Numerical studies of dynamic stability under small random parametric excitations

  • Roman V. Bobryk Institute of Mathematics, Jan Kochanowski University
  • Andrzej Chrzeszczyk Institute of Mathematics, Jan Kochanowski University

Abstract

An efficient numerical procedure is proposed to obtain mean-square stability regions for both single-degree-of-freedom and two-degree-of-freedom linear systems under parametric bounded noise excitation. This procedure reduces the stability problem to a matrix eigenvalue problem. Using this approach, ranges of applicability to the well-known stochastic averaging method are discussed. Numerical results show that the small parameter size in the stochastic averaging method can have a significant effect on the stability regions. The influence of noise on the shape of simple and combination parametric resonances is studied.

Keywords

random vibration, stochastic averaging, mean square stability, bounded noise,

References

Published
Jan 25, 2017
How to Cite
BOBRYK, Roman V.; CHRZESZCZYK, Andrzej. Numerical studies of dynamic stability under small random parametric excitations. Computer Assisted Methods in Engineering and Science, [S.l.], v. 17, n. 2/3/4, p. 89–97, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/125>. Date accessed: 26 jan. 2022.
Section
Articles