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nonlinear analytical solution 非线性解析解
By means of the equivalent nonlinear system met hod, the analytical solution of the joint probability density function of steady- state responses of Coulomb sliding friction rigid structures to vertical Gauss ian white noises is derived. 运用等效非线性系统法推导了库伦摩擦刚性滑移结构在竖向高斯白噪声地面作用下响应的稳态合概率密度函数的解析解。
From the variation principle,an analytical solution of the tangential stiffness matrices with nonlinear effects geometrically, for two-nodal two-dimension curved beam element, has been derived. 利用变分原理，推导了两节点二维曲梁单元几何非线性的单元切线刚度矩阵。
The approximate analytical solution is got by using perturbation method. 通过扰动方法求得问题的近似解析解。
Numerical and analytical solutions are presented. 文章中同时提出解析解与数值解。
An average method is applied to the nonlinear diffusion equation to obtain nonlinear analytical models for the index profiles of two-step ion-exchange splitters. 介绍了在用两步离子交换方法制作光功分器中,在高斯分布为初始条件下采用平均法求出非线性两步离子扩散方程的折射率分布,与实验测出的折射率分布符合得很好。
The comparison between analytical solution and uncorrected solution shows that uncorrected truncation errors can not be ignored. 通过解析解与没有修正的差分解进行对比，结果表明，没有修正的截断误差是不能忽略的。
CAI Ruixian.Derivation of explicit analytical solutions for nonlinear unsteady compressible isentropic flow[J].Chinese Journal of Engineering Thermophysics,2001,22(2):159. [2]蔡睿贤.;非定常可压等熵流非线性方程显式解析解的推导[J]
In Section 2.3,we compute the two-order approximate analytic solution of nonlinear Schrodinger equation. dinger方程一阶近似解析解;在2.;3节;给出了非线性Schr(?)
An analytical solution for one dimensional diffusion of VOCs through composite liners was presented. 本文建立了有机挥发性化合物在复合衬里中的一维扩散模型，并得到了解析解。
Analytical Solution for Passive Q Switching with Cr Ion Doped Saturable Absorber[J]. 引用该论文吴念乐;吕亚军;陆兴华;李家强;李师群.
An analytical solution for the coefficient of restitution of a mass colliding with a slender rod or beam was presented. 给出了物体与细长杆或梁弹性碰撞恢复系数的一种求解方法。
This paper gives out the analytical solution for the quasilinear system of partial differential equations. 本文给出了这两个拟线性偏微分方程组的定解问题的一个求解方法及解析解表达式。
An analytical solution was developed to study the sheltering effect on arc-shaped floating breakwaters. 给出了圆弧型浮式防波堤防浪效果计算的解析方法。
This paper derives stress and strain analytical solution with Lode parameter of deformation zone onround hole flanging. 推导圆孔翻边变形区参数型(罗代参数)的应力和应变的解析解。
An analytical solution for a tunnel in the saturated ground considereding the hydromechanical coupling is obtained. 本文利用解析法给出了饱和孔隙介质地层中考虑地下水渗流力作用下的应力，位移表达式；
The comparison with analytical solutions obtained by other approaches shows that the variational approach is one of the efficient methods in analysing the beam evolution in nonlocal nonlinear media. 通过与其他方法得到的解比较表明，变分法是解析讨论光束在非局域非线性介质中演化规律的方法之一。
Solving the corresponding differential equation, an analytical solution for the surface crack width of concrete covers is derived. 通过求解相应的微分方程，导出混凝土保护层表面裂缝宽度的解析解；
This paper derives stress and strain analytical solution with Lode parameter of deformation zone on round hole flanging. 摘要推导圆孔翻边变形区参数型（罗代参数）的应力和应变的解析解。
The analytical solution of roadway discharge is given,under the condition of rock permeabillty attenuation with mining depth increase. 给出了在岩石渗透性随深度衰减条件下，二维稳定流巷道涌水量的解析解。