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題名 | 水平剪力波在吉普生土層中之解析解=Analgtical Solution of the Response of Gibson Soil Induced by SH Wave |
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作者 | 陳正興; 陳立言; 黃俊鴻; Chen, Cheng-hsing; Chen, Li-yen; Huang, Jing-hung; |
期刊 | 高苑學報 |
出版日期 | 19960200 |
卷期 | 5:1 1996.02[民85.02] |
頁次 | 頁233-241 |
分類號 | 441.12 |
語文 | chi |
關鍵詞 | 吉普生土壤; 水平剪力波; 轉換函數; |
中文摘要 | 吉普生土壤係指剪力模數G 隨地層深度X 呈線性增加之土壤,即G (X) =G+ α X。本文提出水平剪力波垂直入射於吉普生土層之解析解。藉由變 數變換,剪力波傳經吉普生土層時,其運動方程式可表示為零階之 Bessel 方程式,其解析解為以剪力模數 G(X) 之平方根為變數之 Bessel 函數,當 α趨近於 0 時,吉普生土層趨近於均勻土層,故其通解亦逼近於均勻土層之 解析解。本文所推得之方程式可直接用來計算吉普生土層之轉換函數,卓越 頻率及振等模態等。 |
英文摘要 | The Gibson soil was named for a soil profile having its shear modulus linearly increasing along ground depth, i.e., G(x)=G+ α x. This paper presents the analytical solution for SH wave vertically propagating through a Gibson soil. Under the condition of harmonic vibration, the equation of motion for the prescribed problem can be expressed as a Bessel's equation of order zero by using the technique of change of variables. The analytical solution is of the form of Bessel functions with their arguments proportional to the square root of the shear modulus G(x). When α approaches zero, the asymptotic solution will approach the analytical solution of an uniform soil already published elsewhere. The analytical solution derived herein can be used to calculate the transfer functions, the modal frequencies and associated modal shapes of a vibrating Gibson soil layer. |
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