Natural frequencies of beams under compressive axial loads

Abstract

A study of the influence of a constant axial compressive load on natural frequencies and mode shapes of a uniform single-span beam with ten different combinations of end conditions is presented. The relative critical buckling load is found to be the same for sliding-free, clamped-free and sliding-pinned beams, and similarly for free-free, pinned-free, pinned-pinned, clamped-sliding and sliding-sliding beams. Analytical results indicate that the variation of normalized natural frequency with normalized axial force is exactly the same for pinned-pinned, pinned-sliding and sliding-sliding beams and can be expressed in a closed form. Numerical results show that this closed-form expression roughly describes the above variation for sliding-free, clamped-clamped and clamped-sliding beams in a fundamental vibration mode. Further, in this mode, apart from a region close to buckling, the above variation is almost the same for clamped-pinned, pinned-free and free-free beams. The above closed-form expression could also be used for a beam with any kind of end conditions when the beam vibrates in a high mode. It is observed that Galef's formula, previously assumed to be valid for beams with all types of end constraints, is valid only for a few.