本文目的在於使用延伸的分佈質量轉移矩陣法(CTMM)，來求解一均勻或不均勻Timoshenko樑附帶多個集中質量、集中質量慣性矩、線性彈簧及扭轉彈簧時，在各種邊界條件下的自然頻率與振態。為達此目的，吾人將一連續的Timoshenko樑細分為數根段樑，將每組相鄰的兩根段樑以一節點連接之，並將上述各種集中元素附著於各個節點上。因此，吾人只須調整各根段樑的剖面積與長度，以及附加於各節點上的各種集中元素之大小，即可輕易建立一附帶多個集中質量、集中質量慣性矩、線性彈簧及扭轉彈簧之均勻或不均勻Timoshenko樑的數學模型。根據此數學模型，吾人便可進行任意邊界條件下攜帶任意集中元素之Timoshenko樑的自由振動分析。吾人可令左右兩端節點處之線性彈簧常數與扭轉彈簧常數皆為無限大而得兩端固定樑，令左右兩端節點處之線性彈簧常數與扭轉彈簧常數皆為0而得兩端自由樑，令一端之線性彈簧常數與扭轉彈簧常數皆為無限大而另一端之線性彈簧常數與扭轉彈簧常數皆為0而得一懸臂樑等等。另外，吾人針對均勻或不均勻樑附帶多種集中元素的情況下，分別根據Euler樑理論及Timoshenko樑理論來求其自然頻率與振態，並探討旋轉慣性與剪切變形效應的影響。

The purpose of this thesis is to extend the continuous-mass transfer matrix method (CTMM) to determine the natural frequencies and associated mode shapes of the uniform or non-uniform Timoshenko beams carrying any number of point masses, rotary inertias, translational springs and rotational springs with various classical or non-classical boundary conditions. To this end, a continuous Timoshenko beam is subdivided into several beam segments with any two adjacent beam segments connected by a node, and then each kind of concentrated elements is attached to each node. So, it is easy to establish the mathematical model of a uniform or non-uniform Timoshenko beam with various boundary conditions by only adjusting the cross-sectional area and length of each beam segment, and the associated physical quantity for each kind of concentrated elements. Thus, for a free-free beam, one requires only to set each of the stiffness constant of translational springs and rotational springs at its two ends to be equal to zero. In addition, the shear deformation and rotary inertia effects, the natural frequencies and associated mode shapes of the uniform or non-uniform beam carrying various concentrated elements are determined with Euler beam theory and Timoshenko beam theory.

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