Steady-State Transonic Motion of a Line Load Over an Elastic Half-Space: The Corrected Cole/Huth Solution

Abstract

Similarly, the boundary condition is free from applied stress and the media are £ = 0.2,-n = 0.8. By truncating the infinite algebraic Eq. (3.16) to n = s = 3 for K a a = 0.1 and n = 5 = 4 for K a a = 1.0, 2.0, we find the coefficients A". Figures 2 and 3 show the results of stress concentration factors of calculation. Now, we conclude this paper with the following discussions: (a) From the numerical results indicated above, we can see that the effect of anisotropy on dynamic stress concentration is quite significant in engineering sense. (b) The convergence of Eq. (3.16) depends on wave number K a a and on cavity shapes. For low K a a, a few terms of the series are sufficient; while for high K a a, the convergence is rather slow. So, in this case, the number of terms needed becomes large in order to get reasonably good results. (c) For the square cavity case, the mapping function (4.2) maps the unit circle only to "nearly square cavity" with corners as shown in the figure attached. Such shape of course misses the character of sharp corners. This is the weak point of the method of mapping as noted universally in static case. Increasing the number of terms of the mapping functions is a way to make the corners of the figure rather sharp.

On the super-Rayleigh/subseismic elastodynamic indentation problem

“…However, we should remark that we cannot control 3It is worth noting that the error in Cole and Huth's results demonstrated in [5] was discovered as a result of an apparent lack of consistency between the predictions of equation (2.11) and the asymptotic behaviour observable in other elastodynamic contact and fracture problems.…”

Ground Vibration in the Vicinity of a High-Speed Moving Harmonic Strip Load

“…Cole and Huth [3], considered the same problem for a constant normal line load and obtained analytical forms for the solutions for the displacements, for the subsonic, transonic and supersonic cases, using a Helmholtz decomposition. Georgiadis and Barber [4], corrected the Cole and Huth solution for transonic regime. Fryba [5], also investigated the possibility of shocks in the ground due to a line load moving at constant speed at or beyond the Rayleigh wave speed.…”

Surface responses induced by point load or uniform traction moving steadily on an anisotropic half-plane

“…A more general problem of an inclined point load, i.e., problem for both vertical and horizontal point loads, was given by Eringen and Suhubi (1975). An error in the transonic range given by Cole and Huth (1958) and Eringen and Suhubi (1975) was corrected by Georgiadis and Barber (1993) and Rahman (2001). For three dimensional elastic half-space isotropic solids, the steady state responses with forces moving on the surface have been treated by Eason (1965), 0020-7683/$ -see front matter Ó 2008 Elsevier Ltd. All rights reserved.…”