Basic Theorems in Dynamic Elasticity - UNAM

Representation TheoremsA representation theorem is a formula for the displacement field (at ageneral point in space and time) in terms of quantities that originatedthe motion. As stated by the uniqueness theorem, these quantities maybe body forces within V and applied tractions or displacements over S.Integrated Betti’s TheoremIf we substitute into Betti’s theorem g i = δ in δ(x-ξ) δ(t) for which thecorresponding solution is v i = G in (x,t ; ξ,0) we obtain a formula for u n (x,t)First Representation TheoremUseful Hint