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 half-plane which is clamped along boundary. We then justify solution and generalize our approach to operators form $$(Q(\partial ')-a^2\partial _n^2)(Q(\partial ')-b^2\partial _n^2)$$ ( Q ∂ ′ ) - a 2 n b (where $$\partial '=(\partial _1,\dots ,\partial _{n-1})$$ = 1 , ⋯ $$a>0,b>0,a\ne b)$$ > 0 ≠ with respect Dirichlet boundary conditions at $$x_n=0.$$ x . The $$G_\xi $$ G ξ represented by linear combination fundamental solutions $$E^c$$ E c $$Q(\partial ')(Q(\partial ')-c^2\partial _n^2),$$ $$c\in \{a,b\},$$ ∈ { } that are shifted source point $$\xi ,$$ mirror $$-\xi two additional points $$-\frac{a}{b}\xi $$-\frac{b}{a}\xi respectively.