Low-frequency Dynamics Research Articles

Large step size electromagnetic transient simulations by matrix transformation‐based shifted‐frequency phasor models

To evaluate and improve the performances of control and protection strategies for large-scale AC grids, simulation models that can adopt a much larger time-step, provide instantaneous and wide frequency-band phasor values simultaneously are desirable. However, the traditional electromagnetic transient (EMT) model is numerically expensive and the transient stability (TS) model only preserves low-frequency dynamics. To resolve these issues, the shifted frequency phasor (SFP) modelling is generalised based on specific matrix transformations and SFP models of typical components in large-scale AC grids are derived hereafter. Unlike traditional models, the SFP models can produce instantaneous and wide frequency-band phasor waveforms simultaneously, while the latter matches the envelopes of the former exactly. Moreover, the simulation efficiency is dramatically improved by adopting a much larger time-step. The performance concerning the accuracy and efficiency is compared with the traditional EMT and TS models by simulating a practical large-scale AC grid under different scenarios.

Low-Frequency Dynamics of Flow over a Backward-Facing Step

The low-frequency () dynamics of turbulent flow () downstream of a backward-facing step are examined by low-pass filtering the velocity fields from a long run-time large-eddy simulation. The low-frequency behaviors were found to set the location of streamwise reattachment. Examination of the instantaneous three-component velocity fields showed regions of flow where the streamwise velocity was momentarily driven all the way back to the step face. After the flow reaches the step, it is then directed along the step face in the spanwise direction, resulting in large regions of wall-normal vorticity . These large regions of vorticity are opposed by smaller regions of counter-rotating flow offset in the spanwise direction and were responsible for the spanwise variation of the reattattachment. The low-pass filtered streamwise velocity fields just above the lower wall showed significant spanwise oscillations with a mean wavelength of the streamwise low-pass filtered reattachment position of , consistent with previous studies at different Reynolds and Mach numbers. As the step geometry is homogeneous in the spanwise direction, this shows that this behavior is not the result of wall or edge effects, which is a conclusion that cannot easily be drawn from experimental studies with limited step-height-to-width ratios.

Small-signal modeling and active damping of resonant electromagnetic levitation melting system with experimental verification

It is well-known that levitation melting type induction heating system, fed by resonant inverter, is a complex and nonlinear dynamical system, in which high-frequency electrical-side dynamics and low-frequency mechanical side dynamics are strongly coupled. Such systems are typically operated at resonant electrical frequency in order to both stabilize the open-loop dynamics and maximize the power transfer. While stable, resulting open-loop dynamics is typically nonlinear and highly underdamped, depending on both floating object vertical position and operation frequency. Oscillative behavior of high-temperature work piece being melted is obviously undesired due to safety issues. In order to address the issue, this paper first derives small-signal operation point dependent linearized dynamics of the system, based on the recently established envelope modeling methodology. Then, model reduction is carried out within bandwidth of interest. It is shown that both linearized control-to-output and disturbance-to-output transfer functions may accurately be represented by second-order dynamics with operating point dependent gains, natural frequencies and damping factors within the bandwidth of interest. Once derived, reduced system representations are employed in active damping feedback controller design, in which operation frequency rather than one of mechanical-side variables is utilized as feedback signal, making the proposed algorithm sensorless. It is shown that suggested methodology influences only the damping factor of original system while leaving both gain and natural frequency unaltered and is capable of eliminating oscillative response throughout the whole operation range. Simulations and experimental results are shown to validate both reduced-order linearized dynamics and the proposed active damping methodology.

Gaussian process models for mitigation of operational variability in the structural health monitoring of wind turbines

The analysis presented in this work relates to the quantification of the effect of a selected set of measured Environmental and Operational Parameters (EOPs) on the dynamic properties of low and high frequency vibration, in the context of a vibration monitoring campaign implemented on the blade of an operating wind turbine. To this end, a Gaussian Process (GP) time-series modelling approach is adopted, in which the coefficients of a time-series model are driven by a Gaussian Process Regression on the selected EOPs. The properties of the data acquisition system allow to evaluate low and high frequency dynamics, the former associated with the structural dynamics of the blade, and the latter with the wave transmission properties of the material, assessed with the help of an electro-mechanical actuator installed on the blade. In this form, a multi-temporal-scale approach is adopted here, where a GP Linear Parameter Varying Auto-Regressive model is selected to represent low frequency (structural) dynamics, while in parallel a GP Continuous Wavelet Transform model is used to represent high frequency dynamics (associated with wave transmission properties in the material). In both cases the blade is considered in its healthy state as well as in various operational regimes, including idle, and rotating at two different set points. As a result, it is demonstrated that GP time-series modelling succeeds in evaluating and isolating the influence of different EOPs in the features of the vibration response of the wind turbine blade, and at the same time, normalize their effects to enhance the detectability of damage.

