Vibration of an axially loaded heterogeneous pinned-pinned beam with an intermediate roller support

The present paper is devoted to the issue of what effect the axial load (compressive or tensile) has on the eigenfrequencies of a heterogeneous pinned-pinned beam with an intermediate roller support (called a PrsP beam). This problem is a three point boundary value problem (eigenvalue problem) associated with homogeneous boundary conditions. If the Green functions of the three point boundary value problem (BVP) are known the eigenvalue problem that provide the eigenfrequencies for the beam loaded axially can be transformed into an eigenvalue problem governed by a homogeneous Fredholm integral equation. The later eigenvalue problems can be reduced to an algebraic eigenvalue problem which then can be solved numerically by using an effective solution algorithm which is based on the boundary element method.