含飽和流體多孔柱之步階響應

本文旨在探討含飽和流體多孔柱之步階響應分析，所應用的分析方法有二，第一種方法使用拉普拉斯轉換後之Biot動態統御方程組，給予材料參數及邊界條件，直接解析算出多孔柱在上表面中心點位移頻域函數之理論解，第二種方法乃應用有限元素頻域分析(FEFDA)，執行多孔柱之動態分析，兩種方法所求得頻域的位移解，可藉由傅立葉轉換，而得到時域的位移結果。研究模擬首先驗證分析方法之正確性，使用Biot動態統御方程組頻域理論解與有限元素頻域分析，進行含飽和水多孔砂岩柱之動態行為分析，所得到上邊界垂直位移曲線與前人所發表之結果一致。其次透過幾何或參數之變化，利用二維有限元素頻域分析，探討含飽和流體多孔柱動態行為之影響因子。由於多孔柱孔洞中含有流體在與固體相互作用下，會具有特殊的動態消散特性，分析結果顯示流體黏滯係數越大或孔洞率提高，消散係數與位移都會相對增加，故藉由流體的變化及孔洞率的改變，可精準調整含飽和流體多孔柱的動態行為反應。

關鍵字

多孔柱；位移； Biot理論；有限元素頻域分析

並列摘要

This thesis aims to explore the step response of a fluid-saturated porous column. Two analysis methods are applied. The first method involves the use of the Biot’s dynamic governing equation after Laplace transformation with material parameters and boundary conditions to directly compute the theoretical solution of midpoint displacement function in frequency domain. The second method involves the Finite Element Frequency Domain Analysis (FEFDA) applied to execute porous column dynamic analysis. The displacement solution of frequency domain obtained using the two methods then utilizes Fourier transformation to obtain the time domain displacement results. In the study, the analysis methods were first verified for correctness. Through the theoretical solution and FEFDA of Biot’s dynamic governing equation in the frequency domain, the dynamic behavioral analysis was conducted on the water-saturated porous sandstone column to obtain the top boundary vertical displacement curve coincided with the results published by predecessors. Secondly, through geometric or parameter changes, two-dimensional FEFDA was adopted to explore the impact factors contributing to the dynamic behavior of a fluid-saturated porous column. Since the porous column containing fluid, through interaction with solids, display the special characteristic of dynamic dissipation, the analysis results show that the higher the viscosity coefficient of fluid or porosity, the higher the dissipation coefficient and displacement. Therefore, fluid or porosity changes can facilitate the accurate adjustment of dynamic behavioral response of a fluid-saturated porous column.

並列關鍵字

Porous Column ； Displacement ； Biot Theory ； Finite Element Frequency-Domain Analysis

參考文獻

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含飽和流體多孔柱之步階響應

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