Harmonic Resonance Analysis of Shale Gas Distribution Network with Phased Load

Based on the background of achieving carbon peaking and carbon neutrality, the development and application of new high-power compressors, electric grid drilling RIGS and electric fracturing pump system provide new equipment support for the electric, green and intelligent development of shale gas fields in China. However, the harmonic pollution of shale gas grid becomes more serious due to the converter and frequency conversion device in the system, which easily causes harmonic resonance problem. Therefore, the harmonic resonance of shale gas grid is comprehensively analyzed and treated. Firstly, the working mechanism of compressor, electric drilling RIGS of the harmonic impedance model of electric fracturing pump system is established. Secondly, the main research methods of harmonic resonance analysis are introduced, and the basic principle of modal analysis is explained. Modal analysis method was used to analyze. Finally, harmonic resonance is suppressed. The results show that there may be multiple resonant frequency points in the distribution network changes, but these changes are relatively clear;if the original resonant frequency point of the resonant loop does not exist, the resonant frequency point disappears. The optimal configuration strategy of passive filter can effectively suppress harmonic resonance of distribution network in shale gas field.

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density（PSD） and signal-to-noise ratio（SNR） are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.

Harmonic Analyses of Hydrodynamic Characteristics for Gap Resonance Between Fixed Box and Vertical Wall

Two marine structures arranged side by side with a narrow gap may suffer from violent free-surface resonance,which would cause green water on deck,dramatically raise hydrodynamic loads on structures and seriously threaten the operation safety.The CFD-based open-sourced software,OpenFOAM?,is employed to simulate the twodimensional fluid resonance inside a narrow gap between a fixed box and a vertical wall induced by regular waves with different wave heights.The topographies with various plane slopes are placed in front of the wall.The focus of this article is on the influences of the incident wave height and the topographic slope on the nonlinear characteristics of various hydrodynamic parameters(including the wave height in the gap,the vertical wave force,and the horizontal wave force on the box)during gap resonance.The ratios of their high-order to the corresponding 1 st-order components under different sets of the incident wave height and the topographic slope are analyzed.It is found that the relative importance of all the high-order components increases gradually with the incident wave height for all the three parameters.The topographic influence on them closely depends on the type of the parameters and the incident wave height.In addition,the occurrence of the 2 nd-order gap resonance phenomenon can cause the 2 nd-order wave height and horizontal force to be significantly larger than the corresponding 1 st-order components.

Primary resonance of fractional-order Duffing–van der Pol oscillator by harmonic balance method

The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems.

Analysis of the Electric Locomotives Neutral-section Passing Harmonic Resonance

For the further analysis and suppression of the electric locomotives neutral-section passing overvoltage, on the basis of theoretical analysis of the neutral-section passing harmonic resonance conditions, this paper establishes simplified harmonic resonance simulation models of the electric locomotives neutral-section passing using MATLAB/Simulink, and makes the overvoltage simulation analysis of the existing electric locomotives neutral-section passing system in the event of a harmonic resonance. Results show that when the system harmonic resonance occurs, the operating overvoltage of the neutral-section passing is serious intensified by the overvoltage of the harmonic resonance, which will make the voltage of the pantograph collector head exceeding 100kV. This amplitude of the overvoltage will breakdown the air gap, which will be a serious threat to the safety operation of the electric railway. However, this kind of neutral-section passing overvoltage hasn’t cause the attention in the field and theoretical studies, which need more analysis and verification in the further study.

Stochastic Resonance in a Harmonic Oscillator Fluctuating Intrinsic Frequency by Asymmetric Dichotomous Noise

The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain （OAG） is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics： intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.

Double coherence resonance of the FitzHugh Nagumo neuron driven by harmonic velocity noise

The effect of noise frequency on the FitzHugh-Nagumo neuron is investigated by the use of the harmonic velocity noise, which has a direct frequency parameter and no zero frequency part of the power spectrum. It is shown that the neuron has the resonance characteristic strongly responding to the noise with a certain frequency at fixed power, and there is double coherence resonance related to the frequency and the intensity. If the harmonic velocity noise lacks low frequency ingredients, there is no synchronization between the frequency of the neuron and that of the noise. Thus the low frequency part of the noise plays an important role in creating the synchronization.