Low-Frequency Vibrational Motions of Polystyrene in Carbon Tetrachloride: Comparison with Model Monomer and Dependence on Concentration and Molecular Weight

In this study, the low-frequency vibrational dynamics of polystyrene (PS) in CCl4 was investigated by femtosecond Raman-induced Kerr effect spectroscopy. Ethylbenzene (EBz) was also investigated as a model monomer of the polymer to elucidate the unique dynamical features of PS in solution. The broadened low-frequency spectrum of the PS/CCl4 in the frequency region below 150 cm-1 is significantly different from that of the EBz/CCl4. Difference spectra between the PS or EBz solutions and neat CCl4, normalized to an internal vibrational mode of CCl4, clearly show a much lower spectral intensity for the PS/CCl4 than the EBz/CCl4 in the low-frequency region below ca. 20 cm-1. This indicates that translational motions are suppressed in the PS/CCl4 compared to the EBz/CCl4. Moreover, the high-frequency motion at ca. 70 cm-1, mainly due to phenyl ring librations, occurs at higher frequency in PS (78 cm-1) than EBz (65 cm-1). In addition, the results of concentration-dependent experiments show that the first moment (M1) of the low-frequency difference spectra of both PS/CCl4 and EBz/CCl4 is almost independent of the concentration. The molecular weight dependence of the low-frequency spectrum in the PS/CCl4 shows that the M1 value of the low-frequency spectral band of PS shifts to higher frequencies when the molecular weight of PS increases up to Mw = ∼1000, which corresponds approximately to the decamer, and then remains constant upon further increasing the molecular weight.

Envelope dynamics of resonant inverter driven electromagnetic levitation melting system with experimental verification

The paper presents a methodology for nonlinear envelope dynamics derivation of a levitation melting type induction heating system, fed by a resonant inverter, based on recently established work piece electro-mechanical model. The work piece under consideration is formed by an aluminum sphere, floated by conical-shaped copper coil. Resonant power converter is used to drive the induction heating system due to the fact that significant impedance of the work piece coil at high operation frequency (several tens of kilohertz) limits the power transferred to the load and therefore needs to be cancelled by corresponding capacitive impedance. Since the application requires levitation of the object being heated up, low-frequency (several hertz) dynamics appears, related to floating body movement. As a result, high-frequency electrical signals become modulated by low-frequency oscillations induced by mechanical side dynamics. It is known that power transfer in sinusoidal excited electrical system is governed by magnitudes and related phases of currents and voltages. Consequently, in order to assess both the low-frequency dynamics of levitated object mechanical motion and the amount of power transferred, information regarding envelope behavior of electrical-side signals is sufficient. Once established, envelope model of the electrical subsystem combined with typical model of the mechanical subsystem describe mechanical side parameters (position, speed and acceleration) exactly as if full electrical model would have been utilized. Moreover, envelope model significantly decreases simulation time and memory requirements of simulation platform. The proposed modeling approach is validated by comparing full and envelope model simulation results, accompanied by results obtained from experimental prototype.

Assignment of Terahertz Modes in Hydroquinone Clathrates

Hydroquinone (HQ) and its clathrate are materials of growing interests, due to their promising applications in energy related science and industries. Recently, many studies have been performed to understand the properties of these materials. Terahertz (THz) spectroscopy is a powerful tool for studying the properties of these materials by non-destructively probing their low-energy (meV) dynamics. Although terahertz spectra of HQ and its clathrates have been measured, a report on the correspondence between THz spectra and low frequency dynamics is still lacking. In this paper, we measure the temperature-dependent THz spectra of both α-HQ (the non-clathrate form) and β-HQ clathrate, with Ar and CO2 as guest species. We also perform density functional theory (DFT) simulations on these materials, in order to assign the spectral features. We find an excellent match between the experimental and the DFT calculated spectra. Using the simulation result, we build connections between the THz spectra and the atomic motions in these materials. In addition, we also perform DFT simulations on β-HQ-He, β-HQ-Ne, and β-HQ-Kr to study the patterns in the change of THz spectra as the guest species changes.

