Study on the SH-Waves Scattering from a Shallow Elliptic Layered Sedimentary Valley

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Project title

Code/計畫編號

NSC100-2221-E019-041

Translated Name/計畫中文名

淺橢圓沈積層山谷SH波散射之研究

Project Coordinator/計畫主持人

Deng-How Tsaur

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2345657

Year

2011

Start date/計畫起

01-08-2011

Expected Completion/計畫迄

31-07-2012

Bugetid/研究經費

400千元

ResearchField/研究領域

土木水利工程

"對於沉積層山谷SH 波散射問題，過去已有學者針對“圓弧形＂及“共焦橢圓形＂這兩種形狀做過探討，而有關“非共焦橢圓形＂的例子則是比較少見。從推導級數解的角度來看，“圓弧形＂的例子僅需以Bessel、Hankel 及三角函數等簡單函數即可推得；而“共焦＂與“非共焦＂橢圓形的例子，雖然皆以較複雜的Mathieu 函數來處理，可是， “共焦＂的情況並不需要進行座標變換即可求解，換言之，極複雜的Mathieu 函數加法公式並不會使用到，所以，相對於“非共焦＂的情況來說，“共焦＂的例子是比較容易處理的。或許，這就是“非共焦＂橢圓形問題之級數解顯少出現的緣故。因此，為了得到比“圓弧形＂及“共焦橢圓形＂更具一般性的結果，在上年度執行《半橢圓形部分填滿沖積山谷SH 波散射問題之研究(NSC 99-2221-E-019-017)》的基礎上，本計畫擬針對《淺橢圓沉積層山谷之SH 波散射問題》，以理論解析的方式，配合Mathieu 函數的加法公式，或適當的座標變換公式，推導出此問題的級數解，其可求解共焦及非共焦橢圓形的情況。再者，擬探討不同入射波頻率、角度及沉積層之密度、剪力波速等參數改變時，其對地動反應特性的影響。最後，本計畫之計算結果應可提供給其他數值方法及相關地震工程研究做參考。" "Scattering problems induced by layered sedimentary valleys of circular-arc and confocal elliptic cross-section had been studied by some researchers. However, the cases of non-confocal elliptic shapes were rarely investigated in the literature. From the viewpoint of deriving series solutions to these problems, only simple functions, such as Bessel, Hankel and trigonometric functions, are involved in the circular-arc cases. Although complicated Mathieu functions have to be introduced in both the cases of confocal and non-confocal elliptic shapes, coordinate transformations are unnecessary for confocal cases. In other words, the usages of very complicated addition formulas of Mathieu functions are precluded. Hence, the treatment of confocal cases is easier than that of non-confocal cases. Maybe, this is the reason that series solutions to non-confocal elliptic problems are scarce. Thus, to get solutions more general than those to the circular-arc and confocal elliptic cases, the present project is mainly aimed at solving scattering problems triggered by a shallow elliptic layered sedimentary valley. Based on the performance of the project in the last year, entitled ‘Study on the SH-waves scattering from a partially filled semi-elliptical alluvial valley (NSC 99-2221-E-019-017)’, the methodology of theoretical analysis is exploited again herein. Addition formulas of Mathieu functions and appropriate formulas of coordinate transformations are adopted to derive series solutions to the problems under consideration, including the confocal and non-confocal elliptic cases. Furthermore, the effects of the frequency and angle of incidence of incident waves, and the density and shear wave velocity of the sedimentary layer on the characteristics of ground motions are analyzed and discussed. In addition, computed results of this project can serve as a cross-reference for other numerical methods and researches pertaining to earthquake engineering."

Keyword(s)

SH 波
散射
沉積山谷
馬修函數
SH waves
scattering
sedimentary valley
Mathieu function

DSpace CRIS

Study on the SH-Waves Scattering from a Shallow Elliptic Layered Sedimentary Valley

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