Rj. Nagem et al., THE GENERAL AND ASYMPTOTIC SOLUTION OF THE ELASTIC WAVE-EQUATION IN AN UNBOUNDED MEDIUM, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 441(1911), 1993, pp. 157-167
Citations number
6
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
New forms and new properties are given for the general solution of the
three-dimensional dynamic equation for the displacement vector in an
isotropic linear elastic solid. The general initial value problem in a
n unbounded medium with no sources is solved. The general solution at
an arbitrary time is given in terms of two asymptotic vector fields. O
ne is thereby able to obtain the complete and exact solution, includin
g initial conditions, which corresponds to a specified or desired asym
ptotic solution, valid for large times in the future. The complete ela
stic field energy of an arbitrary exact solution is also shown to depe
nd, in a simple way, only on the two asymptotic vector fields.