本文目的在探討使用一種統一的方法，來求解一均勻(或不均勻) 的單跨距(或多跨距)樑，在攜帶任意個數集中元素情況下的自然頻率與對應振態的可行性，其集中元素包括：集中質量（大小為 ）、線性彈簧（勁度係數為 ）及螺旋彈簧（勁度係數為 ）等。為達此目的，吾人將一連續樑細分為許多根段樑，再將每相鄰的兩根段樑以一節點連接之，然後，在各個節點附加上述三種集中元素。使用此一概念，吾人只須調整某些段樑的剖面積與集中元素的大小，便可建立許多種不同邊界條件，攜帶任意個集中元素的均勻(或不均勻) 、單跨距(或多跨距)樑的數學模型，以便進行自由振動分析。

The purpose of this paper is to use a unified approach to solve the free vibrations of uniform（or non-uniform）single-span（or multi-span） beam carrying various concentrated elements. The concentrated elements include the concentrated mass and the corresponding translational and rotational spings. In order to achieve the goal, consider a beam made up of different but uniform sections. Between the next two sections, we connect them with one node carrying the three concentrated elements. For the reason, we can just only change the section areas of every beam segment, and the situations of concentrated elements on every node to build various boundary conditions. Then we can take these math models to free vibration analysis.

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