Harmonic Behavior Research Articles

Nonlinear harmonic resonant behaviors and bifurcation in a Two Degree-of-Freedom Duffing oscillator coupled system of Tension Leg Platform type Floating Offshore Wind Turbine

The surge-heave coupled motion model of a Tension Leg Platform type Floating Offshore Wind Turbine (TLP FOWT) is first established. By taking the tendons stretching and platform set-down motion into consideration, the nonlinear model is a Duffing oscillator coupled system. We analyze the nonlinear feature in the surge-heave coupled motions by the semi-analytical algorithms in nonlinear dynamics. The harmonic balance method is applied to obtain the analytical solutions of the nonlinear system under wind and wave excitations. The analytical solution verifies the excellent accuracy. To further achieve the heave motion response, we organize the bifurcation analysis and discuss the effects of the dynamic parameters on the heave responses. The results reveal the multi components of heave motion, which consist of constant, primary harmonic resonate and higher order harmonic resonate. In addition, the change of dynamic parameters has various effects on the response. The increment of wave load leads to the expansion of heave response, and an instantaneous expansion appear. Both linear surge and heave damping only affect the amplitudes of heave motion. The nonlinear surge stiffness and heave stiffness can barely affect the primary harmonic resonance amplitudes, but they present different effects on the higher order harmonic resonance component.

RF, harmonic distortion and linearity analysis of core-shell junctionless-FET using NQS small signal model

Abstract This paper deals with the performance analysis of Core-Shell (C-S) Junctionless (JL) FET structure in the RF domain application. The analysis begins with the non-quasi static (NQS) small signal model representation and from there the extraction of RF-parameters; and there after the harmonic distortions, linearity FOMs and Y-parameter are analyzed in detail. The device is investigated based on the variations of core/shell-thicknesses and shell-dopant concentrations. Y-parameters are evaluated from the NQS small signal model. In the RF domain analysis, the parameters such as, Cgs, Cgd, Rgs, Rgd, fT and τm are assessed to determine its RF merits. Using the two-port equivalent model, the Y-parameters (Y11, Y12, Y21, Y22) are evaluated and investigated. The second and third order harmonic distortions (HD2, HD3) are calculated using IFM method and studied in detail. In addition to that, second, third harmonic intercept voltages (VIP2, VIP3) and third order intermodulation distortion (IMD3) are also assessed for its linearity performances in domain specific applications. The proposed device is designed using the Silvaco ATLAS TCAD. The device is calibrated with the experimental data that shows a close match between the two. The proposed device is found to exhibit good linearity and very low harmonic distortion behavior by modulating the shell-doping and thickness.

Spectral Analysis of Proton Eigenfunctions in Crystalline Environments

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number Nw, reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal.

Ultrafast Electron-Electron Scattering in Metallic Phase of 2H-NbSe_{2} Probed by High Harmonic Generation.

Electron-electron scattering on the order of a few to tens of femtoseconds plays a crucial role in the ultrafast electron dynamics of conventional metals. When mid-infrared light is used for driving and the period of light field is comparable to the scattering time in metals, unique light-driven states and nonlinear optical responses associated with the scattering process are expected to occur. Here, we use high-harmonics spectroscopy to investigate the effect of electron-electron scattering on the electron dynamics in thin film 2H-NbSe_{2} driven by a mid-infrared field. We observed odd-order high harmonics up to 9th order as well as a broadband emission from hot electrons in the energy range from 1.5 to 4.0eV. The electron-electron scattering time in 2H-NbSe_{2} was estimated from the broadband emission to be almost the same as the period of the mid-infrared light field. A comparison between experimental results and a numerical calculation reveals that competition and cooperation between the driving and scattering enhances the nonperturbative behavior of high harmonics in metals, causing a highly nonequilibrium electronic state corresponding to several thousand Kelvin.

