臺灣博碩士論文加值系統

本研究係考慮雙線性遲滯系統於雙頻外力作用下，探討其因外力頻率比n的改變所產生的振幅反應特性。分析結果顯示系統反應隨著n由1開始遞增，可出現截然不同之反應特徵；在n小於1.1時，系統出現顯著之拍頻現象，而當n接近偶數時，則以顯性之振態疊加呈獻。為進一步釐清此一反應差異所引發之工程意涵，本文定義一反應振幅係數 以觀察系統在穩態反應下之振幅強弱，研究亦推導線性狀態下之 解析解，用以比較非線性計算出之 值。比較結果發現 值具顯著之雙峰現象，直接呼應外力之雙頻特色，遲滯迴圈之非線性特質產生不同程度之勁度軟化效應，而導致雙峰偏移與 值大小之調整。

Dynamic responses of bi-linear hysteretic systems under two-frequency excitations characterized by a frequency ratio, n, are studied in this thesis. The analytical results show markedly different response characteristics as the excitation parameter n increases from unity. The classical beat phenomenon can be found for most cases with an n smaller than 1.1. On the other hand, a two-mode superposition in displacement is obvious when n is closer to an even number. To further explore its engineering implication, the indicated response features are compared based on a steady-state amplitude parameter referring to the Response Amplitude Factor, . An analytical expression of the parameter is first derived for the linear system and is then compared with numerical solutions evaluated for the nonlinear systems. The spectra demonstrate a two-peak response feature that conforms to the external excitation frequencies. The effects of stiffness softening are also clear as evidenced by a left-switch trend in the response peaks as the degree of nonlinearity increases. However, the variation in the peak magnitude is difficult to quantify

第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究方法與內容 3
第二章 雙線性雙頻系統介紹 5
2.1 前言 5
2.2 系統反應的特徵簡介 6
2.2.1 雙線性系統(Bi-linear system) 6
2.2.2 拍頻現象(Beat Phenomenon) 7
2.2.3 共振現象(Resonance Phenomenon) 8
2.2.4 拍頻和共振現象之差異 8
2.3 雙線性遲滯系統受雙週期性外力作用下之運動方程式 10
2.3.1 系統敘述與特性反應 10
2.3.2 此系統拍頻現象之敘述 11
2.3.3 顯性振態疊加 14
2.3.4 此系統之線性與非線性下和拍頻方程式關係 14
第三章 雙線性遲滯系統於雙頻外力反應之特性 16
3.1 前言 16
3.2 系統敘述與特性反應 16
3.3 線性與非線性系統之反應特性探討 18
3.3.1 線性系統情況探討 18
3.3.2 非線性系統情況探討 21
3.3.3 小節 25
3.4 線性系統和非線性系統之2D圖形情況共同探討 28
3.5 線性系統和非線性系統之3D立體圖形探討 29
3.6 檢核非線性圖形是否正確 31
第四章 結論與建議 32
參考文獻 34

【1】Yang, Y.B., Yau, J.D., and Wu, Y.S.(2004), Vehicle-Bridge Interaction Dynamics, World Scientific.
【2】Yang, Y. B., Yau, J. D., and Hsu, L.C.(1997).“Vibration of simple beams due to trains moving at high speeds”, Engineering Structures, Vol. 19, No. 11, pp.936-944.
【3】姚忠達 淡江大學建築技術系教授，題目:高鐵連續桁架橋受車行之減振分析－複合型TMD/MTMD系統行，政院國家科學委員會專題研究計畫成果報告.
【4】黃震興，邱哲明，「使用雙線性遲滯隔震器之橋樑等效線性分析」，結構工程，第十卷，第四期，第27至42頁(1995).
【5】T.T. Baber, Nonzero mean random vibration of hysteretic systems, ASCE Journal of Engineering Mechanics, 110 (7) (1984) 1036-1049.
【6】Y.J. Park, Equivalent linearization for seismic responses.
I: formulation and error analysis, ASCE, Journal of Engineering Mechanics, 118 (11) (1992) 2207-2226.
【7】O. Ditlevsen, L. Bognar, Plastic displacement distributions of the Gaussian white noise excited elasto-plastic oscillator, Probabilistic Engineering Mechanics, 8 (1993) 209-231.
【8】A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Weley-
Interscience , New York, 1979.
【9】S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, 1990.
【10】W.D. Iwan, The steady-state response of a two-degree-of-freedom bilinear hysteretic system, Trans. ASME,Journal of Applied Mechanics, Series E, 87 (1965) 151-156.
【11】P SRINIVASAN, Mechanical Vibration Analysis,(1983) 114
【12】郭盛胤，“遲滯系統之飄移行為與外力頻率關係研究”，國立台灣科技大學營建工程系碩士論文，民國95年7月.
【13】Koizumi K, Analysis of vibration with collision and applications to leaf beating machine. Doctor thesis, University of Tokyo, Precision Mechanical Engineering; 1980 [in Japanese].
【14】Fa-Gung Fan and Goodarz Ahmadi, Seismic responses of secondary systems in base-isolated structures, Engineering Structures, Volume 14, Issue 1, 1992, Pages 35-48.
【15】Thomas A. Duffey, Christopher Romero, Strain growth in spherical explosive chambers subjected to internal blast loading, International Journal of Impact Engineering 28 (2003) 967–983
【16】Harris CM. Shock and vibration handbook. New York: McGraw-Hill, 1996.
【17】Burton R. Vibration and impact. New York: Dover, 1968.
【18】王金村，《科學發展》2005年6月，390期，60∼65頁.
【19】W.D. Iwan, A distributed-element model for hysteresis and its steady-state dynamic response, ASME J. Appl. Mech. 33 (1966), pp. 893–900.
【20】W.D. Iwan. Steady-state dynamic response of a limited slip system. ASME, J. Applied Mechanics, 35 (1968)322-326.
【21】Ching-Tung Huang, Shen-Yin Kuo，Drift response of bilinear hysteretic systems under two-frequency excitations. International Journal of Non-Linear Mechanics 41 (2006) 888 – 904
【22】T.K. Caughey, Sinusoidal excitation of a system with bilinear hysteresis, Trans. ASME, Journal of Applied Mechanics, Series E, 82(1960) 640-643.
【23】Danilo Capecchia and Fabrizio Vestronia, Periodic response of a class of hysteretic oscillators, International Journal of Non-Linear Mechanics Volume 25, Issues 2-3, 1990, Pages 309-317.