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Investigation on nonlinear coupled vibration of columns. Bridicko, Jan

Abstract

The oscillation of a column subjected to periodic axial end excitation was analytically and experimentally investigated. The initial crookedness of the column and the longitudinal inertia of a column element give rise to coupled, longitudinal-flexural oscillations. A snap-thru phenomenon and complex subharmonics of natural flexural modes of oscillation also occur at certain axial end excitation frequencies. Furthermore; at certain excitation frequencies, a coupling between longitudinal and torsional oscillations is found to exist. A theory providing qualitative and quantitative information about coupled longitudinal-flexural oscillations and complex subharmonics was developed for a column with hinged ends. In order to test the validity of the theory an experimental apparatus was set up to excite the column axially, with transducers monitoring the response of the column. The experimental results were in very good agreement with the theoretical predictions. A column with built-in ends was also tested and its response was similar to the column with hinged ends. Thus, the results of the experimental investigation suggest that the results of the theory developed for a column with hinged ends are also applicable to a column with built-in ends. Coupled longitudinal-flexural oscillations were observed when the axial end excitation frequency was equal to the natural longitudinal frequency of the column. Large amplitude oscillations in both longitudinal and flexural vibration modes occurred at this frequency. When the frequency of axial end excitation was equal to the natural flexural frequencies of the column, large amplitude flexural oscillations resulted, Flexural oscillations were also observed when the frequency of the axial end excitation was one half, one third, …. up to one eighth of the natural flexural frequencies of the column, A spectrum analysis of the strain signal showed that the flexural response then comprised two fundamental motions, one with the frequency of the axial excitation and one with frequency equal to the associated natural frequency. The resulting amplitudes of flexural oscillations at these frequencies were smaller than those observed when the frequency of the axial end excitation was equal to the natural flexural frequencies of the column. The flexural oscillations occurring at these axial end excitation frequencies were identified as the complex subharmonics of natural flexural frequencies, A snap-thru phenomenon occurred when the axial end excitation frequency was twice the frequency of natural flexural frequencies. Under certain circumstances the column then oscillated flexurally with one half of the excitation frequency. The amplitudes of flexural oscillations were comparable to those occurring when the frequency of the axial end excitation was equal to natural flexural frequencies of the column. Large amplitude flexural oscillations occurring at natural flexural frequencies, complex subharmonics and snap-thru phenomena, though excited by the axial end excitation, did not cause appreciable increase in amplitudes of longitudinal oscillations. Finally, large amplitude torsional oscillations occurred when the axial end excitation was of the same frequency as the predicted torsional natural frequencies. Again no appreciable increase in amplitudes of longitudinal oscillations was observed. Flexural oscillation phenomena here described, also occurred during flexural in-plane oscillation of a column.

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