ISSN:
0170-4214
Schlagwort(e):
Mathematics and Statistics
;
Applied Mathematics
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
Notizen:
One considers an elastic halfspace with depth (x1) dependent density Q and Lamé moduli (λ,m̈). Impulsive stresses τli = δ(x2, x3)δ(t) for x1 = 0 are applied with displacement responses ui = gi(t, x2, x3) at x1 = 0 (i = 1, 2, 3). Let vi(t, x1) = ∫∫uidx2dx3 (i = 1, 2 is enough) and set w(t, x1) = ∫∫x2u1dx2dx3. One obtains a system of 3 differential equations for v1, v2, and w to which the spectral techniques of inverse scattering theory are applied as in [25]. The inverse problems for the uncoupled vi can then be solved to produce 2 functions A1 and A2 involving (Q, λ, μ) as functions of “bound” variables y1 and y2 containing (Q, λ, μ), between which a relation then is determined. Analysis of the coupled equation for w then leads to a Fredholm integral equation whose solution provides an additional relation between (Q, λ, μ) from which (Q, λ, μ) can be determined as functions of x1. The integral equation is reduced to a Volterra type equation by results and techniques of transmutation and then solved by a modification of standard techniques. A number of features and results of independent mathematical interest arise from the transmutation theory.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1002/mma.1670040105
Permalink
