APPLICATION OF CYCLOSTATIONARY PROPERTIES OF PERIODIC SIGNALS FOR POWER ANALYSIS IN ELECTRIC CIRCUITS

Предложен циклостационарный подход к анализу мощности электрических цепей, возбуждаемых источниками периодических токов и напряжений. Получены теоретические выражения для характеристик мгновенной мощности на основе взаимной спектральной ковариационной функции и показана их связь со средней и полной мощностью. Проведен анализ гармонического распределения мощности в линейной цепи при периодическом воздействии. На примере численного расчета резонансной цепи продемонстрированы этапы циклостационарного анализа и получены основные характеристики мощности. The paper proposes a cyclostationary approach to the power analysis for electric circuits excited by sources of periodic currentsorvoltages.Theformalexpressions forcharacteristics of instantaneous power are obtained on the basis of cross spectral covariance function and their relation to the average and apparent power is established. The analysis of the harmonic distribution of the power in a linear circuit under periodic excitation is carried out. The main stages of the method are illustrated with a numerical simulation example.

Nonlinear Dynamics of Suspended Cables under Periodic Excitation in Thermal Environments: Two-to-One Internal Resonance

The temperature change is a non-negligible factor in examining the vibration behaviors of the cable structures. For this reason, the paper aims at investigating the thermal effects on suspended cables’ resonant responses considering two-to-one internal resonances. Firstly, a nonlinear continuous condensed model of the suspended cable under periodic excitation in thermal environments is adopted. Then, a multidimensional discretized model is constructed via the Galerkin method. Following the multiple scaling procedure, the modulation equations with both polar and Cartesian forms are obtained, which are solved numerically. A complete dynamic scenario is presented through bifurcation diagrams, phase portraits, time history curves, Fourier spectra, and Poincaré sections in three internal resonant cases. Numerical examples show that a small change in the static configuration due to thermal effects induces some noticeable changes in dynamic behaviors. The response amplitude, the nonlinear spring behavior, the resonant and stability region, the multi-periodic and chaotic motions are all dependent on temperature changes. Additional Hopf bifurcations might be found due to temperature changes, and it may lead to some more complicated dynamic characteristics. A good agreement between the perturbation and numerical solutions is observed to confirm the results’ correctness and accuracy.

Two-Color TeraHertz Radiation by a Multi-Pass FEL Oscillator

In this paper, we show that an electron beam produced by a super-conducting linac, driven in a sequence of two undulator modules of different periods, can generate two-color Terahertz radiation with wavelengths ranging from 100 μm to 2 μm. The generated pulses are synchronized, both MW-class, and highly coherent. Their specific properties and generation will be discussed in detail. Besides the single-spike pulse structure, usually observed in oscillators, we show that both the THz pump and probe can be modulated in a coherent comb of pulses, enabling periodic excitation and stroboscopic measurements.

Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing–Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow-varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow-varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold/fold bursting, symmetric fold/supHopf bursting, symmetric subHopf/fold cycle bursting, and symmetric subHopf/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.