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

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.