Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section

In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically not tackled directly, but instead a 1D scalar model known as the telegraphist's model is used. We aim at justifying, by means of asymptotic analysis, a time-domain “homogenized” telegraphist's model. This model, which includes a nonlocal in time operator, is obtained via asymptotic analysis, for a lossy coaxial cable whose cross section is not homogeneous.     

端部激励相位差下斜拉索的非线性振动

斜拉桥中拉索承受着多种端部激励,可激发大幅空间振动．以斜拉索为对象,探究不同端部激励间相位差对其非线性振动的影响．首先,推导斜拉索无量纲离散控制方程,引入考虑相位的三向端部激励得到一般化模型;然后,针对拉索下端存在的纵桥向、竖向和横桥向激励的两两组合,受大幅或小幅激励,及其在主共振区或主参数共振区几组因素,共计12种工况,采用数值分析法分别研究了各工况下不同激励相位差时的斜拉索稳态响应．研究发现：激励相位差能加剧与激励频率相近的面内、外模态振动;在任意端部激励组合下,激励相位差不仅可使斜拉索非线性振动出现定量变化,还可改变内共振的表现形式．面内、外激励组合下,相位差对拉索响应幅值的影响以π为周期变化,且当相位差趋于π/2 + kπ (k = 0, 1, 2…)时影响最为突出;而面内激励组合下,以2π为变化周期,当相位差为π + 2kπ (k = 0, 1, 2, …)时其对稳态幅值的影响最显著．其原因是：面外激励关于拉索所在的竖直面对称,故其本质上以π为周期;而面内激励无此对称性,仍以2π为周期．因此,有无面外激励参与决定了激励间相位差对斜拉索响应的影响规律．     

悬索大挠度风振响应的有限体积法分析

基于Lagrange原理,建立了一套新的悬索大挠度动力特性和动力响应分析的有限体积法列式,推导了结点力向量、质量矩阵和单元刚度矩阵的显式表达式。该列式的一个显著特点是直接利用工程应变定义结构变形,其物理意义明确,列式简单,适用于各种垂度和荷载情况的悬索大挠度动力分析。实例动力特性和随机风振响应分析表明,该有限体积列式不仅计算效率高,而且具有良好的计算精度。     

张力对斜拉桥拉索镀锌钢绞线腐蚀行为影响

应用伏安极化法和中性盐雾腐蚀试验研究了张力作用下斜拉桥拉索镀锌钢绞线在5%NaC l溶液中腐蚀行为.腐蚀产物理化性质由XRD、TG-DTA等测试表征.结果表明,镀锌钢绞线的腐蚀电流,即腐蚀速率随试验前施加的张力增加而增大,其产生白锈的盐雾试验周期小于1,经15~22 kN张力作用后的镀锌钢绞线,产生红锈的盐雾试验周期为16,而经0、10 kN张力作用的钢绞线,产生红锈的周期则延长至23,钢绞线腐蚀产物主要是Zn5C l2(OH)8.H2O、Zn4(CO3)(OH)6.H2O和ZnO.     

Development of superconducting power devices in Europe

Europe celebrated last year (2008) the 100-year anniversary of the first liquefaction of helium by H. Kammerling Onnes in Leiden. It led to the discovery of superconductivity in 1911. Europe is still active in the development of superconducting (SC) devices. The discovery of high critical temperature materials in 1986, again in Europe, has opened a lot of opportunities for SC devices by broking the 4 K cryogenic bottleneck.     

预应力钢梁体外索的张力增量分析

将预应力钢梁看作梁与索的组合结构,充分考虑了二者之间的相互作用．利用变分原理推导出在外荷载作用下,体外索张力增量的计算公式,并通过预应力钢梁模型试验对计算结果进行了验证．     

Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part II: Global Analysis

The nonlinear dynamics of the same experimental model of an internally resonant hanging elastic cable considered in Part I [1] are addressed here from the point of view of the global system behaviour in the control parameter space. Synthetic results of systematic response measurements, made at different amplitudes of the support motion in frequency ranges including meaningful external resonance conditions, are reported and discussed. Attention is devoted to the detection of the most robust classes of motion. Quite complicated overall pictures of regular response regions with variable contributions from different planar and nonplanar cable modes are observed, as well as several regions of quasiperiodic and chaotic responses. Sample quantitative characterizations of nonregular motions are presented. Some experimental results are also observed against the background of the nonlinear dynamic phenomena exhibited by a theoretical model of a continuous cable with four-degrees-of-freedom.     

斜拉索模态试验参数研究

试验模态分析是斜拉桥索力测试中广泛应用的方法。该方法的关键之一是采取合理的试验方案获取可靠的响应信号以识别出正确的索振动频率。本文通过试验,详细讨论了斜拉索模态测试中若干试验参数,如激振类型、激振位置、传感器位置以及频率分辨率对试验结果的影响;比较环境激励与锤击激励的效果,验证了环境激励的方法也可以准确识别索的频率;最后给出了较为合理的斜拉索模态试验方案,用该方案确定的索力与理论计算结果相差不超过 1. 5%。     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated.