Influence of Longitudinal Inertia of Mass Element on Non-Linear Component of Beam Natural Frequency |
| S. Uzny, Ł. Kutrowski, M. Osadnik
Czestochowa University of Technology, 42-201 Czestochowa, Poland |
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| In this paper the problem of non-linear vibrations of the beam was considered. A system with a mass element mounted at the end of the structure with a mass much larger than the mass of the beam was under consideration. This element during transverse vibrations generates additional longitudinal force associated with its inertia. The occurrence of this force results in the appearance of a non-linear relationship between the amplitude of vibration of the system and its natural frequency. The boundary problem of non-linear vibrations was formulated on the basis of the Hamilton principle, taking into account the Bernoulli-Euler theory and the non-linear relationship between deformation and displacement (von Karman theory). Numerical simulations were carried out taking into account the impact of longitudinal inertia of the mass element on the non-linear component of natural frequency at different amplitudes of beam vibrations. |
DOI:10.12693/APhysPolA.138.302 topics: free non-linear vibrations, beam, mass element |