Proceedings Vol. 19 (2013)
ENGINEERING MECHANICS 2013
May 13 – 16, 2013, Svratka, Czech Republic
Copyright © 2013 Institute of Thermomechanics, Academy of Sciences of the Czech Republic, v.v.i., Prague
ISSN 1805-8248 (printed)
ISSN 1805-8256 (electronic)
list of papers scientific commitee
pages 390 - 398, full text
The set of a heavy metallic ball which is rolling freely inside a semispherical dish with larger diameter, being fixed to structure, is frequently used as tuned mass damper of vibration. Ratio of both diameters, mass of the rolling ball, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The ball damper is modelled as a non-holonomic system. Hamiltonian functional including an adequate form of the Rayleigh function is formulated in moving coordinates using Euler angles and completed by ancillary constraints via Lagrangian multipliers. Subsequently Lagrangian differential system is carried out. Together with rolling conditions the governing system of seven equations is formulated. Later Lagrangian multipliers character is analysed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation. Discussion of basic dynamic properties of the system is provided.
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