递进式N×N型采样方式次谐波海洋湍流相位屏模拟方法

以N×N型采样方式次谐波法为基础,引入了递进式采样,提出了一种递进式N×N型采样方式次谐波法,用于数值模拟海洋湍流相位屏。该方法利用Nikishov提出的海水折射率波动谱模拟海洋湍流相位,通过相位结构函数和补偿效果验证该方法生成相位屏的准确性。通过改变递进区域个数、补偿阶数和谐波次数,比较分析相位屏参数对改变对相位屏准确性的影响。此外,将所提方法与N×N型采样方式次谐波法、改进的次谐波补偿法和改进的次谐波法进行比较。结果表明:递进式N×N型采样方式次谐波法只需谐波次数为11时,补偿效果即可达到0.9995,并且在准确度相同的情况下具有更快的模拟速度。

均匀磁场下二维拓扑绝缘体边缘态的多重Andreev反射研究

研究均匀磁场下的二维拓扑绝缘体在超导隧道结中的电压偏置约瑟夫森结的输运性质,电流-电压特性显示了马约拉纳束缚态的存在。在亚谐隙结构中,也可以观察到磁场对超导能隙的影响。研究结果表明,在S波超导体/正常金属/S波超导结的隧道谱中存在亚谐隙结构。透明度只影响超导结的零偏压电导值的大小,而不影响亚谐隙结构的位置。但是在磁场作用下,亚谐隙结构会发生变化,不再固定出现在特定位置。这一结果对应于拓扑螺旋态中超导和铁磁序之间的相互作用。

星载220 GHz分谐波混频器设计

为满足星载辐射计系统应用,提出了一款220 GHz次谐波混频器。基于平面GaAs肖特基二极管3D电磁模型,混频器电路和结构优化设计采用HFSS和ADS联合仿真实现。通过在50μm厚的石英基板上倒装反向并联二极管对以及采用纳米银胶将基板粘接在硅铝波导腔的工艺方式,设计并加工实现了一款210~240 GHz分谐波混频器,单边带最小变频损耗仿真结果为7.33 dB,实测变频损耗优于9.6 dB。按照某卫星规定的各项环境试验条件验证其在不同环境条件下的性能,结果证明该混频器试验前后一致性较好。

基于反步控制的特定次谐波电流补偿研究

电网中广泛采用非线性负载,由此造成的谐波污染问题日益严重,有源电力滤波器是解决谐波污染的有效手段之一。基于谐波提取算法,兼顾稳态响应以及参数选取,提出将反步法引入谐波补偿的设计,对谐波电流跟踪控制器进行重新构建。依据反步法理论进行控制器的设计,能够达到较好的稳态补偿效果,其参数的选取较易。在MATLAB/Simulink中进行PI控制与反步控制的仿真对比,结果验证了所提控制策略对特定次谐波补偿的有效性,直流侧电容电压的反步控制较PI控制超调小、响应速度快,仿真结果证明了反步控制具有更高的补偿精度以及较快的动态响应。

一类附加斜弹簧支撑的悬臂梁碰撞系统的全局动力学

本文研究了双侧非对称刚性约束下附加斜弹簧支撑的悬臂梁碰撞系统的次谐分岔和混沌的全局动力学。由于斜弹簧支撑结构的刚度项为超越函数,给解析研究系统混沌和次谐分岔造成很大的困难。本文近似拟合了该系统的刚度项,并对比分析了近似系统和原系统的同宿轨道及其内部的次谐轨道。将Melnikov方法发展应用于非光滑的碰撞悬臂梁系统,给出了发生同宿混沌和次谐分岔的阀值条件。利用光滑流形的特征乘子结合碰撞函数分析了碰撞次谐轨道的稳定性,并分析了次谐分岔与混沌的关系。基于阀值条件研究了阻尼、激励频率、激励幅值以及碰撞恢复系数对混沌和次谐分岔的影响,进一步验证了理论分析的正确性。

一种斜坡补偿电路的设计

阐述在采用电流模为控制架构的开关电源电路中,需要引入斜坡补偿电路来避免因系统占空比大于50%以后,而带来的次谐波振荡。提出一种全程斜坡补偿办法,通过负反馈结构,实现线性补偿。

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose （SV） mode, is studied by a direct numerical simulation （DNS） method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous （SS） low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing ＋~. When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.

The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus Gs=10MPa and shear viscosity μs=1.49N.S/m^2 are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church＇s model theoretically and experimentally. Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.

ON SECONDARY INSTABILITY WITH RESPECT TO THREE DIMENSIONAL SUBHARMONIC DISTURBANCES IN BOUNDARY LAYER

The general equations of secondary instability with respect to three-dimensional subharmonic disturbances are derived and applied to Blasius boundary layer in the present paper.The theoretical results of evolution and spatial distribution of subharmonic disturbances are compared with experimental data.The re- suits show the important role of the process of route to transition in low-disturbance environments,and indi- cate that spatial mode is more rational than temporal mode.

