Abstract
Purpose: development of a mathematical model of vibrations for a rod carrying an attached mass, based on the general equation for rod vibrations.
Design/methodology/approach: This paper deals with vibration of a rod carrying a small attached mass in a nonlinear formulation. Rod systems are widely used in construction. Masts, towers, television broadcast stations, TV towers, vertical pipes, etc. These structures often have balconies, antennas, and other elements which influence the vibrational state of the entire structure. Neglecting this component during structural analysis leads to accidents and casualties, which should be avoided. Accidents involving these structures have occurred throughout history. In order to prevent such accidents, the analysis process should be improved based on a better insight into the shell oscillatory mechanism. Development of a new mathematical model is based on the general equation for vibrations. Consideration has been given to the attachment point of the attached mass and influence of such mass on the natural frequency response. The first and second natural frequencies have been determined. It has also been determined that the presence of a small attached mass acts as a factor which triggers interaction between the bending and radial modes.
Findings: The article presents a new vibration analysis model for a rod carrying an attached mass.
Originality/value: The new mathematical model can be used for structural analysis and in design bureaus carrying out vibration analysis for rods and rod structures.
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The study was carried out using the equipment of the Center for Collective Use “New Materials and Technologies” on the basis of KnASU.
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Sysoev, E.O., Dobryshkin, A.Y. (2021). Vibrations of a Rod Carrying a Small Attached Mass. In: Shakirova, O.G., Bashkov, O.V., Khusainov, A.A. (eds) Current Problems and Ways of Industry Development: Equipment and Technologies. Lecture Notes in Networks and Systems, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-69421-0_18
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DOI: https://doi.org/10.1007/978-3-030-69421-0_18
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