谐振

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

The stealth warplane for the microwave radar usually have complicated structures with the coating of wave absorption. On the base of calculation and modeling of the geometrical structure of the warplane in real size, the HF RCS of the air crafts under two different polarizations in different direction have been calculated with the FDTD. The result shows that the above mentioned stealth warplane have the obvious characterstics of frequency resonance, polarization and the relatively large RCS in HF Band 10-30dBm2, which can be used as the theoretical reference for selection of working frequency for sky wave OTH Radar and it also means that the sky wave OTH radar has good capability of anti-stealth targets quantitatively.

对微波雷达具有隐身作用的飞机，其形体较为复杂且表面涂敷有强吸波材料在对一种具有隐身几何外形结构实际尺寸飞机进行计算建模的基础上，文中采用FDTD技术得到了两种极化状态下该飞机无涂敷时不同方向上的短波雷达截面RCS值其结果显示了这种隐身几何外形飞机在短波波段有明显的频率谐振特性、极化特性和较大的RCS10-30dBm2，可为天波超视距雷达在选择工作频率时提供理论参考，并定量地说明天波超视距雷达具有较优的反隐身目标能力

Based on the analysis of some configurations of the lossless snubber circuit, a lossless snubber circuit topology is proposed, corresponding theoretical analysis, simulation and experiment on IGBT is carried out.

在对已有的无损耗缓冲电路分析基础上提出了一种适用于IGBT的谐振无损耗缓冲电路的拓扑结构，并进行了理论分析和实验研究。

The solar plexus,ie the network of nerves in the abdomen

太阳神经丛。新出现的电网谐振。

The influence of the pump power and laser beam radius on the spherical aberration coefficient is discussed.

实验验证了球差效应对激光谐振腔中基模光束质量的影响，与理论分析符合得很好。

The spherical aberration of thermal lens of the active media influences the mode profile, the single-pass loss, the output power and other properties of a laser system.

激光晶体热透镜的球差效应会影响谐振腔的输出光束质量，以及腔内损耗和输出功率等特性。

It is found that the levitation force can be remarkably enhanced by choosing optimum value of R or D, and the possibility of this enhancement for spherically curved reflectors is the largest.

发现通过选择最优化的R或D值，可以显著提高声悬浮力，并且谐振模式数越小，反射端截面半径越大，提高的程度就越大。

These results further extend the applicability of SR in signal processing.

这些结果进一步拓展了随机谐振在信号处理中的应用。

In order to get a better effect of standing wave, the ...

为了获得比较好的驻波效果，超声传感器采用了发射和接收双头结构，双头通过谐振杆成90度垂直安装。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。