Reordering of vertical vibration modes in an axially compressed beam on a Winkler foundation

Abstract

This study reveals a special vibration characteristic of an axially compressed Timoshenko beam on a Winkler foundation, namely that the vibration configuration in the sequence of the natural frequencies may undergo a reordering in response to changes in certain parameters. New explicit analytical expressions of the natural frequencies are derived, which considers both the shear and rotatory inertia effects in the beam. The key independent dimensionless parameters that control the modal reordering phenomenon are then identified from the resulting frequency. By examining the vibration response of structures with various parameters over the full range of axial loads, it is observed that the frequencies of some initial low- and high-order vibration modes approach each other and then veer away, thus causing a reordering in the vibration modes. The fundamental reason for the occurrence of this phenomenon is also discussed in detail. Finally, the effect of the key structural parameters is investigated, it is shown that the structure having a greater slenderness ratio or a greater relative stiffness between the foundation and beam is more prone to experience a vibration modal reordering under axial pressure.