本文使用Biot動態統御方程組，於拉普拉斯域應用有限元素理論建立多孔介質三維六面體之剛度矩陣，並引用前人建立之多孔介質二維三角形及四邊形元素、多孔樑元素與多孔板二維四邊形元素等之剛度矩陣，最後伴隨多點拘束法完成流體位移剛度矩陣及耦合結構之有限元素頻域分析。 研究模擬時以多孔介質模擬聲場，建立加肋多孔板與聲場耦合之模型。藉由加肋多孔板與聲場耦合系統之分析結果驗證確立多孔樑、多孔板、加肋多孔板、聲場及加肋多孔板與聲場耦合之有限元素頻域分析之正確性。接著透過幾何及材料參數變異分析，探討影響耦合結構模態頻率和振幅之影響因子。分析結果顯示，除邊界限制對模態頻率有顯著影響外，加肋多孔板因內含之流體與固體架構耦合作用而有之動態消散特性與流體體積模數亦為影響系統模態頻率之主要因素。另外，消散特性亦影響聲場中各點之模態振幅。於此，可確立本文所建立之加肋多孔板與聲場耦合之有限元素頻域分析，確能達成特定區域聲響行為改善之目標。 This study applied Biot''s dynamic governing equations in Laplace domain and used the finite element theory to build the stiffness matrix of a porous medium 3D hexahedron element. Then, the matrices of porous medium 2D triangular element as well as quadrilateral element, porous beam, and porous plate 2D quadrilateral element derived by other researchers are adopted. Finally, the multipoint constraint approach is applied to generate the stiffness elements that related to the fluid displacements and complete the Finite Element Frequency Domain Analysis (FEFDA) of a stiffened porous plate coupled with a porous medium.
This study used porous medium to simulate acoustic field and built a model of a stiffened porous plate coupled with an acoustic field. Based on the analysis results of the system of a stiffened plate coupled with an acoustic field, the FEFDA results of the porous beam, the porous plate, the stiffened porous plate, acoustic field, and the coupling of the stiffened porous plate and the acoustic field were verified. Then, through the geometric analysis and material parameter variance analysis, the influential factors of modal frequency and amplitude in the coupling structure were explored. According to the analysis results, besides the significant influence of boundary restraints on modal frequencies, the dynamic dissipation effects caused by the coupling of the fluid with the solid skeleton and the bulk modulus of the fluid were also the main factors influencing the system modal frequencies. In addition, the FEFDA of the stiffened porous plate coupled with the acoustic field conducted by this study could indeed achieve the goal of improving the acoustic behaviors of certain areas.