在此基础上，用多尺度法求得稳态下主共振的分岔方程。
A bifurcation equation of the steady state main resonance was obtained based on the multiple scales method.
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.
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.
应用多尺度法求得了系统主共振情况的一次近似解，并进行了数值计算。
By means of the method of the multiple scales the first approximate solution of the primary resonance of the system is acquired, and numerical calculation is carried out.
应用多尺度法求得了系统主共振的分岔方程和不同参数下的主共振响应曲线。
The bifurcation equation of the primary resonant of the system is acquired by the method of multiple scales.
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.
采用多尺度法研究拉索大幅振动的各种可能性，运用精细时程积分法数值求解振动方程。
The multiple scale method (MSM) is introduced to analyze the characteristics of cable's vibration, and the precise time-integration method (PTIM) is used to solve vibration equations.
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.
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.
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.
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.
本文采用新的弹性约束项，得到的优化方程不但容易计算而且有明确的物理意义，本文讨论了用有限差分法解这个方程的方法，对于复杂形状的轮廓匹配可以用多尺度法来解决。
The solution method is based on a finite difference approach, for which we present convergence characteristics. A multi-smoothing scheme is proposed to improve the convergence of the matching process.
作者利用信号的小波变换在多尺度边沿上的综合特性，提出了一种新的QRS波检测法。
A new adaptive matching filtering algorithm, based upon synthetic characteristics of wavelet transform of signal along margins of various scales for QRS detection, is developed.
代表性体积元法是研究复合材料这类具有多尺度、离散分布多相体的有效手段。
Representative volume element (RVE) is an effective method for analyzing composites with characters of multi-scale and random distribution.
在此基础上研究了利用等式约束与不等式约束的惩罚函数法对平面多杆机构进行尺度最优综合的有关问题。
Some problems of optimum synthesis of planar multi-bar linkages are studied by the penalty function method with equality and inequality constraints.
为求解二维的奇异摄动反应扩散边界层问题，研究了新的多尺度有限元法。
The multi-scale finite element method is applied in the 3-D groundwater flow simulation problems in heterogeneous porous media.
本发明公开了一种基于多尺度线调频基稀疏信号分解的齿轮故障诊断方法。
The invention discloses a gear fault diagnosis method based on multiscale linear frequency modulation-based sparse signal decomposition.
本发明公开了一种基于多尺度线调频基稀疏信号分解的齿轮故障诊断方法。
The invention discloses a gear fault diagnosis method based on multiscale linear frequency modulation-based sparse signal decomposition.
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