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題名 | 非直線彈性強迫振動之研究 |
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作 者 | 劉光銘; 廖清照會; | 書刊名 | 中正嶺學報 |
卷期 | 1:1 民59.07 |
頁次 | 頁27-34 |
分類號 | 334.7 |
關鍵詞 | 非直線彈性強迫振動; |
語文 | 中文(Chinese) |
中文摘要 | 吾人在分析非直線彈性物系之振動時,經常道遇到數學上的困難,此項困難尤以強迫振動為甚。迄今極大多數非線性強迫振動之解都由近似法求得,其結果與實際情相去較遠,難以滿足設計一般精密機械之需求。 T. J Harvey氏曾經研究非線性單自由度守恆系(Conservative system)之無阻尼振動(Undamped vibration )問題,得出一種利用自由振動求解強迫振勁的簡單法則。此法則的主要概念,系運用一種所謂“固有激勁函數(Natural forcing function)〞,使其所引起之強迫振動與自由振動同形。這種固有激動函數之波形,雖然與工程上常見的正弦激動函數不同,但Harvey 氏闡明其所提供的基本公式適用於任何二階系統(Second order system),不論該系具有何種形式之復原力(Restoring force),均能求得有效的正確解。 再早幾年, M.A. Sadowsky氐曾經發表一篇論文,演繹數種非線性彈簧系之特性,並以較簡形式求得此類彈簧系自由振動之正確解。Sadowsky氏特別舉出十種彈簧,其中二者之解為初等函數,餘者則為橢圓函數。 本文即將Harvey氏之關念加以整理,並自Sadowsky氏所提供之彈簧系中選出幾種常用者,利用Harvey氏之方法,求出其強迫振動之正確解。此外並由作者試舉一種截段性彈簧(Piecewise linear spring),詳加分析以例釋其應用,並連同上述結果一併供作工程上之參考及先進學者之指正。 |
英文摘要 | T. J. Harvey presents the idea of employing known solutions of FREE vibrations of nonlinear single-degree-conservative system to obtain solutions of FORCED vibrations of these system. The forcing function is taken to be of the same form as the free response and the solutions are obtained quite easily. Harvey makes the point that while this excitation is not the sinusoidal excitation that many analysts have attempted to study, for many purposes there is reason to prefer some alternate form of excitation if by doing so useful solutions are readily obtained. In a paper of several years back, M. A. Sadowsky derived the characteristics of several nonlinear spring systems for which the free vibrations could be obtained in rather simple form. In particular, Sadowsky introducted two new springs which give solutions in terms of the elementary functions and several others which give solutions in terms of the Jacobi elliptic functions. Since there are actually only a few fully developed cases of forced nonlinear vibrations available to analysts for testing the power and accuracy of analytical methods and for other purposes, it appeared to be of interest to apply the viewpoint of Harvey to several of the particular cases given by Sadowsky so as to work out all the details of the corresponding cases of forced vibration, The major content of this paper is the full development of these cases. In addition, however, the viewpoint of Harvey is applied to one case of piecewise linear springs simply for the purpose of illustrating such applications and for the purpose, as well of obtaining additional case of nonlinear vibrations. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。