Observations of near-inertial waves induced by parametric subharmonic instability

Near-inertial waves(NIWs), which can be generated by wind or the parametric subharmonic instability(PSI) of internal tides, are common in the South China Sea(SCS). Moored current observations from the northern SCS have revealed that the PSI of semidiurnal(D_2) internal tides is another source of NIWs. The objective of this study was to examine the energy variance in the PSI of D_2 tides. The PSI of D_2 internal tides generated NIWs and waves with frequencies around the difference frequency of D_2 and f. The observed NIWs induced by PSI could be distinguished clearly from those elicited by typhoon Krosa. Shortly after Krosa entered the SCS, NIWs began to intensify on the surface and they propagated downward over subsequent days. The near-inertial currents were damped quickly and they became relatively weak before the waves were reinforced beneath the mixed layer when wind stress was relatively weak. Rotation spectra indicated an energy peak at exactly the difference frequency D_2–f of the NIWs and D_2, indicating nonlinear wave-wave interaction among D_2, f, and D_2–f. Depth-time maps of band-pass fi ltered velocities of D_2 –f showed the waves amplifi ed when the NIWs were reinforced, and they intensifi ed at depths with strong D_2 tides. The energies of the NIWs and D_2 –f had high correlation with the D_2 tides. The PSI transferred energy of low-mode D_2 internal tides to high-mode NIWs and D_2–f waves. For the entire observational period, PSI reinforcement was observed only when mesoscale eddies emerged and when D_2 was in spring tide, revealing a close connection between mesoscale eddies and NIWs. Mesoscale eddies could increase the energy in the f-band by enhancing the PSI of D_2 internal tides. Thus, this represents another mechanism linking the energy of mesoscale eddies to that of NIWs.

1/2 SUBHARMONIC RESONANCE OF A SHAFT WITH UNSYMMETRICAL STIFFNESS

The 1/2 subharmonic resonance of a shaft with unsymmetrical stiffness is studied. By means of the Hamilton's principle the nonlinear differential equations of motion of the rotating shaft are derived in the rotating rectangular coordinate system. Transforming the equations of motion from rotating coordinate system into stationary coordinate system and introducing a complex variable, the equation of motion in complex variable form is obtained, in which the stiffness coefficient varies periodically with time. It presents a nonlinear oscillation system under parametric excitation. By applying the method of multiple scales (MMS) the averaged equation, the bifurcating response equations and local bifurcating set are obtained. Via the theory of singularity, the stability of constant solutions is analyzed and bifurcating response curves are obtained. This study shows that the rotating shaft has rich bifurcation phenomena.

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions(that is, all its Floquet multipliers lying on the unit circle on the complex plane C).

HETEROCLINIC ORBIT AND SUBHARMONIC BIFURCATIONS AND CHAOS OF NONLINEAR OSCILLATOR

Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

The 1：2 subharmonic resonance of the labyrinth seals-rotor system is inves- tigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics （CFD）. Based on the multiple scale method, the 1：2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated.The analysis is based on a special Zhuravlev transformation,which reduces the system to the one without impacts or velocity jumps,and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses.The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset.A perturbation-based moment closure scheme is proposed for the case of nonzero offset.The effects of damping,detuning,and bandwidth and magnitudes of the random excitations are analyzed.The theoretical analyses are verified by the numerical results.The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

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.

Observations of semidiurnal M 2 internal tidal parametric subharmonic instability in the northeastern South China Sea

Near-diurnal vertically-standing waves with high vertical wavenumbers k z were observed in the velocity and shear fi elds from a set of 75-d long ADCP moored in the northeastern South China Sea(SCS)away from the“critical”latitude of 28.8°.These enhanced near-diurnal internal waves followed a fortnightly spring-neap cycle.However,they always happened during semidiurnal spring tides rather than diurnal springs although strong diurnal internal tides with the fortnightly spring-neap cycle were prevailing,suggesting that they were generated via subharmonic instability(PSI)of dominant semidiurnal M 2 internal tides.When two semidiurnal internal tidal waves with opposite vertical propagation direction intersected,both semidiurnal subharmonic and super harmonic waves were largely intensifi ed.The observed maximum diurnal velocity amplitudes were up to 0.25 m/s.The kinetic energy and shear spectra further suggested that frequencies of daughter waves were not always perfectly equal to M 2/2.The superposition of two daughter waves with nearly equal frequencies and nearly opposite k z in a PSI-triad leaded to the vertically-standing waves.

BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE

Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.

1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES

The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.

A 1/3 PURE SUBHARMONIC SOLUTION AND TRANSIENT PROCESS FOR THE DUFFING'S EQUATION

The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.