periods of sigma in interplanetary magnetic field (σB); 5.6, 4.2, and 2.2 day of electric field (Ey) and 5.6, 3.3, and 2.4 day of southward component of magnetic field (Bz) in the 5 min average data. During the recent solar minimum, we have observed one solar rotational period and its second, third, fourth, fifth, sixth, seventh, eighth, tenth, eleventh, and twelfth subharmonics. The observed subharmonics of solar rotational period make the current solar minimum very special and noteworthy to study.

To study synodic period and its subharmonics, we have utilized hourly average data of solar wind plasma field, geomagnetic index, and galactic cosmic ray intensity along with 5 min average data of selected solar wind field parameters during the recent minimum of Solar Cycle 24. Wavelet analyses of hourly average data reveal 28.1, 13.1, and 6.8 day of sigma in interplanetary magnetic field; 27.1, 13.1, and 9.0 day of plasma speed; 27.1, 13.6, 3.9, and 2.2 day of interplanetary electric field; 27.1, 13.6, 3.8, and 2.2 day of southward component of magnetic field; 26.2, 13.6, 8.6, and 3.0 day of geomagnetic Ap index; and 28.1, 11.0, 9.3, 7.0, and 1.6 day periods of galactic cosmic ray intensity. In addition to these prominent short‐term periods, we have significantly observed 6.6, 3.3, and 1.7 day periods of sigma in interplanetary magnetic field (σB); 5.6, 4.2, and 2.2 day of electric field (Ey) and 5.6, 3.3, and 2.4 day of southward component of magnetic field (Bz) in the 5 min average data. During the recent solar minimum, we have observed one solar rotational period and its second, third, fourth, fifth, sixth, seventh, eighth, tenth, eleventh, and twelfth subharmonics. The observed subharmonics of solar rotational period make the current solar minimum very special and noteworthy to study. Key Points: Fourth subharmonics of variance of IMF is stronger than synodic periodSignature of 3.8, 2.2 days periods in the hourly average Ey and Bz time seriesSignificant presence of fifth, sixth, eighth, eleventh, and twelfth subharmonics in high‐resolution data [ABSTRACT FROM AUTHOR]

By the aids of variational methods, we study the existence of periodic and subharmonic solutions, and the minimality of their periods, for the nonautonomous first order Hamiltonian system J u ˙ (t) + ∇ H (t , u (t)) + h (t) = 0 under some kind of sublinear nonlinearity conditions. Our results are new and generalize and extend some results in the literature. [ABSTRACT FROM AUTHOR]

- There are presented the results of the research conducted by the authors on the response of the dynamic system composed of dynamic equipment with rotating inertial force excitation and with elastic asymmetric connections. In this case, it is highlighted that the dynamic system generates subharmonic vibrations of order ½ which can be damaging to buildings as well as to the serving staff. [ABSTRACT FROM AUTHOR]

This work deals with the preliminary investigations of a 200-kW induction cage motor with a supply voltage featuring subharmonic injection. The results of the field calculations in the MAXWELL environment are presented for subharmonics of various frequencies. It was found that subharmonics occurring in real power systems can cause overheating and premature failure of this type of machine.

Objectives: Hoarseness is primarily perceived as breathiness or roughness. Despite the various tools that quantitatively assess hoarseness, roughness has been difficult to quantify because of its complex acoustic structure, such as subharmonics. The parameter obtained from the two-stage cepstral analysis is promising for evaluating roughness. Thus, this study aimed to improve the accuracy of the parameter using a customized pitch setting and investigate the relationship between roughness and subharmonics., Study Design: The design is a retrospective study., Methods: Two-stage cepstral analysis was used to analyze the voice recordings of 455 participants, speech impaired and normal controls, using the Analysis of Dysphonia in Speech and Voice and Praat software. For validation, the ground truth of subharmonics was visually quantified using a narrowband spectrogram. The reliability and validity of the two-stage cepstral analysis and subharmonics measures on spectrograms were evaluated., Results: The two-stage cepstral analysis showed a very strong correlation (r = 0.963) between the two software programs. Intra- and inter-rater reliability of the subharmonics measures on spectrograms were also good. Two-stage cepstral analysis showed that even with customized pitch settings, the diagnostic systems and correlations for perceptual roughness and subharmonics were weak to moderate. The subharmonics measures on spectrograms showed a strong correlation with roughness and moderate diagnostic accuracy of subharmonics., Conclusions: The two-stage cepstral analysis showed some improvement in diagnostic accuracy and correlation with customized pitch settings, but it did not sufficiently detect subharmonics or roughness. The analysis using subharmonics measures on spectrograms proved the high correlation between subharmonics and roughness, indicating that developing acoustic analysis parameters that sufficiently detect subharmonics is necessary., (Copyright © 2023 The Voice Foundation. Published by Elsevier Inc. All rights reserved.)

This work is devoted to preliminary investigations concerning the effect of an inertia moment and load-speed characteristics on currents, power losses and windings temperature of an induction machine supplied with voltage containing subharmonics. The results of numerical simulations are presented for a totally-enclosed fan-cooled cage induction motor of rated power 3 kW. The computations were carried out with a field method and a hybrid field-circuit method. The results of preliminary investigations show that load properties may have significant influence on currents, power losses and windings temperature of an induction machine under considered power quality disturbances.