A New Method of Two-stage Planetary Gearbox Fault Detection Based on Multi-Sensor Information Fusion

Due to their high transmission ratio, high load carrying capacity and small size, planetary gears are widely used in the transmission systems of wind turbines. The planetary gearbox is the core of the transmission system of a wind turbine, but because of its special structure and complex internal and external excitation, the vibration signal spectrum shows strong nonlinearity, asymmetry and time variation, which brings great trouble to planetary gear fault diagnosis. The traditional time-frequency analysis technology is insufficient in the condition monitoring and fault diagnosis of wind turbines. For this reason, we propose a new method of planetary gearbox fault diagnosis based on Compressive sensing, Two-dimensional variational mode decomposition (2D-VMD) and full-vector spectrum technology. Firstly, the nonlinear reconstruction and noise reduction of the signal is carried out by using compressed sensing, and then the signal with multiple degrees of freedom is adaptively decomposed into multiple sets of characteristic scale components by using 2D-VMD. Then, Rényi entropy is used as the optimization index of 2D-VMD analysis performance to extract the effective target intrinsic mode function (IMF) component, reconstruct the dynamics signal in the planetary gearbox, and improve the signal-to-noise ratio. Then, using the full-vector spectrum technique, the homologous information collected by numerous sensors is data layer fused in the spatial domain and the time domain to increase the comprehensiveness and certainty of the fault information. Finally, the Teager–Kaiser energy operator is used to demodulate the potential low-frequency dynamics frequency characteristics from the high-frequency domain and detect the fault characteristic frequency. Furthermore, the correctness and validity of the method are verified by the fault test signal of the planetary gearbox.

Recurrent-Neural-Network-Based Predictive Control of Piezo Actuators for Trajectory Tracking

Precise trajectory tracking of piezo actuators (PEAs) in real time is essential to high-precision systems and applications. However, the real-time tracking accuracy is rather limited as the PEA cannot be accurately modeled over large bandwidth and displacement range due to its nonlinearities. In this article, we propose to use recurrent-neural-network (RNN) to model the PEA system and develop a nonlinear predictive controller for PEA trajectory tracking. Considering the computation efficiency, first, an RNN is trained to model the nonlinear dynamics of the PEA system at high-frequency range. Then, a second-order linear model is proposed to account for the PEA low-frequency dynamics. Therefore, the PEA dynamics is modeled by the nonlinear model consisting of the RNN and the linear model, which is further used for nonlinear predictive control of the displacement. To increase the prediction accuracy, an unscented Kalman filter is designed to estimate the states of the nonlinear model. The nonlinear predictive control problem is solved based on a gradient descent algorithm, in which a method for analytically calculating the gradient of the cost function is developed. The proposed technique was experimentally implemented on a nano piezo stage for demonstration and its performance was compared with that of a PID controller. The accuracy of an iterative learning control approach was used as a benchmark for comparison as well. The results showed that high precision trajectory tracking of PEAs in real time can be achieved using the proposed technique.

Low-Frequency Dynamics and Its Correlation of Nanoscale Structures in Amorphous Solids

Unlike the crystalline solids, the atomic arrangements in amorphous solids lack long-range translational and orientational order. Despite intense research activity on their structures, the details of how the atoms are packed in amorphous solids remain mysterious at present. Here, we propose a structure feature like polymers and estimate the nanoscale of short-range order (SRO) and medium-range order (MRO) in this description according to the boson peak in amorphous solids. The result supports the concepts that (a) the low-frequency local vibrations are defined by the characteristic length of nanoscale clusters and (b) a decisive scale correlation of solvent atoms, SRO and MRO is about 1:3:7 in amorphous solids.

Electron spin resonance in spiral antiferromagnet linarite: Theory and experiment

We present combined experimental and theoretical investigation of the low-frequency ESR dynamics in the ordered phases of magnetic mineral linarite. This material consists of weakly coupled spin-1/2 chains of copper ions with frustrated ferro- and antiferromagnetic interactions. In zero magnetic field, linarite orders into a spiral structure and exhibits a peculiar magnetic phase diagram sensitive to the field orientation. The resonance frequencies and their field dependence are analyzed combining microscopic and macroscopic theoretical approaches and precise values of magnetic anisotropy constants are obtained. We conclude that possible realization of exotic multipolar quantum states in this material is greatly influenced by the biaxial anisotropy.

Different Influence of Grid Impedance on Low- and High-Frequency Stability of PV Generators

Recently, the stability issues when renewable energy sources are connected to the weak grid have obtained great attention. The popular view thinks that the grid impedance is adverse to the system stability. However, in this paper, it is first found that for the photovoltaic (PV) generator, the grid impedance has different influence on the system stability depending on the frequency range when the complete model of the PV generator is taken into consideration. That is, the increase of grid impedance can suppress the low-frequency ( 300 Hz) stability. Concretely, for the low-frequency range mainly dominated by the power loop and voltage loop of the PV generator, the describing function method is adopted to overcome discontinuity and nonlinearity of the power loop. Then, the low-frequency dynamics such as power oscillation can be analyzed accurately. For the high-frequency range mainly dominated by the phase-locked loop and current loop of the PV generator, the impedance analysis method is adopted to reveal the high-frequency instability mechanism. Through these analyses, the different influence of grid impedance on the low- and high-frequency stability of PV generators can be clearly distinguished. All the conclusions are verified through the real-time hardware-in-loop tests.

