多孔隙材料板波傳頻散行為之模擬及量測

Measurement and Modeling for Dispersion Behavior of Porous Plate

高琮貿(Chong-Mau Kao)

指導教授 ： 楊哲化

國立臺北科技大學/機電學院/機電整合研究所/碩士(2010年)

摘要

多孔隙材料(porous material)為一種含有孔洞分佈所構成的網狀結構之材料。由於此種材料含有孔洞的分佈，造成材料的體積會小於實際緻密的體積，其比值即為孔隙率(porosity)。多孔隙材料的材料係數（密度、彈性模數等）受到孔隙率的影響而變化，因此在檢測中可利用孔隙率之特性作為一種量測的標準。
本研究主要利用理論以及實驗兩種方法，探討不同孔隙率之多孔隙材料板在不同流體環境下藍姆波的波傳行為之頻散關係，並以各種量測途徑取得理論所須之各種材料參數。
理論部份將運用Boeckx所提出的多孔隙平板理論模型作為基礎，以模擬多孔隙材料板在不同孔隙率、不同流體（空氣與水）之藍姆波波傳行為。而實驗部份為利用雷射激發超音波，探頭接收作為量測多孔隙材料板之導波頻散關係的方法。
研究對象為不同多孔隙材料板，如透氣陶瓷材料（氧化鋁）與多孔金屬板（316L不銹鋼），以探討不同材料板、不同孔隙率以及不同流體下各導波之頻散關係。研究結果發現，多孔隙材料之孔隙率對於密度與彈性模數之影響可透過頻散關係呈現，且理論模型與實驗量測之頻散關係結果相當吻合。研究中亦發現改變多孔隙材料板之密度、蒲松比、剪力模數與獨立的孔隙率時，其頻散關係曲線將有偏移現象，對未來可提供為發展超音波量測於多孔隙材料板之重要依據。

關鍵字

多孔隙材料板 ； 孔隙率 ； 非破壞檢測技術 ； 頻散關係

並列摘要

Porous materials are a kind of the netted structures which is compared of pores distribution. Since the porous materials are pores distribution, the volume of material will be less than the volume of solid, those ratio is namely porosity. The material coefficients of foam, such as density, elastic modulus, etc, will change by porosity. Therefore, it can be used the characteristic of porosity as a standard for detection.
The study is focused on theory and experiment for the dispersion relation of Lamb waves propagating in porous plates with different porosities and fluids. And it is obtained material parameters for theory by various measurement methods.
In theoretical part, it will base on the model of porous plate which is proposed by Boeckx, and simulate Lamb waves propagating in porous plates for different porosities, fluids (air and water). Then, in experimental part, it measures the dispersion relation of porous plates by the method of laser ultrasonic exciting, transducer receiving.
In this research, there are different materials, such as porous ceramic materials (alumina), and porous metal plates (316LSS), and it is investigation on dispersion relation for different porous plates, porosities, and fluids. For all the studied cases, the theoretical modeling dispersion curves agree with the experimental measured dispersion, and successfully investigate the effects of porous plate on dispersion relation, including density, Poisson’s ratio, Shear modulus, and independent porosity.

並列關鍵字

Porous plate ； Porosity ； Dispersion ； Nondestructive

參考文獻

[1] Ronald G. Munro, “Effective medium theory of the porosity dependence of bulk moduli,” J. Am. Ceram. Soc., vol. 84, no. 5, 2001, pp. 1190-1192.

[2] H. Lamb, “On the flexure of an elastic plate” Proc. London Math. Soc., vol. 21, no. 1, 1889, pp. 70-90.

[3] L. Rayleigh, “On waves propagateded along the surface of an elastic solid,” Proc. London Math. Soc., vol. 17, no. 1, 1887, pp.4-11.

[4] R. D. Mindlin, “Waves and vibrations in isotropic, elastic plates,” Proc. Symp. Naval Struct. Mech., 1960, pp. 199-232.

[5] M. A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range,” J. Acoust. Soc. Am., vol. 28, no. 2,1956, pp. 168-178.