本計畫採用Biot多孔彈性動態方程組，推導頻域多孔樑元素、頻域多孔板彎曲元素及多孔樑與板受彈性支撐之剛性矩陣，計畫中將以有限元素頻域分析與動態實驗探討含飽和流體之多孔樑與板於簡支、固定及彈性支撐下的側向彎曲振動與阻抗行為。 計畫規劃以二年度進行含飽和流體多孔樑與多孔板之有限元素頻域彎曲振動與阻抗分析研究。第一年度已應用Biot多孔彈性理論於尤拉樑假設下完成多孔彈性薄樑彎曲振動動態方程組、頻域多孔樑元素剛性矩陣之推導，並使用有限元素頻域分析探討多孔樑受不同邊界限制、幾何及材料參數變異下之彎曲振動與阻抗行為。實驗方面也已陸續完成材料選用及夾具製作，而實驗規劃上也完成無因次參數變異之影響探討。上述分析成果已陸續發表於本年度之研討會中。 本第二年度計畫將以含飽和流體之多孔薄板為研究重點，執行多孔板彎曲有限元素頻域分析與實驗驗證。探討與驗證含飽和流體多孔薄板邊界受簡支、固定與彈性支撐、幾何及材料參數變異之彎曲振動與阻抗行為。本計畫完成之多孔樑與多孔薄板有限元素頻域分析程式與試驗能量，不僅有助於提昇各型含飽和流體之多孔樑與薄板側向振動與阻抗分析及設計效率，也可迅速提供含飽和流體多孔性結構等不斷拓展應用領域的分析使用。 In this project, Biot theory is applied to derive the frequency domain stiffness matrixes of the porous beam element and the porous plate bending element for analyzing both structures subjected to elastic restraints. In the study, finite element frequency domain analyses and dynamic experiments will be applied to examine the transverse vibration and impedance behaviors of the fluid saturated porous beam and plate under simple, fixed, and elastic restraints on their edges. The transverse vibration and impedance studies of the fluid saturated porous beam and plate are proposed to be accomplished in two years. In the first year, the frequency domain stiffness matrix of porous beam is derived. Subsequently, the transverse vibration and impedance behaviors of the fluid saturated porous beam influenced by the variations of edge restraint, shape, as well as material property are analyzed by the finite element frequency domain porous beam analyses. The preliminary analytical results are validated and published in the conferences, and the related porous materials and fixtures for the dynamic experiments are also selected and accomplished recently. In the second year, the efforts of the project will focus on the dynamic behaviors of the fluid saturated porous plate. The transverse vibration and impedance experiments as well as the finite element frequency domain porous plate analyses will be applied. The influences of the variations of edge restraint, shape, as well as the material property on the transverse vibration and impedance behaviors of the porous plate will be investigated. At the end of this project, the finite element frequency domain analyses and the experiments achieved can be used in improving the efficiency of the vibration and impedance analyses of the fluid saturated porous beam and plate. The techniques developed can also be rapidly applied in every application aspect of the fluid saturated porous structures.
