含飽和流體多孔彈性圓板之脈衝響應

Impulse Responses of Fluid-Saturated Poroelastic Circular Plates

陳正輝(Jheng-Huei Chen)

指導教授 ： 蔡慧駿

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00803

摘要

本文應用Biot多孔彈性理論與古典板理論，推導含飽和流體多孔彈性板的彎曲振動統御方程組。再於頻域中應用Galerkin型態有限元素法推導多孔彈性板三角形與四邊形元素的剛性矩陣及荷重向量。並藉由脈衝負荷作用與彈性邊界限制完成多孔彈性板的彎曲振動有限元素頻域分析，探討含飽和流體多孔彈性圓板的脈衝響應。
透過分析彈性板的無因次頻率係數及驗證前人發表的多孔彈性板數值與實驗結果，顯示有限元素頻域分析確可準確模擬多孔彈性圓板因材質、負荷及邊界限制等變化影響的彎曲振動行為。含飽和流體多孔彈性圓板具有流體與固體架構交互作用的動態消散特性，由多孔圓板撓度振幅的衰減可發現流體黏滯係數愈大其振幅衰減愈顯著，流體體積模數增加亦顯著提升多孔圓板的基礎自然頻率，藉由流體的改變可調整多孔彈性圓板的基礎自然頻率與撓度。最後研究應用無因次有限元素頻域分析探討各無因次參數變異於邊界固定支撐多孔彈性圓板脈衝響應的影響。結果顯示無因次固體有效密度及固體與流體的耦合有效密度分別對基礎自然頻率及撓度振幅的影響最為顯著。

關鍵字

Biot多孔彈性理論 ； 古典板理論 ； 多孔彈性圓板 ； 脈衝響應 ； 有限元素頻域分析 ； 無因次分析

並列摘要

In this study, Biot’s poroelastic theory and classical plate theory are applied to derive the governing equations of flexural vibrations of fluid-saturated poroelastic plates. The Galerkin type finite element approach is applied to derive the stiffness matrices and load vectors of triangular as well as quadrilateral poroelastic plate elements in the frequency domain. After applying the impulsive loadings and adjusting the elastic restraints, the finite element frequency domain analysis of flexural vibrations of poroelastic plates can thus be accomplished. The impulse responses of fluid-saturated poroelastic circular plates are explored.

Upon examining the results of the non-dimensional frequency parameters of elastic plates as well as the numerical and experimental results of poroelastic plates published by other researchers, it is validated that the finite element frequency domain analysis can obtain accurate results which are influenced by material properties, loadings and boundary restraints for the flexural vibrations of poroelastic circular plates. A fluid-saturated poroelastic circular plate can present a dynamic dissipation effect owing to the interactions of the fluid and the solid skeleton. Upon examining the reduction in deflection amplitude of poroelastic circular plates, it is found that the dissipation effect is an increasing function of fluid’s viscosity, and the fundamental natural frequency is an increasing function of the bulk modulus of the fluid. Accordingly, the fundamental natural frequencies and the deflections of poroelastic circular plates can be adjusted by changing the properties of the saturated fluid. At the end of this study, the dimensionless finite element frequency domain analysis is applied to explore the influence of dimensionless parameters on the impulse responses of clamped poroelastic circular plates. The results indicated that the value of dimensionless effective mass of the solid has a pronounced effect on the fundamental natural frequency, and the value of dimensionless mass coupling parameter between the fluid and the solid has a pronounced effect on the deflection amplitude.

並列關鍵字

Biot's Poroelastic Theory ； Classical Plate Theory ； Poroelastic Circular Plates ； Impulse Responses ； Finite Element Frequency Domain Analysis ； Dimensionless Analysis

參考文獻

30. 蔡慧駿、葉豐輝、陳央澤、廖聖善，“應用有限元素頻域法於含飽和流體多孔薄板之彎曲振動分析”，中華民國力學學會第三十四屆全國力學會議論文集，2010。

1. M. A. Biot, “General Theory of Three-Dimensional Consolidation”, Journal of Applied Physics, Vol. 12, No. 2, pp. 155-164, 1941.

2. M. A. Biot, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid”, Journal of Applied Physics, Vol. 26, No. 2, pp. 182-185, 1955.

3. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range”, Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 168-178, 1956.

4. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid II. Higher Frequency Range”, Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 179-191, 1956.