A Novel Approach to Elastodynamics: II. The Three-Dimensional Case

Details A Novel Approach to Elastodynamics: II. The Three-Dimensional Case A Novel Approach to Elastodynamics: II. The Three-Dimensional Case

2010-10-14

arxiv.org/abs/1010.2947v1

Mathematics

Analysis of PDEs

Scientific paper

A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying arbitrary initial conditions and Lamb's boundary conditions. A particular case of this problem, namely the case of homogeneous initial conditions and normal point load boundary conditions, was first solved by Lamb using the Fourier-Laplace transform. The general problem solved here can also be analysed via the Fourier transform, but in this case, the solution representation involves transforms of \textit{unknown} boundary values; this necessitates the formulation and solution of a cumbersome auxiliary problem, which expresses the unknown boundary values in terms of the Laplace transform of the given boundary data. The new approach, which is applicable to arbitrary initial and boundary conditions, bypasses the above auxiliary problem and expresses the solutions directly in terms of the given initial and boundary conditions.

Affiliated with

Also associated with

No associations

Rating

A Novel Approach to Elastodynamics: II. The Three-Dimensional Case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Novel Approach to Elastodynamics: II. The Three-Dimensional Case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Novel Approach to Elastodynamics: II. The Three-Dimensional Case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285997