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 摘要一附帶任意數量彈簧─質量懸吊系統的樑，假使其左端及右端的每個安裝點和樑的每一邊都被認為是節點，然後考量在相鄰接的兩個樑段的每個安裝點和結合每個彈簧─質量懸吊系統的力矩方程式之中變形的相容性和力平衡狀態，同時在 的方程式中可以得到v個附著點， 中之元素是在第v段和第 樑段的分割與在第v個彈簧的質量其相對應的模態位移之特徵函數的積分常數所組成的。那是相當顯而易見的，假使 考量到結位移向量，而 為在第v個附著點（聯合第v個和第 個樑段）的元素勁度矩陣。有鑑於最後的事實，透過考慮到整個樑的邊界條件，我們可以使用數值組合法為全部的附著點（組合全部的樑段）來取得有限元素法中所要使用的聯立方程式 。求解 （其中 代表行列式）可得受拘束樑（附帶數個彈簧─質量懸吊系統）其自然頻率的正解，並且將 的每一個相對應的值代入每一個附著點相關的特徵函數之中，就會決定其相對應的振態。目前並沒有採取類似NAM的方法來求取此模型之自然頻率和相對應振態之正解。
 ABSTRACT For a beam carrying any number of spring-mass systems, if the left side and right side of each attaching point and each end of the beam are regarded as nodes, then considering the compatibility of deformations and the equilibrium of forces between the adjacent beam segments at each attaching point and incorporating with the equation of motion for each spring-mass system, a simultaneous equations of the form may be obtained for the v-th attaching point, where the elements of are composed of the integration constants for the eigenfunctions of the v-th and (v+1)-th beam segments and the associated modal displacements of the v-th sprung mass. It is evident that if is considered as the nodal displacement vector, then will be equivalent to the element stiffness matrix for the v-th attaching point (associated with the v-th and (v+1)-th beam segments). In view of the last fact, ome may use the numerical assembly method (NAM) for the conventional finite element method to obtain the simultaneous equations, , for the overall attaching points (associated with the overall beam segments) by taking into account of the boundary conditions of the whole beam. The solutions of = 0 (where denotes a determinant) give the “exact” natural frequencies of the constrained beam (carrying multiple spring-mass systems) and the substitution of each corresponding values of into the associated eigenfunctions for each attaching point will determine the corresponding mode shapes. Since no assumptions were made in the present approach (NAM), the natural frequencies and the corresponding mode shapes obtained are the exact ones.
 目錄誌謝 ii摘要 iiiABSTRACT iv目錄 v表目錄 vii圖目錄 viii符號與縮寫 ix1. 緒論 11.1 前言 11.2 研究方法 32. 理論推導 42.1 不均勻 Euler樑之運動方程式及特徵函數 42.2 不均勻樑在第v個集中元素的附著點之係數矩陣 72.3 不均勻 Euler 樑左端之係數矩陣 122.4 不均勻 Euler 樑右端之係數矩陣 132.5 不均勻Euler樑附帶彈簧─質量懸吊系統時的整體係數矩陣及頻率方程式 152.6 不均勻Euler樑在各種支撐情況下的係數矩陣 、 163. 數值分析結果與討論 193.1 不均勻Euler樑無附帶與有附帶彈簧─質量懸吊系統之驗證 193.2 不均勻Euler樑無附帶任意個彈簧─質量懸吊系統之分析 203.3 不均勻Euler樑附帶任意彈簧─質量懸吊系統之分析 273.3.1 不均勻Euler樑附帶一個彈簧─質量懸吊系統 273.3.2 不均勻Euler樑附帶三個彈簧─質量懸吊系統 323.3.3 不均勻Euler樑附帶五個彈簧─質量懸吊系統 374. 結論 42參考文獻 43附錄 46
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