Declining extraction costs and process efficiencies have incented the revival of the oil and gas sector postrecession. The application of drilling rigs has been done more efficiently. These loads are very large, temporary in nature, and mobile. The drilling of each well can be done as quickly as a few hours and typically not more than a few days. These massive loads are complex to own, maintain, and operate, as a result few specialized drillers share the market. Because of the requirements for variable speed and control, drilling rigs are driven by variable frequency drives (VFDs), which are in their clear majority of older technologies such as six-pulse thyristor bridge or SCR-driven motors. These technologies are known to impose steep ramp rates (up and down) as well as rich harmonic content and variable, typically low, power factor. Furthermore, the locations of drilling rigs are typically remote, where distribution systems, if present, are weak, which lead to large background voltage distortions when such loads are present. This paper presents measurements, simulations, and analytical assessments of the characteristics and effects of harmonics and interharmonics (IHs) generated by top-drive and mud-pump VFDs in a large drilling rig operated in Alberta, Canada. Measurement results reveal very high harmonic and IH generation. To further refine the impact assessment of these harmonic emissions, the harmonic attenuation effect of the VFDs is quantified to avoid overestimating the harmonic generation of the loads. The thermal impact of the current harmonics on the coupling transformer is also quantified. [ABSTRACT FROM AUTHOR]

The present paper is focused on the analysis of the adhesion integrity of Single Lap Joints (SLJ). The technique adopted for the monitoring is based on the employment of vibration signals generated and received by piezo sensors attached on the specimens surfaces on the two opposite sides of the adhesive. Undamaged joints, when subjected to harmonic excitation, behave linearly exhibiting a spectral response including just the excitation frequency. As soon as the adhesive fails, harmonic excitation induces a rich variety of spectral components in the joints response, including subharmonics and superharmonics. A new approach is presented based on the beating resulting from the superposition of harmonic waves. The interpretation of the spectral content of the joint response is based on an analytical model of the single lap joint with different amounts of debondings associated with a nonlinear behaviour. Local Defect Resonance (LDR) conditions are promoted with the consequent superposition of defect with main structure vibration. Analytical results are compared with experiments and Finite Elements (FE) simulations demonstrating the consistence of the formulation. An efficient method for the Structural Health Monitoring (SHM) of the bonded single lap joints is provided, able to correlate the joint vibrational response to the debonding extension through the analysis of the response spectral content. • Beatings in the structural dynamic response of bonded Single Lap Joints (SLJ). • Simplified two degrees of freedom spring-mass model simulating SLJ. • Novel SHM method for the evaluation length of debonding. • Subharmonics and harmonics as indicator of damage. • Appearance of the defect first natural frequency according to the principles of LDR. [ABSTRACT FROM AUTHOR]

Highlights • Subharmonics and 2/3 ultra-subharmonics of a bio-inspired structure are systematically studied. • Results of the subharmonics and bifurcations are of generic significance. • The flexible control of subharmonics for the bio-inspired structure is verified by experiment. • Topological properties of subharmonic responses and bifurcation sets are explored in detail. Abstract This paper deals with ultra-subharmonics and subharmonics of a novel nonlinear isolation system with a bio-inspired structure. The analytic formulations of frequency-responses, bifurcation sets and stability of the subharmonic (1/2, 1/3, and 1/4 order) and ultra-subharmonic (2/3 order) responses are exhaustively derived. Due to the generic form of the nonlinear equation, the results about the subharmonic or ultra-subharmonic properties might be actually applicable to a wide variety of physical and engineering problems. The influences of the structural parameters of the bio-inspired structure on nonlinear responses and bifurcation sets are discussed in detail. Furthermore, the obtained theoretical results are validated by numerical simulations and vibration experiments. From the results, the substantial topological distinction of the bifurcation sets between the 1/3 subharmonic resonance and 2/3 ultra-subharmonic resonance are revealed. The discontinuous relationship between the 2/3 ultra-subharmonic response and excitation amplitude is clearly unveiled. A novel phenomenon is observed that 1/4 subharmonic resonance could appear even though there are only quadratic and cubic nonlinear terms in the vibration equation. Other than the coexistence of two different 1/2 (resp. 1/4) subharmonic solutions, the appearance of only one 1/2 (resp. 1/4) subharmonic solution in a certain frequency range is also uncovered. Furthermore, it is shown experimentally that, suppression or enhancement of the subharmonic response can be achieved by tuning the structural parameters of the bio-inspired structure. Such new findings could be of significance for the design and practical applications of the bio-inspired isolation system. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

In some power networks, components of frequency less than the frequency of the fundamental voltage harmonic called subharmonics or subsynchronous interharmonics occur. In this paper, the effect of voltage subharmonics on currents, power losses, speed fluctuations and electromagnetic torque is examined. The results of numerical computations using the finite element method for an induction cage motor of rated power of 5.6 MW and four motors of rated power of 200 kW with different numbers of poles are presented. An extraordinary harmful effect on high-power induction motors is demonstrated. Among other effects, voltage subharmonics cause significant torque pulsations whose frequencies may correspond to the elastic-mode natural frequency. Possible resonance can result in excessive torsional vibration and the destruction of a power train.