目 錄

摘 要 1

關(guān)鍵詞 1

Abstract 1

Key Words 1

1 引 言 1

1.1架空電纜懸鏈線理論的研究進(jìn)展及意義 2

1.1.1國內(nèi)外架空懸鏈線理論進(jìn)展 2

1.1.2懸鏈線理論研究的意義 2

1.2反問題的研究現(xiàn)狀及其意義 3

1.2.1研究現(xiàn)狀 3

1.2.2研究意義 4

2 架空電纜懸鏈線理論正問題研究 4

2.1架空電纜懸鏈線受力分析 4

2.1.1載荷纜繩的受力分析 5

2.1.2無負(fù)荷纜繩的受力分析 5

2.2 懸鏈線函數(shù)的凹凸性 7

2.3 函懸鏈線函數(shù)的對稱性 8

2.4重量分布函數(shù)的變化對懸鏈線函數(shù)的影響 8

3 架空電纜懸鏈線理論反問題研究 10

3.1重量分布函數(shù)的奇偶性 10

3.2懸鏈線函數(shù)的變化對重量分布函數(shù)的影響 10

結(jié)束語 11

參考文獻(xiàn) 12

致 謝 12

 

摘 要：在架空電纜的設(shè)計(jì)中，架空電纜懸鏈線理論是人們公認(rèn)的最接近真實(shí)情況的設(shè)計(jì)理論，但是由于懸鏈線函數(shù)屬超越函數(shù)，計(jì)算上的困難使其在工程應(yīng)用中極為不便，尤其在計(jì)算機(jī)不甚普及的過去。經(jīng)過不少學(xué)者、專家的不斷研究，迄今已形成3種代數(shù)函數(shù)法：拋物線、懸索曲線、攝動(dòng)法來取代懸鏈線作近似計(jì)算，但這3種代數(shù)函數(shù)的近視值與實(shí)際值誤差較大。為此，近年來不少學(xué)者致力于架空電纜懸鏈線理論的研究，本文在此基礎(chǔ)上，運(yùn)用數(shù)學(xué)中的微積分定理，迭代積分、弧長、泰勒多項(xiàng)式、雙曲線函數(shù)等數(shù)學(xué)定理，對懸鏈線正問題、反問題的相關(guān)量進(jìn)行研究。

關(guān)鍵詞：架空電纜；懸鏈線理論；反問題

 

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