Fundamental boundary matrices for 36 elementary boundary value problems of finite beam deflection on elastic foundation

Abstract

We consider the boundary value problem of finite beam deflection on elastic foundation with two point boundary conditions of the form $ u^{(p)}(-l) = u^{(q)}(-l) = u^{(r)}(l) = u^{(s)}(l) = 0 $, $ p < q $, $ r < s $, which we call elementary. We explicitly compute the fundamental boundary matrices corresponding to 7 special elementary boundary conditions called the dwarfs, and show that the fundamental boundary matrices for the whole 36 elementary boundary conditions can be derived from those for the seven dwarfs.

Keywords

• beam
• boundary matrix
• characteristic equation
• deflection
• dwarf
• elastic foundation
• fundamental boundary matrix
• integral operator
• spectrum