依据所建立的非线性模型，获得垂直入射纵波在非线性法向变形节理处传播的透射和反射系数的解析解。
Based on the established model, the analytic resolution of transmitted and reflected coefficients is obtained when the normal incident P-wave propagates to the nonlinear normal deformative joint.
说明采用七自由度单元的有限元法进行矩形截面简支梁的弯翘分析，有很高的精度，可以代替繁琐的解析解。
The result shows seven-freedom unit finite element method has high precision to analyse simple beam of rectangular section, it can replace complex analytic solution.
本章同样使用优级数法讨论一类带时滞的迭代微分方程解析解的存在性。
In this chapter, existence of analytic solutions of an iterative differential equation with state-dependent delays is studied by using a similar 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.
采用摄动法求得了其近似解，得到了载流梁在磁场中的横向固有振动频率及位移解析表达式。
The perturbation method was employed to get the control equation's approximate solution. The analytical expressions of beam's natural lateral vibration frequency and displacement were derived.
本文首次提出精确解析法，用以求解任意变系数微分方程在任意边界条件下的解。
In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary, boundary condition.
由于使用格林函数法求局部解析解，提高了计算精度。
Because of the use of Green - function method to solve local analytic solution, its accuracy is increased.
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.
针对机构模型建立了约束方程，利用解析法求解机构的位置正反解，并绘制出机构装配简图。
Constraint equation was established according to mechanical model, utilizing the analysis, solving the forward and inverse position solution, and drawing the mechanical assembling sketch.
将控制方程的线性化与调和平衡法组合起来，建立周期及周期解的解析逼近公式。
By combining the linearization of the governing equation with the method of harmonic balance, we have established analytical approximate formulas for the period and the periodic solution.
为预防微风振动对输电线路的破坏、有别于传统的能量平衡法，研究了微风振动的半解析解。
Differing from the traditional energy balance method (EBM), the aeolian vibration has been researched by the semi-analytical solution.
通过分析，针对混凝土材料，提出了可给出弹体减速度时间历程解析解的法向膨胀理论。
For concrete material, a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given.
爆轰波与惰性介质相互作用的计算。可以用解析解和作图法求解。
There are two methods, analytical and graphical, in calculating the interaction of detonation waves with a non-reactive medium.
本文用解析法和有限元法分析了连续多支承压杆的稳定性及其近似解与精确解。
This paper analyzes the stability of continuous and multi-support compressed pillars using analysing method and finite element method.
在复数域内利用分离变量法，得到了这类方程的级数形式的解析解，而最后的解是实数形式。
By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained.
采用可变长度单摆的力学模型对秋千振荡给出初等分析，采用微扰近似法导出了秋千的非线性参数共振解析解，并进行了讨论。
A variable length simple pendulum model is introduced, elementary analysis and perturbation analytic solution of nonlinear differential equation for parametric resonance are presented.
以位移模型为基础，用有限元中的分离变量法的理论，求解了圆柱壳自由振动的固有频率，计算结果与壳体解析解相一致。
This paper calculate inherent frequency of the free vibration of the cylinder shell with the theory of the separated variable method on the basis of displacement model.
采用加权平均法可以得到该方程的近似的解析解，同时提高了计算精度。
The analytical approximate solution of the equation is been obtained and the calculated precision is improved simultaneously by using the Weighted Average Method.
由于边界元法是半解析半数值解法。在解边界积分方程时会遇到解的存在与唯一性问题。
Because the boundary element method is half analytical and half numerical, there exist the problems of the existence and uniqueness of the solutions.
但这是一个涉及多个变量、多种响应的动态耦合过程，尚无法用解析法解算。
However, this is a dynamic coupling process involving several variables and responses, and has not been solved by analytical method yet.
将任意分布的电流源产生的电磁场看作是电偶极子产生的电磁场的叠加，利用镜像法推导了上半空间中的垂直直流电偶极子在两层媒质中产生电磁场的解析解。
The analytical expressions of the electromagnetic field generated by the DC electric dipole in the upper space for the two-layer mode were obtained by using the method of mirror image.
本文介绍了一种求解地下水流问题的有限分析法，该方法将解析解结合到数值方法中，从而提高了计算精度，改善了稳定性。
This paper introduces a finite analytic method of solving groundwater flow. This method combines analytic solution with numerical method, and can rise computational accuracy and improve the stability.
用蒙特卡洛法计算了平面二极管并与解析解进行比较，相对误差为0.8％；
The planar diode is calculated by means of MCM and compared with the analytical solution. The relative error is 0.8%.
本文应用特征线法给出一维爆震波在爆震管内的传播过程的解析解。
The paper used the characteristics line method to calculate the one-dimensional detonation wave propagation process inside a detonation tube.
应用谐波平衡法对系统三阶非线性微分方程组解析分析，与数值解比较验证了解析解的正确性和有效性。
The method of harmonic balance is applied to study the non-linear dynamic response of the third-order nonlinear partial differentiation system.
采用有限元-人工透射边界法求出平面波在无限长圆柱上的散射近场，并与解析解进行比较，进而对几种凹面体电磁波散射近场求解。
A finite element artificial transmitting boundary method is presented for electromagnetic wave scattering from a perfectly conducting circular cylinder and a number of concave objects.
用解析法求得了无限长园柱壳一边固定，另一边受力偶作用的精确解。
The exact solution of infinitely long circular cylindrical shell with one end fixed, the other end loaded by a couple is obtained.
利用待定函数法研究了非线性轨道微分方程的解析解，求出了一类情形下的四类解析解。
In this paper , the undermined function method has been used to study the analytic solution of nonlinear orbit differential equation. In a case four kinds analytic solution are given.
用简易坐标投影法计算了其位置分析的正、逆解析解。
The forward and inverse analytical solutions of its positional analysis were computed by the use of simple and easy coordinative projection.
用简易坐标投影法计算了其位置分析的正、逆解析解。
The forward and inverse analytical solutions of its positional analysis were computed by the use of simple and easy coordinative projection.
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