### Abstract

Vibrations of systems with instantaneous or stepwise energy losses,
e.g., due to impacts with imperfect rebounds, dry friction forces(s) (in
which case the losses may be treated as instantaneous ones by
appropriate introduction of the response energy) and/or active feedback
“bang-bang” control of the systems' response are
considered. Response of such (non-linear) systems to a white-noise
random excitation is considered for the case where there are no other
response energy losses. Thus, a simple linear energy growth with time
between “jumps” is observed. Explicit expressions for the
expected response energy are derived by direct application of the
stochastic differential equations calculus, which contains the expected
time interval between two consecutive jumps. The latter may be predicted
as a solution to the relevant first-passage problem. Perturbational
analysis of the relevant PDE for this problem for a certain vibroimpact
system demonstrated the possibility for using the solution to the
corresponding free vibration problem as a zero order approximation. The
method is applied to an s.d.o.f. system with a feedback inertia control,
designed according to a certain previously introduced “generalized
reversed swings law”. Extensive Monte-Carlo simulation results are
presented for this system as well as for several previously analyzed
ones: system with impacts; system with dry friction; system with
stiffness control; pendulum with controlled length. The results are
compared with those due to the asymptotic stochastic averaging approach.
Both methods are shown to provide adequate accuracy far beyond the
expected applicability range of the asymptotic approach (which requires
both excitation intensity and losses to be small), with direct energy
balance being generally superior.

Original language | English |
---|---|

Pages (from-to) | 913-923 |

Journal | Journal of Sound and Vibration |

Volume | 248 |

Issue number | 5 |

DOIs | |

Publication status | Published - 13 Dec 2001 |

## Fingerprint Dive into the research topics of 'Energy Balance for Random Vibrations of Piecewise-Conservative Systems'. Together they form a unique fingerprint.

## Cite this

Yurchenko, D., & Dimentberg, M. F. (2001). Energy Balance for Random Vibrations of Piecewise-Conservative Systems.

*Journal of Sound and Vibration*,*248*(5), 913-923. https://doi.org/10.1006/jsvi.2001.3853