The Morphology of the Asteroidal Dust around White Dwarf Stars: Optical and Near-infrared Pulsations in G29-38

More than 36 yr have passed since the discovery of the infrared excess from circumstellar dust orbiting the white dwarf G29-38, which at 17.5 pc it is the nearest and brightest of its class. The precise morphology of the orbiting dust remains only marginally constrained by existing data, subject to model-dependent inferences, and thus fundamental questions of its dynamical origin and evolution persist. This study presents a means to constrain the geometric distribution of the emitting dust using stellar pulsations measured at optical wavelengths as a variable illumination source of the dust, which reradiates primarily in the infrared. By combining optical photometry from the Whole Earth Telescope with 0.7–2.5 μm spectroscopy obtained with SpeX at NASA’s Infrared Telescope Facility, we detect luminosity variations at all observed wavelengths, with variations at most wavelengths corresponding to the behavior of the pulsating stellar photosphere, but toward the longest wavelengths the light curves probe the corresponding time variability of the circumstellar dust. In addition to developing methodology, we find the pulsation amplitudes decrease with increasing wavelength for principal pulsation modes, yet increase beyond ≈2 μm for nonlinear combination frequencies. We interpret these results as combination modes derived from the principal modes of identical ℓ values and discuss the implications for the morphology of the warm dust. We also draw attention to some discrepancies between our findings and theoretical expectations for the results of the nonlinearity imposed by the surface convection zone on mode–mode interactions and on the behavior of the first harmonic of the highest-amplitude pulsation mode.

Frequency sweep study on the generation of dual-mode second harmonics (DMSH) on an isotropic nonlinear elastic cylindrical rod by T(0,1) mode

Nonlinear ultrasonic (NLU) guided wave (GW) measurements are more sensitive to microscale defects than linear measurements. This nonlinear phenomenon is helpful for early-stage damage detection in material for nondestructive evaluation (NDE) and structural health monitoring (SHM) applications. The amplitude of the higher harmonics generated in the material serves as the basis for the NLU measurement. Recent studies have reported the presence of dual-mode second harmonic (DMSH) on an isotropic nonlinear elastic plate and cylindrical structures. The fundamental non-dispersive mode shear horizontal SH0 and torsional T(0,1) modes can generate simultaneously propagating dual-mode second harmonic(DMSH) on plate and cylindrical guided media respectively. For the case of cylinders, at phase matching condition two dominant second harmonic fundamental longitudinal (l(0,1)) and orthogonal torsional (t(0,1)┴) mode are generated with significant amplitude. The particle vibration of the t(0,1)┴ mode was present in both orthogonal directions compared to conventional T(0,1) mode and hence called orthogonal torsional mode. The present work aims to study the behaviour of DMSH at different frequencies through a frequency sweep study on a weakly nonlinear elastic cylinder of circular cross-section via numerical simulations and validated experimentally for some selected cases. The wave propagation of the T(0,1) mode at several selected frequencies from 300 kHz to 2.2 MHz is chosen to explore the second harmonic mode for better understanding. At frequencies below 1.25 MHz, l(0,1) mode is faster than t(0,1)┴ mode; above 1.25 MHz, it was the other way around. The behaviour of harmonics was observed to be in accordance with the group and phase velocities at the corresponding frequencies in the dispersion curves. The evidence for the presence of DMSH was validated experimentally for some selected frequency cases at different propagation distances. The significance of DMSH is explored via numerical simulations and found that t(0,1)┴ mode is sensitive towards material degradation, while all other generated wave modes were not affected. Research shows that enough energy is available in the generated DMSH to be noticed experimentally and in numerical simulations. This improved understanding of the generation of DMSH across different frequencies would be helpful in new advanced NLU-based NDE and SHM applications.

Growth and physiochemical properties of semi organic ammonium pentaborate dihydrate single crystal

Abstract The slow evaporation technique was used to produce nonlinear optical ammonium pentaborate dihydrate (APBDH) single crystals. The crystal lattice parameters and structure of APBDH crystal was determined by single crystal X-ray diffraction (S-XRD) technique with the triclinic space group. The optical band gap of the grown crystal was determined using UV–Vis spectrophotometer. There is no absorption peak was observed in the entire visible region of the spectrum. The functional groups of the APBDH crystal were identified through Fourier transforms infrared (FTIR) and Fourier transform Raman (FR-Raman) analyses. The thermal decomposition and thermal stability of the grown crystal was measured using TG-DTA analyses. The laser damage threshold (LDT) analysis was used to know the ability to withstand the influence of laser on the grown crystal. Photoconductivity of the grown crystal was studied and its photocurrent and dark current behavior was examined. The surface morphology of the APBDH crystal was evaluated using HR-SEM analysis. The APBDH crystal was exhibited second harmonic generation behavior and its efficiency was calculated with different particle sizes.

