1) the method of multiple scales
多尺度法
1.
By means of the method of multiple scales for nonlinear oscillations the approximation solution of primary parametric resonance of the system is acquired.
应用非线性振动的多尺度法求得系统主参数共振的近似解,并进行数值计算。
2.
By means of the method of multiple scales for nonlinear oscillations, the first approximate primary parametric resonance of the system is acquired.
应用非线性振动的多尺度法求得系统满足主参数共振条件的一次近似解,并进行数值计算,分析定常解的稳定性。
3.
By means of the method of multiple scales the approximation solation of primary Parametric resonance of the system is obtained.
应用弹性理论和Galerkin方法建立Winkler地基梁在温度场中受简谐激励作用的非线性动力方程,应用非线性振动的多尺度法,求得系统主参数共振的近似解。
2) Method of multiple scales
多尺度法
1.
By means of the method of multiple scales for nonlinear oscillations,the approximate solution of primary resonance of the system was acquired,and a numerical analysis was carried out.
应用非线性振动的多尺度法,求得系统主共振的近似解,并进行了数值计算。
2.
By using the method of multiple scales for nonlinear vibration analysis, the first approximate solution of 3 superharmonic resonance of the system is obtaind.
本文研究W inkler地基梁在温度场中受简谐激励作用的3次超谐共振问题,应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程,根据非线性振动的多尺度法求得系统满足3次超谐共振情况的一次近似解,分析了温度、阻尼、激励幅值、地基刚度等参数对系统的影响。
3.
Applying the method of multiple scales for nonlinear vibration, the first approximation solution of primary parametric resonance an.
根据非线性振动的多尺度法求得系统主参数共振-主共振情况的一次近似解,并进行数值计算。
3) multiple scale method
多尺度法
1.
The motion equations of stay cables, which are established based on Hamilton’s principle, are solved approximately using the multiple scale method.
基于Hamilton原理,建立了斜拉索由桥面侧振引起的非线性振动方程,并运用多尺度法求得该方程的近似解析解。
2.
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.
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。
3.
Based on the nonlinear governing equations got from Hamilton principal in a non inertial system, by using Multiple Scale Method and incremental IHBM Method,the nonlinear parameter vibration of single axle rotating truncated conical thin shells is discussed in the case of different driving source which are rotating angular acceleration and axial exciting force.
基于 Hamilton原理推出的非惯性系下的截锥壳的运动控制方程 ,利用多尺度法和增量型谐波平衡法分别讨论了转角加速度和轴向激振力为激振源的单轴转动截锥壳的非线性参数振动 ,并对结果进行了讨论。
4) multiple scales method
多尺度法
1.
The multiple scales method of Kuzmak-Luke was firstly applied to obtain the periodicity condition of solutions of strongly nonlinear oscillators with generally nonlinear spring, and then Jacobian elliptic functions were used to express the leading .
本文首先应用KuzmakLuke的多尺度法得到有一般非线性弹性力的强非线性振动系统解的周期性条件及用Jacobi椭圆函数表示的平方非线性振动和立方非线性振动的首阶渐近解。
2.
The mathematic model of contact system’s nonlinear vibration characteristics was built and the frequency-amplitude property of each order bending mode was solved by using multiple scales method.
接触系统的抖断是电磁继电器在振动环境条件下的主要失效模式,通过建立接触系统的非线性振动特性分析数学模型,进而应用多尺度法求解得到了各阶弯曲模态对应的频响关系,确定了系统所具有的软弹簧特性,并由此分析了激振力、触头初压力、触头曲率半径以及触头质量等参数对于振动特性的影响规律。
3.
Based on multiple scales method for nonlinear vibration analysis,the first approximation solutions and their corresponding steady state solutions to the primary resonance system were obtained.
根据非线性振动的多尺度法,得到系统满足主共振条件的一次近似解以及对应的定常解。
5) multi-scale method
多尺度法
1.
The non-linear vibration of coupled structure is analyzed with the multi-scale method,and by means of Runge-Kutta s method,the numerical solutions of the differential equations at the frequency ratio of 2:1 are obtained.
研究了在惯性参考系中弹性斜拉索与悬臂梁耦合结构的非线性振动问题,利用Hamilton原理建立了索-梁耦合系统的非线性动力学方程,利用Galerkin方法将索-梁耦合系统的非线性运动偏微分方程离散为一组常微分方程,然后利用多尺度法分析研究索-梁耦合动力学系统的非线性振动,用Runge-Kutta法对数学模型进行数值计算,同时探讨了各种参数对索-梁耦合系统非线性振动的影响,并提出对工程有实际意义的结论。
2.
The equation,on the basis of the mixed linear-plus-cubic damping model and mixed linear-plus-cubic restoring model of nonlinear free rolling of ships,is solved with the multi-scale method of the perturbation theory,and then a complete analytical solution accurate to second-order is presented.
针对以线性加立方项的阻尼力矩和回复力矩模型为基础的非线性自由横摇运动方程,运用奇异摄动理论中的多尺度法,经繁复推导给出了完整的精确至二阶的解析解,解决了消除二阶非线性项中久期项的处理问题。
3.
The first order and second order approximations for steady state responses of the system under principal resonance are investigated with the multi-scale method.
运用多尺度法研究了系统主参激共振的一次、二次近似稳态响应。
6) multi-scale method
多尺度方法
1.
Employ multi-scale method to analyze the stress of thermal sprayed coatings;
用多尺度方法分析热喷涂层应力
2.
Advances in multi-scale method based on the bridging domain decomposition in computational materials science;
计算材料科学中桥域多尺度方法的若干进展
3.
This paper predicts the thermal conductivities,elastic modulus and the thermal expansion coefficients of composite materials with small periodic configuration based on multi-scale method.
基于多尺度方法预报了周期性复合材料的热传导系数、弹性模量和热膨胀系数。
补充资料：变尺度法
分子式：
CAS号：
性质：变尺度法是在解无约束极值问题的梯度法基础上发展起来的，它利用递推的方法计算目标函数的二阶导数及其逆阵，减少了计算量，同时比梯度法收敛快，是目前解决无约束极值问题的最有效的算法之一。
CAS号：
性质：变尺度法是在解无约束极值问题的梯度法基础上发展起来的，它利用递推的方法计算目标函数的二阶导数及其逆阵，减少了计算量，同时比梯度法收敛快，是目前解决无约束极值问题的最有效的算法之一。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条