Premium
Nonlinear random vibrations of a rotating shaft
Author(s) -
Dimentberg M.F.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310169
Subject(s) - nonlinear system , vibration , instability , restoring force , physics , classical mechanics , mechanics , excitation , random vibration , bending , control theory (sociology) , acoustics , computer science , quantum mechanics , control (management) , artificial intelligence , thermodynamics
Bending vibrations of a rotating shaft due to external random excitation are considered for the case of potential instability of the shaft's linear model due to presence of internal or “rotating” damping. A two‐degree‐of‐freedom model with nonlinear elastic restoring forces is studied. An explicit expression is obtained for a stationary joint probability density of displacements and velocities as an exact analytical solution to the corresponding Fokker‐Planck‐Kolmogorov equation. The results are used to develop criterion for on‐line detection of instability for the operating shaft from its measured response.