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.

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