Identification of Structural Nonlinear Dynamic Behavior of Flexible Metallic Columns Under the Action of Self-Weight

Abstract

This work presents a numerical and experimental methodologies specially developed for nonlinear free vibration analysis of very flexible structures. In this work, a clamped-free thin-walled metal column under the action of self-weight is investigated. This structure is characterized for presenting, in most cases, highly nonlinear responses, which can not be reproduced by conventional finite-element software due, mainly, to inertial non-linearities caused by the presence of the “sof tening phenomeno n”. This phenomeno n is related to the lo ss of s tiffness due to the influence of the selfweight together with large rotations, which are inherent to the free vibrations of columns with a high slenderness ratio, leading to important inertial non-linearities. Thus, to overcome this problem, the column is discretized as a sequence of coupled pendulums, retaining the main non-linearities of the problem. The resulting Euler-Lagrange Equations of Motion are solved by the Runge-Kutta integration technique, taking into account the inclusion of the non-linear terms associated to the stiffness of the structural system, aiming to obtain more accurate results, principally, for columns with lengths higher than the critical one. In order to verify the applicability and efficiency of the developed numerical methodology, several experimental free vibration assays were conducted considering the slender metallic column subject to its own weight, in the pre- and post-buckling regimes. As this kind of structure presents a high index of slenderness, its responses can be affected by the introduction of conventional sensors. Therefore, the developed experimental methodology is based on a computerbased vision system that integrates, on-line, the digital image acquisition and its treatment using special image processing techniques. The main characteristic of this methodology is that it performs large displacements measurements without making contact with the structure and thus, not introducing undesirable changes in its behavior, for instance, appreciable changes in mass and stiffness properties. The obtained numerical results presented excellent correlation with the experimental ones, in the pre- and post-buckling regimes, co nsidering the “sof tening phenomeno n”.