Coupling of the flexural, longitudinal, and torsional vibration modes of a column subjected to periodic axial loading was analytically and experimentally investigated. The initial crookedness of the column and longitudinal inertia give rise to coupled flexural-longitudinal vibrations. Further, the Weber effect and longitudinal inertia result in coupling between longitudinal and torsional oscillations. To assess the validity of the theory, an experimental apparatus was set up to axially excite a

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... column using a vibration control generator and an electromagnetic shaker. The experimental results were in good agreement with the theoretical predictions. Coupled longitudinal vibrations exhibiting a frequency ratio of 1:2 were observed. Coupled flexural oscillations were also observed, though a frequency ratio was not established. Further, the experimental results suggest that coupled vibrations other than those theoretically expected were present. In particular, a longitudinal coupled vibration with a frequency ratio of 1:3 was observed, and a corresponding coupled flexural oscillation was present. A coupled torsional mode was experimentally observed when the applied frequency was twice the fundamental torsional frequency. A second coupled torsional mode appeared when the excitation frequency was three times the fundamental torsional frequency. The phase relationship between the coupled vibrations was observed. The resonant coupled vibrations were found to be significant at certain frequencies.