通过具体的碰摩故障诊断实例，对比分析了经典线性方法的局限和多尺度非线性方法的优势。
Based on the specific diagnostic cases of impact-rub fault, the limitation of classical linear method and the advantage of multidimensional method are analyzed by comparison.
首先，用多尺度法导出弱非线性强迫激励系统的频率响应函数。
Firstly, by means of multiple scale method the frequency response function of weakly nonlinear vibration system is derived.
针对其时变、非线性以及长相关性等特点，提出一种多尺度分解的VBR视频业务的特征提取方法。
As to the time variation, non-linearity and long range dependence in VBR video traffic trace, a novel method of feature based on multi-scale decomposition was proposed.
再次，利用多尺度法分析船舶在波浪中接近主共振、亚谐共振和超谐共振时的非线性横摇运动，并给出三种共振的近似解。
Moreover, the multiscale method was used to study the main, ultraharmonic and subharmonic resonances of nonlinear rolling in waves, and the approximate solutions of the three resonances were given.
应用多尺度法得到了超磁致伸缩换能器几何非线性振动系统响应的解析解和频响特性表达式。
Then, the analytic solution of the geometrical nonlinear vibration system and the frequency-response properties of the actuator were analyzed by using multi-scale method.
作为具体问题，采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。
As an example, an approximate analytic solution of nonlinear vibration for a plate strip in lateral magnetic field is obtained by the multi-scale method.
利用多尺度法研究了三个频率激励下滞后非线性系统的组合共振，得到了该系统产生的组合共振解的振幅和频率。
This paper investigates bifurcation and combination re sonance of the hysteretic nonlinear system with three-frequency excitation by Multi-scale Method.
气固系统由于其时空多尺度结构和非线性非平衡特性特征，其机理还远未认识清楚。
Due to the nonlinear and nonequilibrium characteristics and the temporal-spatial multiscale structures, the mechanism behind gas-solid systems are far from fully understood.
建立非线性转子系统运动方程，利用多尺度法求得频率响应方程。
The motion equation of nonlinear rotor-bearing system is established and the frequency responding equation is obtained by multiple-scales method.
以轴向基础窄带随机激励悬臂梁非线性动力学方程组为分析对象，采用多尺度法，获得了系统主参激共振的非线性调谐方程组。
The method of multiple scales was used to solve directly the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance.
以轴向基础窄带随机激励悬臂梁非线性动力学方程组为分析对象，采用多尺度法，获得了系统主参激共振的非线性调谐方程组。
The method of multiple scales was used to solve directly the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance.
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