Green’s functions for coupled boundary value problems

In this article the definition of Green’s function is extended for a class of coupled three-point boundary value problems. With the properties and construction steps clarified, the vibrations of stepped beams are in the spotlight. The related Green’s functions are given both for free vibrations and for axially pre-loaded vibrations as well. The corresponding coupled eigenvalue problems are substituted by eigenvalue problems governed by homogeneous Fredholm integral equations that are solved numerically by transforming them into algebraic eigenvalue problems.