临界阻尼

Because the central difference method is conditional stable, the critical time step and damping were estimated by model analysis, which can guarantee the computation stability. In this paper, the mesh method was used to described the tool surface.

由于中心差分法的计算是有条件稳定，作者对确定系统临界时间步长和阻尼系数的方法进行了研究，采用模态分析理论估计临界时间步长和阻尼，保证了计算的稳定性。

Numerical method is used to investigate the bogie's ateral stability under diverse nonlinear factors. The influence of nonlinearities and conicity on the critical speed is investigated. The nonlinear forces considered in the bogie system include creep-force between the rail and wheel, longitudinal damping and the flange contact force.

利用数值方法研究了不同非线性力作用下转向架的横向稳定性，得到轮轨饱和力、蠕滑力、纵、横向阻尼力、轮缘死区接触力、踏面斜率以及轮轨间隙对转向架系统线性、非线性临界速度的影响规律。

The amplitude has a critical value in its effect on BBD damping, when the amplitude is in excess of the critical value, the damping property of BBD is very good, otherwise, the damping property of BBD is poor.

振幅对BBD阻尼特性的影响有一临界值，当振幅大于此临界值时，BBD的阻尼性能迅速增大，而当振幅小于此临界值时，BBD的阻尼性能较小。

In the spark, operating under the critical damping state, with flash time at about 2 X 10-6 Sec., the ion lines of higher excitation potential first appear and appear shortly.

在放电时间约为2×10~(-6)秒，工作于临界阻尼状态下的火花中，激发电位高的离子线先出现，而且很短暂。

Wind-induced vibration Fluid-structure interaction Added mass Aerodynamic damping Critical wind velocity

风致振动；流固耦合作用；附加质量；气动阻尼；临界风速

A value of one corresponds to a critically damped system.

阿的一个值对应的临界阻尼系统。

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。

As the Coulomb friction of the damper is increased, the vibration amplitude of the rotor system is decreased near the undamped critical speeds, but is increased in a range between the first and the second undamped critical speeds.

随着磁流变液阻尼器的库仑阻尼力的增大，支承在磁流变液阻尼器上的转子系统在无阻尼临界转速处振幅明显下降，但在两阶无阻尼临界转速之间的一定转速区振幅反而增加。

The analysis results indicate that the vibration fractional factor with rotating frequency has a close relationship with both rotating speed of rotor and damping of bearing under constant acceleration. When rotating acceleration is small and damping is large, the transient response is not sensitive to the variation of rotating speed; otherwise the imbalance response with constant acceleration and the response in stable state will build up obvious differences near critical rotating speed.

研究结果表明：在恒加速条件下，转子同频振动分量与转子的转速、支承阻尼等因素密切相关，当角加速度较小且阻尼较大时，其瞬态响应对转速的波动不敏感；而当角加速度较大或阻尼较小时，恒加速过程不平衡响应与稳态响应在临界转速附近将产生明显的差异。

The results show that nonlinear dry friction between mandril and tube conduces to the self excited vibration of tube and the drawing speed is the main factor which determines whether the mandril static balance is stable.

分析结果表明，抖纹产生的主要原因是芯棒与钢管之间的非线性干摩擦力导致芯棒产生自激振动；钢管的拉拔速度及钢管表面润滑层的好坏是决定芯棒的静平衡位置是否稳定的关键因素，提高拉拔速度可将干摩擦阻尼转化为粘性阻尼，同时也使拉拔速度远离临界速度，从根本上消除抖

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。