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層狀橫向等向性介質之SH波傳基本解與反應研究

Fundamental Solutions and Responses for SH Waves in Transversely Isotropic Layered Media

作者:陳佳莉
畢業學校:國立聯合大學
出版單位:國立聯合大學
核准日期:2010-09-10
類型:Electronic Thesis or Dissertation
權限:Copyright information available at source archive--National United University....

中文摘要

本研究旨在以一般化射線法推導SH波於層狀橫向等向性介質中傳播的暫態反應解,並比較等向性與橫向等向性之層狀介質反應的異同性。本文首先引用變數變換法求解無限域介質中之位移反應的積分變換式,然後利用邊界條件及位移、應力的連續條件推導兩平行介質間的反射與透射係數,再將這些係數加入位移積分式中,以連乘積表示SH波於層狀介質中傳遞時所發生的反射及透射行為,此種表示法即為射線積分式。接著採用肯樣法(Cagniard method)求解SH波各個射線路徑積分式的逆拉氏變換,即可得SH波於橫向等向性介質中傳播之位移解。此解包含波源時間函數為脈衝函數與階梯函數的基本解,然後利用基本解與不同波源時間函數或其導數的摺積分即可求得任意波源時間函數的反應解。橫向等向性位移解中包含之主要參數為c_44(垂直向之剪力模數)及c_66(水平向之剪力模數),而在等向性介質中則c_44=c_66。
最後再以數值範例分析SH波在層狀橫向等向性介質的波傳反應,結果可得知在等向性層狀地層參數 〖μ=c〗_44固定的情況下,每一射線之波傳走時隨c=c_66⁄c_44 的比值而異,以1為分界點,當c值愈大波速則愈快,反之則變慢;因此導致位移反應無論是尖峰值的位置、數目及波形皆有很大的差異性。

英文摘要

The fundamental solutions and responses for transient SH waves in a transversely isotropic layered media are derived by using the generalized ray theory and the results are compared with the isotropic cases. Firstly, the variable transformation method are adopted to solve the transformed integral of the displacement in an infinite space, then the boundary conditions and the displacement and stress continuity conditions at the interface between two parallel media are used to derive the transmission and reflection coefficients. Thus the process of transmission and reflection at each interface can be simply represented by the coefficients. The integral imposed with the coefficients multiplied by each other is referred to as a generalized ray integral. Finally the displacements in a transversely isotropic laminates can be obtained by applying the Cagniard s method to solve the inverse Laplace transform of each ray integral. Also two fundamental solutions are derived from two source time functions of which are the Dirac delta function and the step function, respectively. Moreover the responses of the general source time function can be also obtained from the convolution of the fundamental solutions with the source time function or its derivatives. The major elastic constants for SH waves in the transversely isotropic media are c_44 and c_66 where c_44 = c_66 in the isotropic cases. Numerical results show that the ray velocity will get faster when the ratio of c_66⁄c_44 becomes larger as the parameters 〖 =c〗_44 of isotropic layered media are fixed, and hence the peaks and waveforms are quite different with each other.

 

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