Original title: Analytic model of a ball rolling on a spherical surface under harmonic kinematic excitation
Authors: Náprstek, Jiří ; Fischer, Cyril
Document type: Papers
Conference/Event: Colloquium Dynamics of Machines 2013, Praha (CZ), 2013-02-05 / 2013-02-06
Year: 2013
Language: eng
Abstract: The set of a heavy metallic ball which is rolling freely inside a semi-spherical 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 modeled 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 analyzed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation.
Keywords: Hamilton functional with constrains; moving coordinates; non-holonomic systems; non-linear vibration; vibration ball absorber
Project no.: IAA200710902 (CEP), GA103/09/0094 (CEP)
Funding provider: GA AV ČR, GA ČR
Host item entry: Dynamika strojů 2013, ISBN 978-80-87012-44-4

Institution: Institute of Theoretical and Applied Mechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0218053

Permalink: http://www.nusl.cz/ntk/nusl-150402


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Research > Institutes ASCR > Institute of Theoretical and Applied Mechanics
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