Coupling of axial and transverse displacement fields in a straight beam due to boundary conditions

A classical simply-supported beam is modified by tilting the pad constraining the roller. The consequence is that the axial and transverse displacements of the beam are coupled by the boundary conditions. The eigenanalysis methodology is extended to this unusual situation where displacement components are coupled, even though each displacement has a different associated wavenumber. The dependence of the natural frequencies on the tilt angle is evaluated and typical results for the eigenfunctions are presented. The response of the beam to harmonic point force excitation is synthesized by constructing a modal series. Frequency response functions at the drive point for cases where the force is applied in the axial and transverse directions are computed. The results indicate that deviations of the tilt angle from zero affect the displacement in the direction that is orthogonal to the excitation much more than the driven displacement.