臺灣博碩士論文加值系統

摘 要
本文以黏彈塑性振子之結構模型，針對線彈性彈簧和聖維南滑塊建立數學模式進行研究分析。並引用新的估測方法，即相平面法，來計算結構承受週期性外部負載時的穩態行為，將相平面估測法所求出的解和由時間積分法所得出的正確解互相比較，以驗證相平面估測法的準確性。
我們經由平滑因子 來改變傳統的完全彈塑性結構模型，使得傳統的完全彈塑性結構模型具有平滑的彈塑性轉換機制。新的組成模式並應用於振子運動方程式，其中也考慮了黏性阻尼項。對於週期性負載下本文給出數個例子探討具有平滑性之一維黏彈塑性振動行為的動態反應。結構的長時間振動行為大致可以分為三種類型：彈性安定、具有週期性的極限環和非週期性之迴路。
本文亦分析週期性負載下一維雙線性彈塑性模型振動行為所表現出來的反應歷時狀態，以及長時間下具有穩定遲滯圈和極限環的參數空間分佈情況。

Abstract
In this paper a more concise formulation of perfectly elastoplastic model is presented and the dynamic responses of the single-degree-of-freedom (SDOF) viscous-elastoplastic structure under external loading is treated and the exact solutions of the responses are derived for periodic loading. We use a new phase-plane estimation method, which can calculate the steady-state responses of structures under sinusoidal loading. We also compare the estimated results with the exact results calculated by the exact time-marching solutions. We confirm that phase-plane estimation method is very accurate.
We also convert the conventional elastic-perfectly plastic constitutive model into a smooth model by shortening the switch-on time through a smooth factor . Then, the new constitutive model is adopted to combine with the equation of motion for mechanical oscillator. After deriving the governing equations we show the dynamic responses of the new one-dimensional smooth elastoplastic oscillator under sinusoidal loadings for several cases. The long term behavior is classified into three types: elastic shakedown, periodic limit cycle and non-periodic cycle.
In this paper we apply complementary trios and smooth factor to modify elastoplastic model, which is then use to analyze the steady-state responses of single-degree- of-freedom of smoothing and bilinear viscous-elastoplastic os- cillator under sinusoidal loadings, whose long term behavior is found to be hysteresis loop and limit cycle.

目 錄
誌 謝 Ⅰ
摘 要 Ⅲ
Abstract Ⅳ
目 錄 Ⅴ
圖 目 錄 Ⅷ
符 號 說 明 ⅩⅢ
第一章 導論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 研究動機與目的 5
1.4 研究內容 8
第二章 週期性負載下一維黏彈塑性振動行為的研究
10
2.1 含阻尼項之彈性完全塑性結構 10
2.1.1 運動方程式 10
2.1.2 彈性完全塑性模式 10
2.1.3 彈塑性轉換機制 11
2.1.4 雙相線性系統 12
2.2 正弦載重 13
2.2.1 正確解 13
2.2.2 彈塑性運動之轉換 15
2.3 反應 17
2.4 行為的分類 20
2.5 穩態反應的估測 23
2.5.1 相圖的估測 25
2.5.2 力量比 的閉合公式 28
2.5.3 韌性比 的閉合公式 32
2.5.4 遲滯圈的大小 34
2.5.5 彈性安定的範圍以及它的邊界 36
2.5.6 無阻尼的例子 39
2.5.7 相平面法與慢變參數法之比較 40
2.5.8 非週期性之反應 41
第三章 簡單且平滑的週期性負載下一維黏彈塑性振動行為的研究
44
3.1 簡單且平滑的彈塑性模型 44
3.1.1 一個簡單的修正 44
3.1.2 應變和應力之間的平滑關係 46
3.1.3 雙相系統 48
3.2 正弦載重 50
3.2.1 黏彈性運動 50
3.2.2 黏塑性運動 50
3.2.3 彈塑性運動之轉換 51
3.3 反應 52
第四章 週期性負載下一維雙線性黏彈塑性振動行為的研究
55
4.1 雙線性彈塑性結構模式 55
4.2 回復力 58
4.3 彈塑性之機制 59
4.4 雙相線性系統 61
4.5 調和負載 63
4.5.1 正確解 63
4.5.2 彈塑性運動之間的轉換 64
4.5.3 反應 65
4.6 穩態反應之估測 67
4.6.1 穩態反應所需要之方程式 67
4.6.2 力量比 之閉合公式 70
4.6.3 最大位移之閉合式 73
4.6.4 遲滯圈的大小 75
4.6.5 彈性安定 77
4.7 相平面法與慢變參數法之比較 79
4.8 非週期性之反應 80
第五章 結論與未來展望 82
5.1 結論 82
5.2 建議與未來展望 85
參 考 文 獻 86
附 圖 88

參 考 文 獻
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