彈性半無限域承受旋轉表面力之暫態反應

Transient Response of an Elastic Half Space Subjected to Rotating Surface Forces

林家豪(Chia-Hao Lin)

指導教授 ： 葉超雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.03213

摘要

本文分析一沿圓周路徑等速移動之衝擊表面力，對彈性半無窮域所造成的暫態反應。分為兩主題，分別探討扭矩問題和垂直集中力問題；目的在於了解以旋轉型式移動之波源， 在不同移動速度下，對於彈性介質所造成的反應及波傳現象。
扭矩問題部分，在直角座標系統下，以Laplace轉換及Fourier轉換法求得頻率域之反應通解，進行積分反轉換時，分別考慮波之到達時間函數單值或多值情形，
搭配Cagniard-de Hoop法進行Laplace逆轉換求得時間域反應解析解；並分析表面位移數值結果及波傳現象。
垂直集中力問題部分，在圓柱座標系統下，以Laplace轉換及Hankel轉換法求得頻率域之反應通解，進行積分反轉換時，受限於待積函數過於複雜，無法再使用前人之方法求取解析解；因此在複數平面上選取一條最佳收斂的等效路徑，搭配數值積分方法如:高斯積分法及Durbin法，進行積分反轉換，求得表面位移數值結果。
本文對於兩個不同的非軸對稱問題，提供了不同的分析方法，除了得到解析解外，無法使用過去解析方法解決的問題，也以數值積分方法得到良好合理的結果。

關鍵字

衝擊表面力 ； 半無窮域 ； 暫態反應 ； 移動型波源 ； Cagniard-de Hoop法 ； Durbin法

並列摘要

In this thesis,we present the analysis of transient
response of an elastic half space due to impulsive surface loading moving with a constant speed along a circular path.Dividing into two topics,they are torsion problem and point force problem;our purpose is to find out the surface response and wave patterns of an elastic medium sujected to moving sources with different moving speed.
On torsion problem,in Cartisian coordinate system,we derive the general solution of the response in frequency domain by Laplace transform and Fourier transform method,in the process of integral inversion,consider the arrival time function in single-valued or multi-valued separately,we derive the analytic solution of displacements in time domain by Cagniard-de Hoop method,which is used to deal with the Laplace inversion.We also analyze the numerical results of surface displacements and wave patterns.
On point force problem,in cylindrical coordinate system,we
derive the general solution of the response in frequency domain by Laplace transform and Hankel transform method,in the process of integral inversion,limited by highly complexity of the integrand,we can't derive the analytic solution by previous methods.Therefore,we choose the best convergent path in complex plane,with numerical integration methods such as Gaussian quadrature and Durbin method to carry out integral inversion,then we obtain numerical results of surface displacements.
We provide different approches for two non-axisymmetric problems.Besides analytic solutions,proper and reasonable results are obtained by using numerical integration methods, including the unsolved problems by using analytic approachs in the past.

並列關鍵字

impulsive surface loading ； half space ； transient response ； moving source ； Cagniard-de Hoop method ； Durbin method

參考文獻

[21]利岳聲, 半無限域表面承受集中載荷的瞬間解， 國立台灣大學土木工程研究所碩士論文(2009)

[1]Reissner, E. and Sagoci, H. F., Forced Torsional Oscillations of an Elastic Half Space.I, J. Appl. Phys,Vol.15, pp.652-654, 1944.

[2]Sagoci, H. F., Forced Torsional Oscillations of an Elastic Half Space.II, J. Appl. Phys,

[3]Eason, G., On the torsional impulsive loading of an elstic half-space, Q. J. Mech. and Appl. Mech. Vol.17, pp.279-292, 1964.

[4]Pekeris, C. & Alterman, Z. and Abramovici, F., Propagation of SH-torque pulse in a layered solid, Bul. Seism. Soc. Am. Vol.53, pp.39-57, 1963.