Harmonic Line Research Articles

A closed-form solution for a double infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to harmonic line load

The dynamic response of a double infinite beam system connected by a viscoelastic foundation under the harmonic line load is studied. The double infinite beam system consists of two identical and parallel beams, and the two beams are infinite elastic homogeneous and isotropic. A viscoelastic layer connects the two beams continuously. To decouple the two coupled equations governing the response of the double infinite beam system, a variable substitution method is introduced. The frequency domain solutions of the decoupled equations are obtained by using Fourier transforms as well as Laplace transforms successively. The time domain solution in the generalized integral form are then obtained by employing the corresponding inverse transforms, i.e. Fourier transform and inverse Laplace transform. The solution is verified by numerical examples, and the effects of parameters on the response are also investigated.

Theoretical Analysis on Affecting Factors of Power Line Harmonic Radiation

Power line harmonic radiation (PLHR) is an artificial electromagnetic pollution source in the near-earth space environment. Up until now, there has been little quantitative research on its formation mechanism. This paper details a model and solver for electromagnetic waves propagation in a stratified anisotropic ionosphere. In our model, these electromagnetic waves are generated by an arbitrary electric dipole source above a nonideal conductive ground. The matrix-exponent method and a full-wave method are combined to analyze the model, avoiding the problem of numerical overflow and swamping in numerical calculations. The computing results obtained from the proposed method and the observed electric field data by using DEMETER satellite are compared and found to be in good agreement. Furthermore, this paper considers the effects on PLHR propagation in the ionosphere due to dipole source frequency, earth’s conductivity, electron density, geographic latitude, and geomagnetic field orientation. Results show that when the frequency increases, the strength of PLHR penetrating into the ionosphere has an increasing tendency. If the harmonic current remains constant, lower ground conductivity and electron density of the ionosphere result in higher radiation power. PLHR propagates along the direction of the geomagnetic field in the ionosphere, and its strength decreases with the increasing geomagnetic inclination at the same height. In addition, the radiation power of less than 1 W may trigger PLHR.

Correlation Between Power Line Harmonic Radiation and Magnetospheric Line Radiation Over China

Power line harmonic radiation (PLHR) and magnetospheric line radiation (MLR) are recognized as electromagnetic pollutants in the near-earth space, and their correlation has been a controversial issue. An identification procedure based on short-time discrete Fourier transform and Welch power spectrum estimation was applied to detect 114 PLHR events and 328 MLR events that occurred as DEMETER satellite flew over China from 2008 to 2010. PLHR events feature parallel horizontal lines with a frequency interval of 50/100 Hz in spectrogram, whereas MLR events feature multi-parallel spectral lines with frequency drift as a baseline for possible triggered emissions as well as triggered emissions with no baseline. We statistically compared the temporal and geographical distribution, Kp and Dst indices, and propagation characteristics between PLHR and MLR events. PLHR events showed more obvious variations annually than MLR events, and the former had a close relationship with the development of Chinese power system. Both PLHR and MLR presented similar diurnal and seasonal differences, owing likely to the ionospheric state; moreover, they appeared to have no significant connection with geomagnetic activity level. The geographical distributions of PLHR and MLR differed significantly. PLHR events occurred in the range of (20° N–45° N), whereas MLR events were concentrated in southwestern low-latitude regions of (18° N–28°N). Furthermore, PLHR waves were right-hand circularly polarized, whereas MLR waves were approximately linearly polarized. In summary, MLR is more likely caused by natural radiation that is not directly related to PLHR, whereas PLHR is closely related to terrestrial power systems.

Analysis for DC transmission line harmonics originated from AC transformer inrush current and improved method for DC harmonic protection

Large-scale electricity has fed into Central and Southern China through DC transmission lines. Any one of the DC transmission lines suddenly outage will result in a large proportion of power-shortage. Recently, there are many DC harmonic protection misoperations caused by AC disturbance, resulting in DC transmission line exit operation. Therefore, it is necessary to analyse the effect of AC disturbance on DC harmonics and study methods for DC harmonic protections. In this study, based on the theory of switching function, the harmonics interaction in AC–DC systems is studied. The cause of DC line harmonic protection misoperation during unusual AC disturbances, such as inrush current and short circuit, is revealed. The DC line 50 Hz harmonic protection misoperates frequently due to inrush current on site. Taking it for example, an improved method using the second harmonic voltage in AC system bus is proposed. In this method, the 50 Hz harmonics generated by inrush current can be accurately identified by judging the correlation between the AC harmonic voltage and the DC line harmonic current. By automatically adjusting the threshold value of protection, the misoperation can be prevented effectively without affecting the original protection performance. The simulation results verify the correctness of the method.