Investigation of Chaotic and Spiking Dynamics in Mid-Infrared Quantum Cascade Lasers Operating Continuous-Waves and Under Current Modulation

This study investigates chaotic and spiking dynamics of mid-infrared quantum cascade lasers operating under external optical feedback and emitting at 5.5 $\mu {\text{m}}$ and 9 $\mu {\text{m}}$ . In order to deepen the understanding, the route to chaos is experimentally studied in the case of continuous-wave and current modulation operation. The non-linear dynamics are analyzed with bifurcation diagrams. While for quasi-continuous wave operation, chaos is found to be more complex, pure continuous wave pumping always leads to the generation of a regular spiking induced low-frequency fluctuations dynamics. In the latter, results show that by combining external optical feedback with periodic forcing and further induced current modulation allows a better control of the chaotic dropouts. This work provides a novel insight into the development of future secure free-space communications based on quantum cascade lasers or unpredictable optical countermeasure systems operating within the two transparency atmospheric windows hence between 3 $\mu {\text{m}}$ –5 $\mu {\text{m}}$ and 8.5 $\mu {\text{m}}$ –11 $\mu {\text{m}}$ .

Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

This paper investigates the large-scale flow reorientations of Rayleigh–Bénard convection in a cubic cell using proper orthogonal decomposition (POD) analysis and modelling. A direct numerical simulation is performed for air at a Rayleigh number of $10^{7}$ and shows that the flow is characterized by four quasi-stable states, corresponding to a large-scale circulation lying in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, with occasional brief reorientations. Proper orthogonal decomposition is applied to the joint velocity and temperature fields of an enriched database which captures the statistical symmetries of the flow. We found that each quasi-stable state consists of a superposition of four spatial modes representing three types of structures: (i) a mean-flow mode consisting of two stacked counter-rotating torus-like structures; (ii) two large-scale two-dimensional rolls (pair of degenerated modes) which form large-scale diagonal rolls when combined together; and (iii) an eight-roll mode that transports fluid from one corner to the other and strengthens the circulation along the diagonal. In addition, we identified three other modes that play a role in the reorientation process: two boundary-layer modes (pair of degenerated modes) that connect the core region with the horizontal boundary layers and one mode associated with corner rolls. The symmetries of the different POD modes are discussed, as well as their temporal dynamics. A description of the reorientation process in terms of POD modes is provided and compared with other modal approaches available in the literature. Finally, Galerkin projection is used to derive a POD-based reduced-order model. Unresolved modes are accounted for in the model by an extra dissipation term and the addition of noise. A seven-mode model is able to reproduce the low-frequency dynamics of the large-scale reorientations as well as the high-frequency dynamics associated with the large-scale circulation rotation. Linear stability analysis and sensitivity analysis confirm the role of the boundary-layer modes and the corner-rolls mode in the reorientation process.

Dynamics of a supersonic transitional flow over a backward-facing step

The transition mechanism and unsteady behavior behind a backward-facing step (BFS) in the supersonic regime at Ma=1.7 and Reδ0=13718 is investigated using large-eddy simulation (LES). The visualization of the flow field shows that the transition process behind the step is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the K-H vortices, leading to Λ-shaped vortices, hair-pin vortices and finally to a fully turbulent state. The separation system features a broadband low-frequency dynamics in the range of fδ0/u∞=0.003∼0.20 as concluded from the spectral and statistical analysis. Dynamic mode decomposition suggests that the medium frequency motions centered around fδ0/u∞=0.06 are related to the interactions between reattaching and the shedding of large coherent shear vortices, while the lower (fδ0/u∞≈0.01) and higher (fδ0/u∞≈0.1) frequency unsteadiness are associated with the periodical expansion and shrinking of the separation system and the convection of upstream K-H vortices, respectively. All these three unsteady mechanisms are coupled to the laminar-to-turbulent transition process in the different stages.

