特征方程

And the methods how to combine them with the discretized algebraic eigenvalue equation for generalized Rayleigh and Love waves are also given.

推导了这三种边界条件的公式，并且给出了它们进入离散化后的Rayleigh波与Love波的代数特征方程方法。

They are clay, mud shale, gravel, oil shale, mudstone, schist, basalt, limestone, gritstone, dolomite, breccia, granite, and quartzite. We give the feature curve and distribution feature equation of these rocked landslide.

本论文分别对不同滑体岩性，包括从软到硬的粘土、泥页岩、砾类土、油页岩、泥岩、片岩、玄武岩、灰岩、砂岩、白云岩、角砾岩、花岗岩、石英岩十三种具有代表性的岩土体的滑坡推力和剩余抗滑力进行了模拟分析，给出了它们的滑坡推力和剩余抗滑力分布特征曲线，分布特征方程。

So we can analyse the stability of lattice structure as solid web beam without change its geometry dimension. The out-of-plane stability of bending beam, which is made up with 2 beams and loaded by non-directional force, is studied.

对两节梁组成的弯曲梁在非保向力作用下的平面外失稳问题进行了研究，通过建立每节梁临界状态下弯曲和扭转变形微分方程，根据杆件变形的边界条件以及杆件之间的变形协调关系，得出了一端固定一端悬臂的弯曲梁在非保向力作用下平面外失稳的特征方程。

The decay of a stationary perturbation from the Couette-Poiseuille flow in the downstream is sought.

对0到2000之间的雷诺数，计算了平稳扰动的Couette－Poiseuille流的下游特征值，其特征方程类似于Orr－Sommerfeld方程。

By representing the uncertain parameters as interval numbers, the interval dynamic characteristic equations and the dynamic governed equations of the structure are built by means of the interval finite element method.

基于区间模型的结构动力分析将结构中的不确定性参数用区间数来表示，建立了系统的区间动力特征方程和动力控制方程。

The "compressed sparse row data format" is adopted to save storage and the "mode multiplication" is used to improve the computation efficiency, so that the finite integration equation is obtained with low storage and high efficiency. To solve the finite integration equation, which is a large-scale sparse algebraic eigenvalue problem under the condition specified, the Krylov subspace iteration method is introduced and the shift-invert Arnoldi method is proposed to exclude the unphysical static electro-magnetic solution and get the needed eigensolution around the specified eigenvalue.

采用"行索引稀疏格式"压缩存贮技术节约内存，采用大型稀疏矩阵的模式乘法，提高矩阵计算效率，高效获得了离散电场分量满足的有限积分方程；针对有限积分特征方程的求解，论文介绍了大型稀疏矩阵Krylov子空间迭代方法，并提出了位移求逆Arnoldi算法，以排除非物理的静态电磁场解，获得指定频率附近的特征值。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

Considering pencil of matrices with centrosymmetric could not satisfy characteristic equations in practice, it was necessary to study the centrosymmetric solution of the matrix equation least square problems, and to give pencil of matrices with centrosymmetric of the least squares problems in model updating.

对线性结构的有限元动力模型修正问题，通过灵敏度分析，确定要修正的参数，由正交性条件和特征方程得到相应的修正量方程。

Additionally, we analyzed the thermal-decay rules of LPGs. We use temperature-compensating package to reduce the sensitivity of temperature of LPGs. At the end of this paper, we summarized the key technologies required during practical application of LPGs, During this paper, we obtained some inventional results as follow: 1. We deduced waveguide modes of single and many mode fibers by use of Maxwell equation.

论文工作期间，主要取得了以下几方面的成果：一、我们利用Maxwell方程，推导了单模和多模光纤的导波模式，同时利用耦合模原理，简要推导了反射式光纤光栅的模式场分布及相应的模式特征方程；采用弱导光纤近似理论，严格推导了透射式长周期光纤光栅的模式场分布，得到了光栅周期与光波长间的对应关系，这是分析长周期光纤光栅光谱特性的有力工具。

Stability analysis of nonlinear magnetic suspension, the magnetic suspension system model was found based on electromagnet dynamics and voltage balance of the electromagnet coil; The feedback of position and velocity and current are used as the control variable; After the control rule was applied to the electromagnetic system, the louts criterion was used to get the range of the control parameter in which the system was steady-going.

非线性磁悬浮系统的稳定性分析，通过电磁铁动力学和电磁线圈的电压平衡方程，建立磁悬浮系统基本模型。求出系统奇点后，通过系统线性展开求出系统矩阵。用PD控制外加电流反馈量，将控制规律带入系统模型方程组求出矩阵的特征方程，由劳斯判据得知非线性系统稳定的位置反馈系数及取值范围。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失