Droplet dynamics on chemically heterogeneous substrates

Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solutions to the governing partial differential equation. The limitations of the reduced model when the contact line undergoes stronger deformations are partially lifted by proposing a hybrid scheme which couples the results of the asymptotic analysis with the boundary integral method. This approach improves the agreement with the governing partial differential equation, but at a computational cost which is significantly lower compared to that required for the full problem.

Control of the helicity of high-order harmonic radiation using bichromatic circularly polarized laser fields

High-harmonic generation in two-colour ($\omega-2\omega$) counter-rotating circularly polarised laser fields opens the path to generate isolated attosecond pulses and attosecond pulse trains with controlled ellipticity. The generated harmonics have alternating helicity, and the ellipticity of the generated attosecond pulse depends sensitively on the relative intensities of two adjacent, counter-rotating harmonic lines. For the $s$-type ground state, such as in Helium, the successive harmonics have nearly equal amplitude, yielding isolated attosecond pulses and attosecond pulse trains with linear polarisation, rotated by 120$^{{\circ}}$ from pulse to pulse. In this work, we suggest a solution to overcome the limitation associated with the $s$-type ground state. It is based on modifying the three propensity rules associated with the three steps of the harmonic generation process: ionisation, propagation, and recombination. We control the first step by seeding high harmonic generation with XUV light tuned well below the ionisation threshold, which generates virtual excitations with the angular momentum co-rotating with the $\omega$-field. We control the propagation step by increasing the intensity of the $\omega$-field relative to the $2\omega$-field, further enhancing the chance of the $\omega$-field being absorbed versus the $2\omega$-field, thus favouring the emission co-rotating with the seed and the $\omega-$field. We demonstrate our proposed control scheme using Helium atom as a target and solving time-dependent Schr{\"o}dinger equation in two and three-dimensions.

Magnetosonic Harmonic Falling and Rising Frequency Emissions Potentially Generated by Nonlinear Wave‐Wave Interactions in the Van Allen Radiation Belts

AbstractMagnetosonic waves play a potentially important role in the complex evolution of the radiation belt electrons. These waves typically appear as discrete emission lines along the proton gyrofrequency harmonics, consistent with the prediction of the local Bernstein mode instability of hot proton ring distributions. Magnetosonic waves are nearly dispersionless particularly at low harmonics and therefore have the roughly unchanged frequency time structures during the propagation. On the basis of Van Allen Probes observations, we here present the first report of magnetosonic harmonic falling and rising frequency emissions. They lasted for up to 2 hr and occurred primarily in the dayside plasmatrough following intense substorms. These harmonic emission lines were well spaced by the proton gyrofrequency but exhibited a clear falling (rising) frequency characteristic in a regime with the temporal increase (decrease) of the proton gyrofrequency harmonics. Such unexpected structures might be produced by the nonlinear interactions between the locally generated magnetosonic waves at the proton gyrofrequency harmonics and a constant frequency magnetosonic wave propagating away from the Earth.

Sound-structure interaction analysis of an infinite-long cylindrical shell submerged in a quarter water domain and subject to a line-distributed harmonic excitation

The sound-structure coupling problem of a cylindrical shell submerged in a quarter water domain is studied. A semi-analytical method based on the double wave reflection method and the Graf's addition theorem is proposed to solve the vibration and acoustic radiation of an infinite cylindrical shell excited by an axially uniform harmonic line force, in which the acoustic boundary conditions consist of a free surface and a vertical rigid surface. The influences of the complex acoustic boundary conditions on the vibration and acoustic radiation of the cylindrical shell are discussed. It is found that the complex acoustic boundary has crucial influence on the vibration of the cylindrical shell when the cylindrical shell approaches the boundary, and the influence tends to vanish when the distances between the cylindrical shell and the boundaries exceed certain values. However, the influence of the complex acoustic boundary on the far-field sound pressure of the cylindrical shell cannot be ignored. The far-field acoustic directivity of the cylindrical shell varies with the distances between the cylindrical shell and the boundaries, besides the driving frequency. The work provides more understanding on the vibration and acoustic radiation behaviors of cylindrical shells with complex acoustic boundary conditions.

Control of attosecond light polarization in two-color bicircular fields

We develop theoretically and confirm both numerically and experimentally a comprehensive analytical model which describes the propensity rules in the emission of circularly polarized high harmonics by systems driven by two-color counter-rotating fields, a fundamental and its second harmonic. We identify and confirm the three propensity rules responsible for the contrast between the 3N+1 and 3N+2 harmonic lines in the HHG spectra of noble gas atoms. We demonstrate how these rules depend on the laser parameters and how they can be used in the experiment to shape the polarization properties of the emitted attosecond pulses.

