On the Green function of an orthotropic clamped plate in a half-plane

Abstract

First, we calculate, in a heuristic manner, the Green function of an orthotropic plate in a half-plane which is clamped along the boundary. We then justify the solution and generalize our approach to operators of the form (Q(partial ')-a^2partial _n^2)(Q(partial ')-b^2partial _n^2) (where partial '=(partial _1,dots ,partial _{n-1}) and a>0,b>0,ane b) with respect to Dirichlet boundary conditions at x_n=0. The Green function G_xi is represented by a linear combination of fundamental solutions E^c of Q(partial ')(Q(partial ')-c^2partial _n^2),cin {a,b}, that are shifted to the source point xi , to the mirror point -xi , and to the two additional points -frac{a}{b}xi and -frac{b}{a}xi , respectively.