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Article

Fischer, Cyril ; Náprstek, Jiří
Numerical solution of a stochastic model of a ball-type vibration absorber. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 40-49
MSC: 37A50, 60G15, 65C05, 65C20 | DOI: 10.21136/panm.2020.04
Keywords:
stochastic model; Monte Carlo method; stochastic Euler method; dynamical systems; non-holonomic system
Summary:
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
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