本文首先研究如何將小波理論導入有限元素法，並且應用在結構振動的分析。在傳統的有限元素法中，使用多項式當作內插函數來近似結構的位移，單位元素的自由度會被多項式的階數所限制，因於對於要解結構局部高變化梯度的問題就必需提高多項式階數或增加分析的單位元素數目，這都將使計算上更複雜。
　　導入有限元素法後應用在彈性基底樑結構的自然振動分析以及承受移動負荷樑結構的動態分析，來驗證小波有限元素法的可行性和優於傳統有限元素法的收斂性。再將小波有限元素法推展到週期性分布彈性基底樑結構的動態特性分析，來討論週期性分布的彈性基底對在樑上所傳遞的振動波之影響，以及各種參數改變對此效果之影響，並探討是否會對移動負荷通過之後產生振動之影響。

　　The objective of this dissertation is to study the construction of the wavelet-finite element method. In traditional finite element methods, polynomials are used as interpolation functions to construct an element; the degrees of freedom are restricted by the order of polynomial. When the problem with local high gradient is analyzed by using traditional finite element methods, the higher order polynomial or denser mesh must be employed to ensure the accuracy.
　　The wavelet-element is introduced into the finite element procedure and the dynamic problems of a beam structure on an elastic foundation and a beam structure subjected to moving loads. The accuracy and the convergence rate are verified. Then dynamic problems of a beam structure on an elastic foundation subjected moving loads are solved by the present wavelet-element modal to discuss the influence of vibrating wave transmitted on the beam by periodic elastic foundations, and the effect to this phenomenon by changes of several parameters. Furthermore, to discuss whether periodic elastics foundations would affect the vibration produced by passing of moving loads.

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