Enhancement of the Comb Filtering Selectivity Using Iterative Moving Average for Periodic Waveform and Harmonic Elimination.

A recurring problem regarding the use of conventional comb filter approaches for elimination of periodic waveforms is the degree of selectivity achieved by the filtering process. Some applications, such as the gradient artefact correction in EEG recordings during coregistered EEG-fMRI, require a highly selective comb filtering that provides effective attenuation in the stopbands and gain close to unity in the pass-bands. In this paper, we present a novel comb filtering implementation whereby the iterative filtering application of FIR moving average-based approaches is exploited in order to enhance the comb filtering selectivity. Our results indicate that the proposed approach can be used to effectively approximate the FIR moving average filter characteristics to those of an ideal filter. A cascaded implementation using the proposed approach shows to further increase the attenuation in the filter stopbands. Moreover, broadening of the bandwidth of the comb filtering stopbands around −3 dB according to the fundamental frequency of the stopband can be achieved by the novel method, which constitutes an important characteristic to account for broadening of the harmonic gradient artefact spectral lines. In parallel, the proposed filtering implementation can also be used to design a novel notch filtering approach with enhanced selectivity as well.

A general closed-form solution to a Timoshenko beam on elastic foundation under moving harmonic line load

In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy\'s residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.

A Room Away from the Wolves by Nova Ren Suma

Reviewed by: A Room Away from the Wolves by Nova Ren Suma Deborah Stevenson, Editor Suma, Nova Ren A Room Away from the Wolves. Algonquin, 2018 [336p] ISBN 978-1-61620-373-3 $18.95 Reviewed from galleys R* Gr. 8-12 Bina is supposed to be going into exile (well, being taken in by friends) to give her warring family (really her bullying stepsisters) a breather, but instead Bina makes a break for it, heading to Manhattan. There she seeks out and finds Catherine House, the old-fashioned boarding house her mother stayed at in her youth, and she's welcomed as a legacy and given a tiny room. She's thrilled at this connection with the mother she loved, the mother who had possibilities beyond merely acceding to the man in her life, and she enjoys her budding friendship with willful fellow resident Monet. Catherine House is strange, though, in ways that Bina finds increasingly disturbing: the frantic devotion of the other young women there to the house's benefactress, Catherine de Barra, and the legends around her death; the opal ring that belonged to Bina's mother and now seems connected to Catherine; and the seeming inability of its inhabitants to leave. This is Muriel Spark's great boarding-house novel The Girls of Slender Means turned to creepy gothic, and turned to it very well indeed. Suma's writing is taut, potent, and enticing as she establishes Bina's vulnerability and crafts the oppressive, plush, and enigmatic world of Catherine House. As with her previous books, however, the situation is a stage for girls in liminal or marginalized states to play out their emotional transitions, so Bina's family drama and her mother's painful distancing are a keen and anxious harmonic line. The book's structure, with an opening scene set after Bina has been at Catherine House for a month, primes readers to be alert to strangeness but leaves twists in store for them, and there's plenty of room for discussion afterward about the implications. Copyright © 2018 The Board of Trustees of the University of Illinois

Shunt active DC filter based on intelligence controller for HVDC link

A shunt active DC filter (ADF) with current injection suppresses current harmonics from high-voltage DC (HVDC) transmission systems. This paper proposes an ADF based on artificial neural networks (ANNs). The ANNs are very generic, accurate and convenient statistical models. They can emulate numerical model components, which are of complicated non-linear input/output relationships. The neural network in the control system of the ADF estimates the harmonic components of the load current and voltage. The ANN is trained offline using databases from the conventional controller. The simulation is carried out by MATLAB/Simulink and its results confirm that the proposed controller can offer better performance such as suppression of the current variations (current harmonics) in the DC-transmission line.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution. The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction. Thus, it is more realistic than the Winkler model, which only represents compressive soil resistance. However, the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation; hence, the beam under inclined loads cannot be considered in the model. In this study, a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model, which tends to disregard the tangential interaction between the beam and the foundation. The horizontal spring reaction is assumed to be proportional to the relative tangential displacement. The governing equation can be deduced by theory of elasticity and Newton's laws, combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition. Double Fourier transformation is used to simplify the geometric equation into an algebraic equation, thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam. Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution. The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS. Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam. Results are realistic and can be used as reference for future engineering designs.

