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We have described two closely related numerical methods for the solution of eigenvalue problems called 'stabilized iteration' and 'mutually stabilized biiteration'.


A technique for the numerical solution of eigenvalue problems defined by differential equations, based on an operational approach to the Tau method recently proposed by the authors, is shown to be equivalent to a method of Chaves and Oritz.


This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations.


Numerical solution of eigenvalue problems for Hamiltonian systems


Accurate nonperturbative solution of eigenvalue problems with application to anharmonic oscillator

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 A method is provided for the solution of eigenvalue equations of threedimensional rectangular waveguides. The method takes account of the absorption effect of every medium layer in the waveguide, and poses no limitation on the absorption intensity. Calculations based on this method are made for several kinds of GaAs/AlGaAs rectangular and ridge waveguides, and theoretical results are obtained about their optical properties.  本文从理论上给出一种求解三维矩形波导特征方程的方法,其特点是考虑了组成波导的各介质层的全部吸收作用,并对吸收的强弱不作任何限制。然后用此方法对几种GaAs/AlGaAs结构的矩形和脊形波导进行具体计算,得到其光学特性的理论结果。  In this paper, an optimal dynamic design method, based on the idea o perturbation characteristic of generalized eigenvalues and converse solution, is presented, With it, the problems of optimal dynamic design with unacceptable frequency band (involving eigenvalue equation with implicit behaviour constraints) can be solved, The idea of this method is that, as soon as the behaviour constraints of unacceptable frequency band are violated, an unacceptable band of the evading variable is set, By means of the... In this paper, an optimal dynamic design method, based on the idea o perturbation characteristic of generalized eigenvalues and converse solution, is presented, With it, the problems of optimal dynamic design with unacceptable frequency band (involving eigenvalue equation with implicit behaviour constraints) can be solved, The idea of this method is that, as soon as the behaviour constraints of unacceptable frequency band are violated, an unacceptable band of the evading variable is set, By means of the perturbation characteristic of generalized eigen values and the known frequeucy increment that can avoid the unacceptable frequency band, the changes of the elements of stiffness matrix and mass matrix in eigenvalue equation can conversely be calculated. Then the changes of the design variables can be determined, hence the aim of avoiding unacceptable frequency band can be achieved, So the solution of eigenvalue equation with implicit behaviour constraints can be avoided to the possible extent, At the same time, the optimal problem can be solved by transforming the behaviour constraints into the boundary ones, Hence, both the method and the programming of optimal dynamic design are simplified and the times of reanalyses are reduced, The theoretical evidence in which the same eigenvalue does not appear as before (socalled the duplicate eigenvalue) during the course of optimality after setting unacceptable band of avoided variable under certain conditions is given and some conditions in which no duplicate eigenvalues appear are also shown in this paper, Following the above method, a practical example of aero engine rotor optimal dynamic design with 25 design variables is given. The optimality value can be achieved by nonlinear programming combined with the method of perturbation converse solution. The times of reanalyses are 56. In addition, the authors have made the optimal dynamic design of centrifugal pump. The times of reanalyses are 35. This method can also be extended to the optimal dynamic structural design.  本文利用广义特征值的摄动（扰动）特性和逆求的思想提出一个机械动力（态） 优化设计方法，用以求解带频率禁区（含特征方程隐式性能约束）的动力优化设计问 题．给出了本方法可行性的论证。文后举了一个２５维设计变量的飞机发动机转子系 统动力优化设计实例。用数学规划和本文摄动逆求相结合方法求解，重分析５－６次即可。方法直观，程序简单．木方法亦可能推广应用于工程结构优化设计。  A basic method to measure the random variable of runway roughness according to roughness criteria based on power spectral concrpts is derived.The power spectral criteria are primarily used for consideration of aircraft fatigue.According to the theory of generalized harmonic analysis, the power spectral analysis for random processes must be assumed to be stationary, ergodic and to agree with Gaussian distribution. On this assumption,a power spectral curve which provides description of frequency characteristics... A basic method to measure the random variable of runway roughness according to roughness criteria based on power spectral concrpts is derived.The power spectral criteria are primarily used for consideration of aircraft fatigue.According to the theory of generalized harmonic analysis, the power spectral analysis for random processes must be assumed to be stationary, ergodic and to agree with Gaussian distribution. On this assumption,a power spectral curve which provides description of frequency characteristics of roughness for a runway was calculated step by the method decribed in reference 2.The we considered the landing gear and its airframe taxiing on the rough runway as a system with multidegrees of freedom and derived the simultaneous differential equations of motion by using Newton's second law.For simplicity, we used the model matrix as transformation matrix to uncouple the simultaneous differential equations into a set of independent equationsAlso,the method of determining transfer function by means of solution of eigenvalue problems was considered.At last,the carves of exceedances per flight vs the incremental accelaration of airplane during taxiing were introduced.  本文从机场跑道不平度准则出发,基于功率谱概念,介绍了测定跑道不平度随机变量的基本方法.对跑道不平度功率谱曲线的拟合和飞机地面滑行动力响应进行初步分析。   << 更多相关文摘 
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