非线性振动

The forced oscillators have been investigated with the use of the conjugated arithmetic operators and the matrix of the normal form theory.

第三章将非线性系统转换为一个四维的一阶系统，再进行非线性变换，将规范形理论中的共轭算子法和矩阵表示法联合一起应用，研究了强迫振动问题。

We take sech form ansatz and solve the CNLS equations through variational approach. We obtain the analytical expression of nonlinear coupling term, which is in the lagrangian of CNLS. We apply a potential well model to analyze the interaction properties of self-trapping beams in detail, the results show that the interaction do not change the profile of the beams, two beams keep oscillating around their collective center periodically. The amplitude and period of this oscillation are both determined by initial separation of two beams.

我们采用Sech函数为试探函数，用变分法求解CNLS方程，（1）给出了CNLS方程所对应的拉格朗日中的非线性耦合项的解析表达，（2）利用势阱模型详细分析两自陷光束之间相互作用的特性，结果表明，相互作用没有改变孤子的形态，它们分别在与传播方向垂直的方向上绕它们的公共中心做往复振动，振动幅度及周期都取决于两光束的初始分隔。

The dissertation studies the phenomena and characteristics of self-excitation, deduces those phenomena belong to nonlinear non-conservative autonomous steady-state periodic movement.

本文分析研究了轧机主传动系统自激振动的现象和特点，得出轧机主传动系统的自激振动现象属于非线性非保守自治系统的稳态周期运动。

Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘要基于大位移非线性弹性理论的广义变分原理，考虑加劲梁轴向压缩应变能和剪切应变能的影响，建立了协作体系斜拉桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了协作体系斜拉桥的加劲主梁竖向挠曲振动微分方程。

The nuclear of the method is the newly developed HHT for nonstationary and nonlinear time series analysis, which consists of the Empirical Mode Decomposition and Hilbert Spectral Analysis.

该方法对桥梁结构健康性的最终判断依据是基于数据的非线性特征、自由振动和强迫振动的频率对比、桥梁对轻荷载及重荷载的响应。

On the assumption that the unevenness of runway profiles along the direction of taxi - ing is a stationary random function,techniques of piecewise constant-speed taxi ing runs and piecewise linear representation of dynamic properties of airplane landing gears are adopted in this paper to approximately simplify the actual nonlinear and nonstationary random vibration prob-lems to the piecewise linear and stationary ones.

在飞机滑行方向跑道路面不平度为平稳随机函数的假设下，采用滑行过程分段等速化、起落架动态特性分段线性化方法，把原非线性非平稳随机振动问题，简化为分段线性平稳随机振动问题。

The analytical result of this paper provides electric machine with the condition of 1/2 subharmonic resonance under the electromechanical electromagnetic forces.

建立了电机转子机电耦联的非线性数学模型，研究了由电磁力激发的参数振动非线性系统的响应曲线，揭示了各种电磁参数及机械参数对共振的影响。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

The nonlinear is incarnated when the ball is rolling respectively on three concaves. The track driven by motor is in simple harmonic vibration, and the frequency and amplitude of simple harmonic vibration of the track can be considered as adjusting parameters.

以滚球在3个凹形槽上的受力体现作用的非线性，导轨由电机推动作简谐振动，滚球在导轨上作受迫振动，可以把导轨作简谐振动的频率或振幅作为调整参量。

Numerical simulations by assemblies of circular panicles can qualitatively reflect the general characteristics of liquefaction behavior of sand. The interval effect of aspect ratio of elliptical panicle on the mechanical behavior of numerical sample is obtained, and the reason is related to the initial average co-ordination number. The regularity of evolution of fabric in the process of sand liquefaction under cyclic loading can be qualitatively achieved by using the numerical sample randomly mixed of panicles with different shapes. Numerical simulations can not only demonstrate the macro phenomenon of particle breakage, mostly importantly, it can also expose the evolution of particle breakage microscopically, and would contribute to further research of the micromechanics of particle breakage.

研究结果表明：Hertz-Mindlin非线性接触模型适用于变围压条件下砂土力学性质模拟；纯圆颗粒模拟能够定性地反映饱和砂土振动液化的一般规律；颗粒长短比变化对砂土力学性质的影响具有区间效应，其原因与粒间初始平均接触数有关；不同形状随机混合试样能够从定性规律上反映振动液化过程中砂土的细观组构演化规律；数值模拟不仅可得到颗粒破碎宏观响应，而且可以分析内部接触力变化和实现对粘结破裂位置的追踪，从而可进一步研究颗粒破碎细观力学机制。

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。