Characterization of network harmonic impedance for grid connection studies of renewable plants

The impedance of a grid as a function of the frequency, or grid harmonic impedance, indicates the nature of the distortion and, especially, of the resonances that may appear in the system due to the presence of harmonic sources. Modelling this impedance is fundamental to be able to perform grid connection studies of renewable generation plants. However, usually the necessary information is not available, and the impedance is represented in a very simplified way. This paper analyses the different methods proposed in the literature to model the grid harmonic impedance and selects the most suitable for its implementation in PowerFactory simulation software, widely used in the industry for this type of studies. The selected method allows obtaining an equivalent network model that reproduces the harmonic behaviour of the network, without having to model the complete network in detail. A case study that applies the method to analyse the harmonic distortion at the POI of an offshore wind farm is presented.

Incorporating DC bias voltage in poly‐harmonic distortion modeling for RF power GaN transistors

AbstractThis paper presents a novel poly‐harmonic distortion (PHD) model that incorporates the DC input and output bias voltages using Gaussian process regression (GPR). Simulation tests were conducted using a 10‐W gallium nitride (GaN) HEMT transistor from Wolfspeed, and the model implementation test was performed in the Keysight Advanced Design System environment. The results showed that the GPR‐based PHD model exhibited good performance in predicting both fundamental and harmonic behaviors over a wide range of bias variations with significant advantages over basic linear regression methods. Additionally, the model accurately predicted load‐pull simulations. The measurement test was conducted using a 6‐W GaN device, and the results showed a mean error of 2.22% and 4.54% for the fundamental and second harmonic of the reflected wave, respectively.

Improved calculation of core losses of high-speed motors with two different permanent magnets considering higher order current harmonics

In high-speed permanent magnet synchronous motor drives, time harmonics in the current occur owing to the carrier frequency of the inverter, which affects the core losses among the electromagnetic losses. According to Steinmetz’s equation, the core loss depends on the frequency and magnetic flux density, with each term influenced by harmonic currents. Therefore, to accurately predict core loss, it is necessary to consider harmonic currents. This study presents the effects of differences in the resistance, inductance, switching frequency, and harmonic current on the core loss for two models with different PMs at the same output power. Core losses are significantly affected by harmonic current content and magnetic field behavior, making the analysis of harmonic components and magnetic field behavior essential. To achieve this, the stator core was divided into segments to examine the magnetic field behavior owing to harmonic currents in each region, thus facilitating a comprehensive analysis of the core losses. When the results were compared with the experimental data, it was observed that the analysis of harmonic currents significantly improved the accuracy compared to the analysis based solely on sinusoidal currents; in particular, the error rate reduced from 37.8% to 4.1%. Furthermore, it was confirmed that ferrite PMs resulted in smaller core losses owing to harmonic currents than rare-earth PMs. This finding suggests that ferrite PMs are a suitable alternative to high-speed permanent-magnet synchronous motors.

On the behavior of higher harmonics in the evolution of nonlinear water waves in the presence of abrupt depth transitions

The presence of abrupt depth transitions might trigger strong nonlinear effects on propagating water waves near coastal regions. In this study, the dynamics of nonlinear monochromatic waves over a submerged step representing the abrupt depth transitions are investigated both experimentally and numerically. Within the framework of the free-surface Euler equations, a fully nonlinear potential flow model based on a conformal mapping method is established to investigate the higher harmonics. The numerical method has been well validated with experimental measurements. To analyze the wave nonlinearity at the transitions, the higher harmonics are extracted both in the spatial and time domains. It is shown that abrupt depth transitions enhance the higher harmonic amplitudes in the shallower regions on the step. The effects of the incident wave frequency and height are studied. It is found that the higher harmonics induced by the abrupt depth transitions become more significant with increasing wave steepness. An analysis of the evolution of the skewness and kurtosis demonstrates the high asymmetry of the surface elevation on the upstream junction. The asymmetry shows clear nonlinear effect from the higher harmonics.

Quantum and anharmonic effects in non-adiabatic transition state theory.

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. In this paper, the interplay between quantum effects-for motion across or along the seam of crossing-and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N2O ↔ N2 + O(3P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3A'-1A' seam of N2O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ∼20 at 2000K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N-N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (∼250 K for N2O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions-harmonic behavior, classical motion, linear terms, and weak coupling-should be verified on a case-by-case basis.