Probabilistic Multi-objective Framework for Multiple Active Power Filters Planning

In the real-world electrical distribution networks, entering of the non-linear loads, as main sources of harmonic generator, has probabilistic nature. In this paper, with a new point of view, a multi-objective framework is developed for multiple active power filters (APFs) with taking probabilistic features of non-linear loads into account. In the proposed probabilistic multi-objective framework, total harmonic distortion of voltage (THDV), motor load loss function, harmonic transmission line loss, and total APFs current are the four objectives considered in the optimization problem. At the same time, individual and THDV, and maximum allowable size of the APFs are modeled as constraints with predetermined admissible levels. The newly developed framework is a non-convex non-linear mixed-integer optimization problem. Hence, a new hybrid of melody search algorithm and augmented Powell heuristic method is employed and followed by a fuzzy satisfying method to obtain the final optimal solution. The feasibility and effectiveness of the offered framework has been implemented on the IEEE 18-bus distribution test system and IEEE 30-bus distribution test system. The obtained results show the profitableness of the newly developed framework in the APFs planning.

Closed-form solution considering the tangential effect under harmonic line load for an infinite Euler–Bernoulli beam on elastic foundation

• Analytical solution for dynamic response of infinite beam on foundation is developed. • The elastic foundation considered the horizontal tangential effect. • Double Fourier transformation is used for deduction and the residue theorem is employed to obtain the solution. • The analytical solution for the beam under inclined dynamic load is presented. The dynamic response of an infinite Euler–Bernoulli beam resting on an elastic foundation, which considers the tangential interaction between the beam and foundation under harmonic line loads, is developed in this study in the form of a closed-form solution. Previous studies have focused on elastic Winkler foundations, wherein the tangential interaction between the bottom of the beam and the foundation is not considered. In this study, a series of separate horizontal springs is diverted to the contact surface between the foundation and beam to simulate the horizontal tangential effect. The horizontal spring reaction is assumed proportional to the relative tangential displacement. As the geometric equation and linear-elastic constitutive equation of beam under the condition of small deformation have been presented based on the basic principle of elasticity mechanics, the analysis model is built and the governing differential equations about normal and tangential deflections of beam are deduced. Double Fourier transformation and the residue theorem are used to derive the closed-form solution to this problem. The proposed solution is then validated by comparing the degraded solution with the known results and comparing the numerical solution with the analytical solution. We also discuss the case in which the load direction is not vertical to the beam. Results can be used as a reference for engineering design.

Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states.

The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the weak effects of dynamical symmetry breaking caused by finite pulse duration are amplified by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.

VIENNA RECTIFIER LINE HARMONICS REDUCTION USING DC MOTOR APPLICATION.

31Jul 2017 VIENNA RECTIFIER LINE HARMONICS REDUCTION USING DC MOTOR APPLICATION. Aadyasha Patel , S. Nirmala and P. Chandrakala. Assistant Professor, Prince Shri Venkateshwara Padmavathy Engineering College, Chennai.

A Novel Detection Method for Underwater Moving Targets by Measuring Their ELF Emissions with Inductive Sensors.

In this article, we propose a novel detection method for underwater moving targets by detecting their extremely low frequency (ELF) emissions with inductive sensors. The ELF field source of the targets is modeled by a horizontal electric dipole at distances more than several times of the targets’ length. The formulas for the fields produced in air are derived with a three-layer model (air, seawater and seafloor) and are evaluated with a complementary numerical integration technique. A proof of concept measurement is presented. The ELF emissions from a surface ship were detected by inductive electronic and magnetic sensors as the ship was leaving a harbor. ELF signals are of substantial strength and have typical characteristic of harmonic line spectrum, and the fundamental frequency has a direct relationship with the ship’s speed. Due to the high sensitivity and low noise level of our sensors, it is capable of resolving weak ELF signals at long distance. In our experiment, a detection distance of 1300 m from the surface ship above the sea surface was realized, which shows that this method would be an appealing complement to the usual acoustic detection and magnetic anomaly detection capability.

Generation and radiation of high power line harmonics

The problems of frequency spectrum generation, radiation, and reception of signals at high power line (PL) harmonics of 50/60 Hz, and high PL harmonics caused by the use of thyristor power controllers in control circuits of large electricity consumers are discussed. The PL for frequencies of 2–8 kHz is considered a sufficiently effective traveling-wave antenna (the so-called Beverage antenna). The response of the spectrometer to a periodic sequence of PL radiation broadband pulses is discussed. The effects of a slow signal frequency drift at high PL harmonics and the occurrence of pulse components with fast frequency drift on the dynamic spectra, which in the literature is often associated with the magnetospheric trigger radiation, are considered.