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency

The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.

Subharmonic resonance of a clamped-clamped buckled beam with 1:1 internal resonance under base harmonic excitations

The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton’s principle.A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method.A high-dimensional model of the buckled beam is derived,concerning nonlinear coupling.The incremental harmonic balance(IHB)method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve,and the Floquet theory is used to analyze the stability of the periodic solutions.Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited.Bifurcations including the saddle-node,Hopf,perioddoubling,and symmetry-breaking bifurcations are observed.Furthermore,quasi-periodic motion is observed by using the fourth-order Runge-Kutta method,which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited.

Third-Order Nonlinear Optical Response near the Plasmon Resonance Band of Cu2-xSe Nanocrystals

The third-order nonlinear optical properties of water-soluble Cu Se nanocrystals are studied in the near infrared range of 700-980 nm using a femtosecond pulsed laser by the Z-scan technique. It is observed that the nonlinear optical response of Cu Se nanocrystals is sensitively dependent on the excitation wavelength and exhibits the enhanced nonlinearity compared with other selenides such as ZnSe and CdSe. The W-shaped Z-scan trace, a mixture of the reversed saturated absorption and saturated absorption, is observed near the plasmon resonance band of Cu Se nanocrystals, which is attributed to the state-filling of free carriers generated by copper vacancies (self-doping effect) of Cu Se nanocrystals as well as the hot carrier thermal effect upon intense femtosecond laser excitation. The large nonlinear optical response and tunable plasmonic band make Cu Se nanocrystals promising materials for applications in ultra-fast all-optical switching devices as well as nonlinear nanosensors.

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.

Sub-Harmonic Resonances of Periodic Parameter Excited Oscillators with Discontinuities

It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.

STUDY ON LOWER ORDER HARMONIC RESONANCE OF ELASTIC LINKAGES──SUPER HARMONIC RESONANCES

The superharmonic resonances of elastic linkages are studied by using the method of multiple scales under the excitation of its inertial foree。 The analyses demonstrate that the superharmonic resonances caused by the quadratic and cubic nonlinearities due to large elastic deformations of the flexible links and multi-frequencies of the inertial force of linkages are the reason to produce the critical speeds. The results of explaining of the lower order harmonic reso- nances by“1/n' method are verified theoretically。

Spectral shift of solid high-order harmonics from different channels in a combined laser field

We investigate theoretically the spectral shift of the high-order harmonic generation(HHG)in ZnO driven by a combined laser field by solving the two-band semiconductor Bloch equations(SBEs)in the velocity gauge.The combined laser field is synthesized by a fundamental laser pulse and its seventh-frequency laser pulse.When the seventh-frequency laser pulse is added to the rising or falling parts of the fundamental laser field,we find that the spectral blueshift or redshift appears,which is due to the unequal contribution of the rising and falling parts in the fundamental laser field to the harmonics.By analyzing the time-dependent conduction band population in k space,we found that,in addition to the tunneling ionization channel,there is also the resonant electron injection channels which is induced by the seventh-frequency laser pulse.The harmonics generated by the different channels show the spectral redshift or the spectral blueshift,respectively.Through analyzing the k-integrated transient conduction band population of the electrons from different channels,we found that if there is a certain delay in the process of the electron excitation,it will lead to the delay in the harmonic emission,which results in the spectral redshift of the harmonics.

Hybrid simulation of q=1 high-order harmonics driven by passing energetic particles in tokamak plasmas

High-order harmonics q(ψ_(s))=1 energetic particle modes(EPMs)have been observed in toroidal plasmas experiments with neutral beam injection.To investigate these phenomena,linear properties and nonlinear dynamics of these EPMs driven by passing energetic particles(EPs)are studied via the global hybrid kinetic-magnetohydrodynamic code M3D-K.Simulation results demonstrate that passing EPs'effects on high mode-number harmonics(q(ψ_(s))=m/n=2/2,3/3,4/4)instability are more obvious than the q(ψ_(s))=1/1 mode,especially when q-profile is sufficiently flat in the core region.Furthermore,the effects of the pitch angleΛ_0 and beam ion pressure P_(hot)/P_(total)on the features of high n components are also analyzed specifically.It is found that there exists only one resonant condition for these EPMs.In the nonlinear phase,these high mode-number harmonics can induce significant energetic ions redistribution and chirping up phenomena,which differs from the classical fishbone excited by passing EPs.These discoveries are conducive to better apprehend the underlying physical mechanisms of the highorder harmonics driven by passing EPs.