Characterizing relaxation phenomenon and crack propagation during low-temperature harmonic vibrations in heterogeneous metals

This work reveals the relaxation phenomenon induced by the localized atomic segregation during harmonic vibrations, which engenders substantial fluctuations in the dynamic modulus. The relaxation peak occurs when the dynamic modulus undergoes a sudden increase upon temperature reduction to −20 °C. This occurrence is caused by interstitial carbon atoms undergoing segregation and dragging dislocations to accumulate near grain boundaries. It leads to an increase in elastic strain energy, resulting in local stress concentrations and cracks initiation in heat affected zone (HAZ) and weld zone (WZ). The elevated value of the dynamic modulus within the HAZ facilitates a substantial internal accumulation of elastic strain energy. Consequently, this accumulation allows cracks to propagate rapidly along grain boundaries within the HAZ. Secondary cracks form in dispersed localized stress concentration zones in the WZ, which can inhibit crack propagation during harmonic vibration. This work will provide detailed insights and theoretical studies on the harmonic vibrational behavior of heterogeneous metals at low temperatures.

Robust Inter-Turn Short-Circuit Fault Detection in PMSGs With Respect to the Bandwidths of Current and Voltage Controllers

Reliable inter-turn short-circuit (ITSC) fault detection is essential for permanent magnet synchronous generators (PMSGs). The harmonics in machine currents and voltages are affected by the bandwidths of dual-loop controllers, which may lead to the failure of ITSC fault detection based on the current or voltage signature analysis. In this paper, a robust method for ITSC fault detection is proposed to deal with this problem. First, the mathematical model of PMSG with ITSC fault is established. Then, the behaviors of the second order harmonics in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis currents, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis voltages and dc-link voltage with respect to the bandwidths of current and voltage controllers are investigated. After that, a reliable detection method based on two fault detection indicators and adaptive to the bandwidth changes of dual-loop controllers is proposed. The first indicator is simple and easy when only the bandwidth of current controller changes, and the other one weights and sums the second harmonics in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis voltage and dc-link voltage to ensure the robustness and improve the accuracy of ITSC detection when both the bandwidths of current and voltage controllers change. Finally, the effectiveness of proposed method is validated by experiments.

Direction of Arrival Algorithm for Acoustic Sensors Operating Near Resonance

Recently, it has been possible to detect sound direction using phase-sensitive sensors placed much closer to each other than the sound wavelength. A typical setup combines two phase-sensitive sensors placed perpendicular to each other with a third omnidirectional sensor, the latter to determine the bearing quadrant. So far, algorithms that extract the sound direction from the sensor voltages have only been applicable to sensors with identical frequency responses. However, we have developed microelectromechanical systems (MEMS) sensors with simple harmonic oscillator-like resonance behavior for which these algorithms no longer apply. The operation near resonance greatly increases their performance, but the frequency dependencies of any two sensors are different from each other and from the omnidirectional sensor. In this letter, we show how to accommodate these differences, first, by forcing the two sensor peaks to conform to each other in both magnitude and phase, and second, by adjusting the phase of the omnidirectional sensor to approximately match the phases of the resonant sensors near their resonant frequencies. We then present two algorithms to extract the sound direction. We lay out the theoretical basis for our algorithms and present measurements of acoustic noise to show the algorithms’ effectiveness.

How morphological is Hungarian vowel harmony?

There is a significant degree of phonological indeterminacy in front/back harmony in Hungarian (HVH), which manifests itself in lexical variation and/or vacillation. Harmonic behaviour in the zone of variation strongly supports the hypothesis that harmonic classes which individual roots belong to are organized as a paradigmatic system, very similar to inflectional classes. Such lexically determined declension classes are required independently of vowel harmony to account for various other lexically conditioned alternations in Hungarian, e.g., the alternations involving linking vowels in suffixes and yod in 3rd person possessives. A further evidence for the morphologisation of HVH is a paradigm uniformity effect, Harmonic Uniformity, which reduces harmonic uncertainty by making a stem’s harmonic behaviour predictable from that of its root. Thus, HVH is determined by morphology (paradigmatic classes and paradigm uniformity) in addition to (and sometimes overriding) phonology.

