非线性振动

The most common and most widely studied methods of all analytical approximation methods for nonlinear differential equations are the perturbation methods.

非线性振动由于其振动方程的特点，到现在还没有通用的解析求解方法，只能根据系统的特点采用一些特殊的方法来求解。

At the same time the velocity, acceleration and period of vibrating can be calculated by differentiation matrix and barycentric Lagrange interpolation, respectively.

同时，利用微分矩阵和重心Lagrange插值可以方便地求出非线性振动的速度、加速度和振动周期。

Obtaining the displacement of vibration, the velocity and acceleration are directly computed by differentiation matrices. The period of nonlinear vibration is computed by barycentric Lagrange interpolation collocation method.

计算得到振动位移后，采用微分矩阵和重心Lagrange插值计算非线性振动的速度、加速度和振动周期。

In this part, the characteristics of transient responses of flexible rotor systems with arbitrarily distributed mass on isotropic or anisotropic supports passing through several critical speeds seguencially are examined. Here, the current knowledge of rotor dynamics on the eigenproblem of damped free whirling vibration, the generaliged damped mode theary, the transient forced vibration and so on combined with KBM asymptotic method in the nonlinear vibration theory is employed and extended.

作者综合运用并引伸推广转子动力学关于阻尼自由回旋振动的特征问题、广义阻尼模态理论、瞬态强廹振动等現代理论和方法，结合非线性振动理论中的KBM渐近法，提出自己独創見解和覌点，成功地建立起正回旋和逆回旋两种情况下转子通过临界点的瞬态振动一阶微分方程组，可以在临界点的邻域内从事方程的数值积分计算。

And the effects of foundation displacement excitation,temperature,amplitude and asexternal damping on the nonlinear vibration of elliptic paraboloid cable net with the comparison between steel cable and carbon fiber cable were discussed.At last the conclusions are obtained that the temperature have great influence on steel cable and bat not on carbon fiber cable,and the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.

在把碳纤维索网与钢丝索网比较的基础上，讨论分析了位移激励、温度、振幅、外阻尼等因素对椭圆平面双曲抛物面碳纤维索网非线性振动的影响，得到了碳纤维索网对温度变化不敏感，而钢丝索网受温度的影响却很大，且碳纤维索网振动特性优于钢丝索网振动特性的结论。

Some topics for future research, such as nonlinear dynamical behavior of moving strings, vibration of moving viscoelastic strings, control of hybrid systems containing moving strings and control of nonlinear oscillations of moving strings, are suggested.

最后指出该研究方向今后需要研究的若干重要问题，包括运动弦线的非线性动力学行为、黏弹性运动弦线的振动、含运动弦线的混杂系统的控制和轴向运动弦线非线性振动的控制。

Through the Lagrange's equation,the nonlinear vibration equation of a particle non-harmonic oscillator is established;the curves of the restoring force and potential energy varying with coordinates and phase plot are drawn.

利用拉格朗日方程建立了单质点弹簧振子非线性振动方程，作出了回复力、势能随坐标的变化曲线以及相图。应用第一类完全椭圆积分求出了非线性振动周期的精确解。

But the researches on vibration characteristics of motor-driven elastic linkage systems have shown that the dynamic responses of linkage systems are nonlinear and multi-modality. They may bring some nonlinear vibration, such as superharmonic resonances, subharmonic resonances, multiple resonances, and combination resonances, under some circumstances.

然而，弹性连杆机构的非线性振动特性研究表明，机构的动态响应特性十分复杂，并且在一定条件下会产生超谐共振、亚谐共振、多重共振、组合共振等非线性振动行为，这些共振就会对以机构动态性能为目标的优化设计产生重要影响，而使优化设计工作常常只能得到一个局部最优值，甚至只是一个比初始设计略微好些的设计点。

And more seriously,an over complex analysis model may cause the structuralanalysis to be very difficult or even unrealizable.

如在大型复杂结构的振动模态分析、振动控制、非线性振动和响应等分析中，过于复杂的结构分析模型将使这些分析变得十分困难。

Considering of helical gear separate mesh and tooth-back shock, the non-linear vibration equitions of the system are also established, and the non-linear stable cycle solutions of the equitions are evaluated through dividing the timechanging stiffness matrics and dimension the equitions with selfadapt vary-step auto-RK4 numerical method.

考虑了斜齿轮传动的轮齿脱啮和齿后侧冲击，建立了系统的非线性振动方程，并通过对方程时变刚度阵的分块处理及无量刚化，用自适应变步长auto-RK4数值方法求出了系统非线性振动方程的稳态周期解。

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。