臺灣博碩士論文加值系統

根據Wittrick的微分方程式並且加入溫度效應，本文利用Rayleigh-Ritz方法建立了圓柱形螺旋彈簧的一維有限元素運動方程式。對圓柱形螺旋彈簧靜態問題，本文修正之Wittrick的微分方程式可解得其正解，由此正解之位移函數(displacement functions)可求得本文彈簧元素之內插函數，以使用在本文建立之有限元素方程式中求取元素之質量矩陣、勁度矩陣與熱負荷向量等。本文建立之有限元素分析模式分別使用於圓柱形螺旋彈簧的靜態問題及自然頻率與模態分析。本文靜態問題分析中圓柱形螺旋彈簧除承受機械力外另考慮承受溫度變化。本文有限元素分析結果並與正解和文獻中其他彈簧元素的結果比較。由數值結果可展現本文圓柱形螺旋彈簧元素的準確性與效率。

Following the Wittrick’s differential equations modified with including the temperature effect, the present study uses the Rayleigh-Ritz method to develop the one-dimensional finite element equations of motion for the cylindrical helical springs. For the static problems of cylindrical helical springs, the modified Wittrick’s differential equations can be solved for the exact solutions. The displacement functions in the exact solutions are used to derive the interpolation functions which are used in the computation of the mass, stiffness matrices and thermal load of the present spring element. The present finite element model is applied in the static problems and free vibration analyses of cylindrical helical springs, respectively. In the present static analysis, the cylindrical helical springs subjected to uniform temperature change are also considered. The present model performance is compared with that of exact solutions and other finite elements. The accuracy and efficiency of the present spring element are demonstrated through the numerical results.

摘要 I
Abstract II
誌謝 III
目錄 IV
附圖索引 VI
附表索引 VIII
符號表 IX
第一章 緒論 1
1.1 前言 1
1.1.1彈簧的種類與功能 1
1.1.2彈簧材料的性質與選用 3
1.2 文獻回顧 5
1.3 研究目的與內容 8
第二章 建立圓柱形螺旋彈簧之運動方程式 9
2.1 圓柱形螺旋彈簧的幾何方程式 9
2.1.1 空間曲線之路徑座標系(path coordinate system) 9
2.1.2 Frenet-Serret公式 11
2.1.3 圓柱形螺旋彈簧幾何方程式推導 12
2.2 圓柱形螺旋彈簧之運動方程式 15
2.2.1 圓柱形螺旋彈簧的本構與靜平衡方程式 15
2.2.2 推導圓柱形螺旋彈簧的運動方程式 19
第三章 圓柱形螺旋彈簧之有限元素運動方程式推導 23
3.1 有限元素運動方程式推導 23
3.1.1 建立圓柱形螺旋彈簧元素之力與位移向量函數 23
3.1.2 有限元素運動方程式 26
3.1.3 二節點彈簧元素勁度矩陣簡易推導方法 30
3.2 靜態問題正解求法 32
第四章 實例分析與結果 35
4.1 靜態問題分析 35
4.2 動態問題分析 38
第五章 結論與建議 77
參考文獻 79
附錄 一 82

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