Fluidelastic modeling of a weathercock stabilization in a uniform flow

The relaxation dynamics of a weathercock free-to-rotate, in the presence of a uniform flow, as it aligns with the flow direction, is investigated experimentally in a wind-tunnel. The dynamics is observed to conveniently follow a damped harmonic oscillator behavior. At first order, the frequency is set by the aerodynamic coefficients. We show that a quasi static approach fails to precisely describe the relaxation dynamics and that non-stationary corrections are required to model the dynamics. A first strategy is to introduce added mass, added stiffness and added damping to the quasi-static approximation, following what is usually done in the context of vortex-induced vibrations. A second strategy is to introduce empirical corrections, whose scaling is obtained from the analysis of the experimental data. Finally, these two strategies are compared and we discuss the physical interpretations of the non-stationary corrections.

Design of an Optimal Adoptive Fault Ride through Scheme for Overcurrent Protection of Grid-Forming Inverter-Based Resources under Symmetrical Faults

As the integration of inverter-based resources (IBRs) is rapidly increasing in regard to the existing power system, switching from grid-following (GFL) to grid-forming (GFM) inverter control is the solution to maintain grid resilience. However, additional overcurrent protection, especially during fault transition, is required due to limited overcurrent capability and the high magnitude of spikes during fault recovery in IBRs, specifically in the GFM control mode. Furthermore, the power system stability should not be compromised by the employment of additional fault ride through (FRT) schemes. This article presents the design and implementation of an adoptive fault ride through (FRT) scheme for grid-forming inverters under symmetrical fault conditions. The proposed adoptive FRT scheme is comprised of two cascaded power electronic-based circuits, i.e., fault current ride through and a spikes reactor. This adoptive FRT scheme optimizes the fault variables during the fault time and suppresses the fault clearing spikes, without affecting system stability. A three-bus inverter-based grid-forming model is used in MATLAB/Simulink for the implementation of the proposed scheme. Further, a conventionally used FRT scheme, which includes fault current reactors, is simulated in the same test environment for justification of the proposed adoptive scheme. The adoptive FRT scheme is simulated for both time domain and frequency domain to analyze the response of harmonic distortion with the suppression of the fault current. Moreover, the proposed scheme is also simulated under the GFL mode of IBRs to justify the reliability of the scheme. The overall simulation results and performance evaluation indices authenticate the optimal, fault tolerant, harmonic, and spike-free behavior of the proposed scheme at both the AC and DC side of the grid-forming inverters.

Design, Manufacturing and Acoustic Assessment of Polymer Mouthpieces for Trombones

Brass instruments mouthpieces have been historically built using metal materials, usually brass. With the auge of additive manufacturing technologies new possibilities have arisen, both for testing alternative designs and for using new materials. This work assesses the use of polymers for manufacturing trombone mouthpieces, specifically PLA and Nylon. The acoustical behavior of these two mouthpieces has been compared with the obtained from a third one, built from brass. Both additive and subtractive manufacturing techniques were used, and the whole manufacturing process is described. The mouthpieces were acoustically assessed in an anechoic chamber with the collaboration of a professional performer. The harmonic analysis confirmed that all the manufactured mouthpieces respect the harmonic behavior of the instrument. An energy analysis of the harmonics revealed slight differences between the mouthpieces, which implies differences in the timbre of the instrument. Although these subtle differences would not be acceptable when performing with the instrument in an orchestra, they could be perfectly valid for early learners, personal rehearsals or any kind of alternative performance.

Acoustic plane wave detection of intracranial cavitation in a polyacrylamide human head model under blunt impact

Traumatic brain injuries (TBIs) occur in everyday life in the form of blunt impacts, while military personnel experience a combination of blast and blunt impacts from explosives. Damage mechanisms in TBIs, including cavitation, are poorly understood due to the inability to optically monitor brain deformation inside the skull during collisions. To overcome these limitations, high frame rate acoustic plane wave imaging in conjunction with high-speed optical imaging were combined to visualize intracranial cavitation during impact of a transparent brain phantom. The full-scale phantom was composed of 7% and 10% (w/v) polyacrylamide (PAA) andenclosed in a 3D printed skull with acrylic windows for optical image acquisition. This surrogate utilizes simplified geometry to represent key anatomical features such as the gyri, sulci, and ventricles while possessing rheological properties similar to the human brain. Optical and acoustic data correlate cavitation to high-contrast regions. Acoustic spectra show expected harmonic and broadband behavior during cavitation bubble growth and collapse. Further processing with superresolution techniques may enhance cavitation localization providing a stand-alone acoustic tool applicable in various TBI scenarios allowing observations at depth, where optical techniques are limited.