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    題名: 應用有限元素頻域分析探討多孔樑與多孔結構耦合之脈衝響應
    其他題名: Impulse response of porous beams coupled with porous structures by finite element frequency-domain analysis
    作者: 林益誠;Lin, Yi-Cheng
    貢獻者: 淡江大學機械與機電工程學系碩士班
    蔡慧駿;Tsay, Huoy-Shyi
    關鍵詞: 脈衝響應;多孔樑;多孔結構;有限元素頻域分析;Impulse response;Porous Beams;Porous Structures;Finite Element Frequency-Domain Analysis
    日期: 2012
    上傳時間: 2012-06-21 06:47:43 (UTC+8)
    摘要: 本文應用Biot多孔彈性理論,於尤拉樑及平面應力假設下推導多孔樑與多孔板之彎曲振動統御方程組。並於拉普拉斯域下推導多孔樑、多孔板以及多孔介質元素的剛性矩陣。再藉由衝擊負荷與彈性支撐邊界限制進行多孔樑、多孔板、多孔介質之有限元素頻域分析。探討多孔樑、多孔板、多孔介質、加肋多孔板、多孔樑與多孔介質耦合等耦合系統之動態行為,以期契合實際之應用狀態。
    多孔樑、多孔板以及多孔介質因內含之流體與固體架構交互作用而有特殊之動態消散特性。由含飽和多孔樑與多孔板模態振幅衰減之現象可發現流體黏滯係數越大時其消散特性影響相對增加,而流體體積模數主要影響多孔樑和板之模態頻率。因此藉由流體之改變可調整多孔樑與多孔板之模態頻率與振幅。由加肋多孔板模態頻率變動可明顯觀察到,孔洞率提高時消散係數及模態頻率也相對增高。故藉由孔洞率及流體改變可精確的調整加肋多孔板之動態反應。另多孔樑與空間聲場耦合分析結果顯示空間聲場內可同時觀察到多孔樑及聲場耦合的模態頻率且空間聲場內模態頻率和振幅均有顯著改變。
    Under the assumptions of Euler beam and plane stress, this study formulates the governing equations of flexural vibrations for the porous beam and plate using Biot’s poroelastic theory. Then, the stiffness matrices of the porous beam, plate and medium elements are derived in Laplace domain. Thereafter, using the impulsive loading and the elastic boundary conditions, the finite element frequency domain analyses are performed to study the dynamic behaviors of porous beams, plates, and mediums. In order to match the application condition, the dynamic behaviors of stiffened porous plates (porous beam coupled with porous plate) and porous beam coupled with porous medium are also evaluated.
    The porous beam, plate, and medium present a typical dissipation effect due to the interaction between the saturated fluid and the solid skeleton. Upon examining the reduction of modal amplitudes of the saturated porous beam and plate, the dissipation effect is found growing with the increase of the fluid’s viscosity, and the bulk modulus of the fluid has major effect on their modal frequencies. Therefore, by changing of the saturated fluid, the modal frequency and amplitude of the porous beam and plate can be adjusted. From the modal frequency fluctuations of the stiffened porous plate, the increase of both dissipation coefficient and modal frequency are clearly observed with the raise of porosity. Hence, the dynamic behavior of the stiffened porous plate can be precisely adjusted by the changes of the porosity and the saturated fluid. In addition, the analysis results of the coupling of a porous beam with an acoustic field show that the coupled modal frequencies of the porous beam and the acoustic field can be simultaneously observed, as well as the remarkable changes on the modal frequencies and amplitudes.
    顯示於類別:[機械與機電工程學系暨研究所] 學位論文

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