Vibration of an axially loaded heterogeneous fixed–fixed beam with an intermediate roller support

Abstract

The present paper investigates how an axial load can change the natural frequencies of heterogeneous fixed–fixed beams with an intermediate roller support. The problem is treated as a three-point boundary value problem (eigenvalue problem) that is paired with homogeneous boundary conditions. The Green functions are determined for the unloaded and pre-loaded beams as well—in the later case, both for compression and tension. With these, the eigenvalue problems can be transformed into eigenvalue problems governed by a homogeneous Fredholm integral equations. It is then replaced by an algebraic eigenvalue problem, that is solved numerically with an effective solution algorithm which is based on the boundary element method.