Natural Frequency of Elastically Mounted Column Axially Loaded with Mass Element
S. Uzny, Ł. Kutrowski, M. Osadnik
Częstochowa University of Technology, 42-201 Częstochowa, Poland
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In this work, the influence of the loading method of an elastically mounted column on its natural frequency was investigated. The classic way to load these types of systems is to apply an axial force. In the presented approach, the load of the system in the form of a mass element was adopted, which much better reflects the real slender support system, whose task is to support a structure with a specific own weight. During the formulation of the boundary problem, Hamilton's principle and the perturbation small parameter method were used. A series of numerical simulations were carried out, taking into account the influence of the system parameters and the method of loading on the non-linear natural frequency. The main task was to determine the impact of the change in stiffness at mounting points of the system ends on the dynamic behaviour of the structure. It was shown that this stiffness has a significant impact on the natural frequency. It was also indicated that in the problem formulated in this way, the amplitude level of the induced system vibrations is of significant importance - which is not taken into account in the case of a force load. The knowledge of potential resonance frequencies in the case of slender support systems is one of the basic data taken into account in the design process of this type of structures due to their susceptibility to vibrations.

DOI:10.12693/APhysPolA.139.521
topics: free non-linear vibrations, column, mass element