电缆悬链线模型正问题反问题研究.doc

目 录

摘 要 1

关键词 1

Abstract 1

Key Words 1

1 引 言 1

1.1架空电缆悬链线理论的研究进展及意义 2

1.1.1国内外架空悬链线理论进展 2

1.1.2悬链线理论研究的意义 2

1.2反问题的研究现状及其意义 3

1.2.1研究现状 3

1.2.2研究意义 4

2 架空电缆悬链线理论正问题研究 4

2.1架空电缆悬链线受力分析 4

2.1.1载荷缆绳的受力分析 5

2.1.2无负荷缆绳的受力分析 5

2.2 悬链线函数的凹凸性 7

2.3 函悬链线函数的对称性 8

2.4重量分布函数的变化对悬链线函数的影响 8

3 架空电缆悬链线理论反问题研究 10

3.1重量分布函数的奇偶性 10

3.2悬链线函数的变化对重量分布函数的影响 10

结束语 11

参考文献 12

致 谢 12

 

摘 要：在架空电缆的设计中，架空电缆悬链线理论是人们公认的最接近真实情况的设计理论，但是由于悬链线函数属超越函数，计算上的困难使其在工程应用中极为不便，尤其在计算机不甚普及的过去。经过不少学者、专家的不断研究，迄今已形成3种代数函数法：抛物线、悬索曲线、摄动法来取代悬链线作近似计算，但这3种代数函数的近视值与实际值误差较大。为此，近年来不少学者致力于架空电缆悬链线理论的研究，本文在此基础上，运用数学中的微积分定理，迭代积分、弧长、泰勒多项式、双曲线函数等数学定理，对悬链线正问题、反问题的相关量进行研究。

关键词：架空电缆；悬链线理论；反问题

 

Research on inverse

problem is problem of cable catenary model

Abstract：In the design of overhead cable, aerial cable catenary theory is recognized as the most close to the actual situation of the design theory, but because the catenary function is deduced, computational difficulties in the engineering application is extremely inconvenient, especially in the computer is not very popular in the past. The study of many scholars, experts, has been formed 3 kinds of algebraic function method: parabolic curve, suspension, perturbation method to replace the catenary for approximate calculation. But these 3 kinds of algebraic function of myopic value and the actual value error. Therefore, research in recent years, many scholars devoted to a single span overhead cable catenary theory, on this basis, the use of calculus theorem in mathematics, iterated integral, arc length, Taylor polynomial, hyperbola function and other mathematical theorem, conducts the research to the relevant problem, inverse problem is the catenary.

Key Words ：aerial cable ;catenary theory; inverse prodlem