Electromagnetic interference assessment of a train-network-pipeline coupling system based on a harmonic transmission model

The harmonics and resonance of traction power supply systems(TPSSs)aggravate the electromagnetic interference(EMI)to adjacent metallic pipelines(MPs),which has aroused widespread concern.In this paper,an evaluation method on pipeline interference voltage under harmonic induction is presented.The results show that the Carson integral formula is more accurate in calculating the mutual impedance at higher frequencies.Then,an integrated train-network-pipeline model is established to estimate the influences of harmonic distortion and resonance on an MP.It is revealed that the higher the harmonic cur-rent distortion rate of the traction load,the larger the interference voltage on an MP.Particularly,the interference voltage is amplified up to 7 times when the TPSS resonates,which is worthy of attention.In addition,the parameters that affect the variation and sensitivity of the interference voltage are studied,namely,the pipeline coating material,locomotive position,and soil resistivity,indicating that soil resistivity and 3PE(3-layer polyethylene)anticorrosive coating are more sensitive to harmonic induction.Field test results show that the harmonic distortion can make the interference voltage more serious,and the protective measures are optimized.

An Equivalent Fundamental and Odd Harmonic Resonators Controller for a Single-phase Dynamic Voltage Restorer

为提高单相动态电压恢复器（dynamic voltage restorer,DVR）的补偿性能,提出一种基于等效基波及奇次谐波谐振器组的数字控制方法。采用可等效为一组谐振器的延时模块,能够有效抑制电网基波和谐波扰动。给出一种包含两个控制参数和一组零相移陷波滤波器的结构及其设计方法,使系统在保证稳定性的同时,获得较大的谐振增益。其中,延时环节衰减系数可增加谐振器组鲁棒性;控制器比例增益可解决零相移陷波器中使用延时带来的问题;零相移陷波器组既能对消LC谐振峰,也能解决等效谐振器组高增益在高频处的稳定性问题。同时,引入电源电压和负载电流双前馈来保证响应速度,增加了对扰动的抑制能力。所提控制策略结构简单,谐波补偿能力强,动态响应快,易于实现。在2kW单相DVR实验装置上的实验结果验证了该控制方法的正确性。

A Multi-harmonic Method for Studying Effects of Mistuning on Resonant Features of Bladed Disks with Dry Friction Damping

An efficient multi-harmonic method is proposed for studying the effects of mistuning on resonant features of bladed disks with blade-to-blade dry friction damping. This method is able to predict accurately the forced response of bladed disks in frequency domain, which is validated by numerical integration method in time domain. The resonant features of both tuned and mistuned systems are investigated by using this method under various system coupling strengths, viscous dampings, and dry friction darnpings, etc. The results demonstrate that the proposed multi-harmonic method is very efficient for studying the mistuning effects on the resonant response of bladed disks with blade-to-blade dry friction damping, especially considering the combined effects of various system parameters.

Two-Photon Resonant Third Harmonic Generation in Carbon Monoxide

Tunable coherent extreme ultraviolet radiation has been generated in CO by two-photon resonant third harmonic generation via the A^(1) II(v'=4)←X^(1)Σ+(v"=0)transition.The third nharmonic spectrum exhibits resolved and improved rotational lines due to the expansion cooling of the molecular beam.The saturation and the phase-matching of the nonlinear process are also discussed.

Three-Photon Resonant Third Harmonic Generation of H2 in Vacuum Ultraviolet and Extreme Ultraviolet Regions

Tunable coherent vacuum ultraviolet and extreme ultraviolet radiation have been produced in H2 by three-photon resonant third harmonic generation via B1 Σ_(u)^(+)(v’) ← X^(1) Σ_(g)^(+) (v = 0 ) and C^(1) IIu(v’) ← X^(1) Σ_(g)^(+) ( v = 0 ) transitions. Highly resolved third harmonic spectrum exhibits some distinct characteristics. Phase-matching effect of the nonlinear optical process is also discussed.