臺灣博碩士論文加值系統

雷德遲滯阻尼模式動力特性之研究

研 究 生：曾啟倫
指導教授：黃慶東
時間：98年7月

論 文 摘 要
本文探討古典雷德遲滯阻尼模式動力系統在簡諧外力作用下之反應特性，雷德遲滯阻尼具與頻率無關且符合因果論之耗能性質。本文首先探討此系統所產生不穩定震動現象，並給予修正為具滑動與黏滯兩可互相切換之狀態，文中接著定義兩狀態切換的準則式，並以頻率比與阻尼比兩參數比較其反應差異。研究結果發現位移黏滯現象隨恢復力的增加或外力頻率減小而增加，此外黏滯時間也隨之增長。本研究也以等效線性近似方法求得雷德遲滯阻尼系統之等效阻尼比與等效頻率之解析解，分析結果顯示在輕度非線性阻尼下近似解具較佳之反應預測，且其精準度隨非線性程度之提昇而遞減。

Dynamic Response of the Reid's Hysteretic Damping Model

Thesis Advisor : Ching-Tung Huang
Graduate Student : Chi-Luen Tzeng

ABSTRACT
Response characteristics of single-degree-of-freedom dynamic systems with the classic Reid's Hysteretic Damping Model under simple harmonic loading are investigated in this thesis. The Reid's Hysteretic Damping is characterized by its frequency-independent loss modulus and the causality in its time-domain response. The investigation first focuses on an unstable vibration phenomenon of the indicated system and then is resolved with a two-phase switch mechanism in its controlling equation. The two-phase switch mainly involves a sequence of slide-stick motions whose triggering criteria are defined and the resulting response differences are also studied. The study results show that the stick phenomenon in the displacement response is more likely to occur as the restoring force increases or the external excitation frequency decreases. Likewise, the duration of stick state also increases under the above-mentioned conditions. The notion of equivalent linearization is employed to obtain an analytical approximation. A better response prediction is observed for systems with slight to mild nonlinearity, while the solution precision deteriorates as the degree of nonlinearity increases.

目錄
目錄 I
圖目錄 IV
第一章 緒論 1
1.1 研究背景與目的 1
1.2 文獻回顧 2
1.3 研究方法與內容 5
第二章 控制方程式之推導與數值計算 7
2.1 前言 7
2.2 控制方程式之推導 8
2.3 數值解法 9
2.4 恢復力與運動狀態之關係 12
2.4.1 恢復力與位移及速度之關係 12
2.4.2 運動狀態之判斷 13
第三章 黏滯與滑動情形之反應參數分析 17
3.1 前言 17
3.2 滑動與黏滯之控制方程式判斷 17
3.2.1 滑動狀態控制方程式之判斷 17
3.2.2 黏滯狀態控制方程式之判斷 18
3.3 狀態轉換之判別式 19
3.3.1 貫透型(P) 19
3.3.2 反彈型(R) 20
3.3.3 滑動條件 21
3.3.4 古典Reid模式與修正Reid模式之比較 22
3.4 位移與速度反應 22
3.4.1 外力頻率對位移與速度之影響 22
3.4.2 恢復力對位移與速度之影響 23
3.4.3 位移及速度反應譜分析 24
第四章 非線性系統之近似分析 26
4.1 前言 26
4.2 近似分析之推導過程 26
4.2.1 等效線性法(equiv. linearization) 27
4.3 近似方法之比較 31
4.3.1 近似後之位移與速度 31
4.3.2 小結 32
第五章 結論與建議 33
參考文獻 36

參考文獻

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