All-optical detection and evaluation of magnetic damping in synthetic antiferromagnet

Synthetic antiferromagnets (SyAFs), which consist of a thin nonmagnetic spacer sandwiched by two nanolayer ferromagnets with antiferromagnetic coupling, are promising artificial magnets for spintronic memory and have attracted attention for use in future ultrafast spintronics devices. Here, we report an observation of the magnetization dynamics in a SyAF with nearly antiparallel magnetizations using an all-optical pump-probe technique. High- and low-frequency precessional dynamics of the SyAF were clearly observed. The damping of both modes was explained theoretically in terms of the dynamic exchange coupling induced by the spin current.

Simultaneous access to the low-frequency dynamics and ultraslow kinetics of the thermal expansion behavior of polyurethanes

A long-lasting technological and scientific need exists for more detailed understanding of the dynamics of thermo-mechanical properties of polymers. This article demonstrates how low-frequency dynamics and ultraslow kinetics of thermal expansion of polymers are easily measured by the spectroscopic dilatometry technique called “Temperature Modulated Optical Refractometry”. The influence of molecular packing and dynamics is investigated on the kinetic and dynamic glass transition of three visco-elastic polyurethane networks of different crosslink density. A major observation is the potentially massive difference between kinetic and dynamic thermal expansion coefficients for the vitrifying polyurethane networks at a given temperature. The same holds true for the kinetic and dynamic glass transition temperatures Tg kin and Tg dyn, which are observed to differ by 15 K under given cooling and temperature modulation conditions. The here used cooling procedures show how in general the comparison of the low-frequency dynamics with the kinetics allows for a given material to estimate the dynamic response from the kinetic response, and vice versa. First insights are gained into how far the relaxation dynamics of the polyurethane networks spread over a considerably larger temperature interval than those of a linear chain polymer.

Observation of quasi-diamagnetism and a transition from negative to positive in the exchange bias of a NiMnIn Heusler alloy

Heusler alloy composed by NiMnIn was prepared by induction melting in Argon atmosphere. The thermal martensitic and magnetic transitions of the sample were identified by differential scanning calorimetry. The quasi-static magnetic properties were observed by field-colled, zero-field-colled, and isothermal magnetization curves in a wide range of temperature. Moreover, AC susceptibility measurements were employed to analyze the low-frequency magnetization dynamics. The martensitic state of the sample leads to magnetic disturbances of quasi-diamagnetism and exchange bias behavior. The exchange bias field presented a transition from negative values to positive values with the temperature increasing. Therefore, the results open a way for technological applications of the NiMnIn Heusler alloy, with potential perspectives for the development of spintronic devices.

Low-frequency phonon dynamics and related thermal properties of axially stressed single-walled carbon nanotubes

Synthesis temperatures of composite materials are usually far less than the ones of their use, thus carbon nanotubes (CNTs) embedded into a polymer matrix undergo significant axial stress. We develop a continuous theory, which describes the dynamics of stressed single-walled (SW-) CNTs and predicts their low-frequency phonon spectra. The changes in dispersion laws of SWCNT low-frequency phonon modes due to the axial stress of different signs are discussed. Then, the results obtained are used to analyze low-temperature (T < 70 K) heat capacity and thermal conductivity of individual nanotubes. We demonstrate that compressive stress leads to increase in heat capacity CV of an individual SWCNT, while tensile stress causes CV to decrease. In the latter case at T → 0 heat capacity diminishes according to a linear law ~T instead of a power one ~T1/2. Nevertheless, according to our results, axial stress hardly affects low-temperature thermal conductance of SWCNTs. Influence of investigated effects on the corresponding macroscopic properties of CNT-based composite materials are also discussed.

Low-frequency dynamics of the flow around a finite-length square cylinder

Fluctuating pressure on the side faces, lee-ward face and free end of a finite-length square cylinder is measured simultaneously, together with the velocity in its free-end shear flow, to reveal their inherent connection. The width (d) of the tested model is 40 mm, and the aspect ratio is 5. All experiments are conducted in a low-speed wind tunnel at an oncoming flow velocity (U∞) of 10 m/s. The corresponding Reynolds number based on U∞ and d is 27,000. It is found that, the fluctuating pressure on the side faces and free end has remarkable low-frequency instability with the frequency of about 1/10 of the well-known spanwise Karman vortex shedding. Besides, a high-frequency component, corresponding to Karman vortex shedding, is also found in the fluctuating pressure on cylinder side faces. The low-frequency instability is in phase over the entire cylinder span, while the high-frequency component tends to be out of phase, especially at the lower part of the cylinder. The free-end shear flow flaps at the low frequency and strongly correlates with the modes of spanwise vortex shedding. Particularly, when the free-end shear flow flaps to its lower position, alternate spanwise vortex shedding with high pressure fluctuation occurs; when it flaps to its upper position, the occurrence probability of co-shedding with low pressure fluctuation increases significantly especially near the cylinder free end.