Stochastically perturbed rotating shafts

Lalit Vedula, N. Sri Namachchivaya

Research output: Contribution to conferencePaperpeer-review


The objective of this work is to study the long term effects of small symmetry-breaking, dissipative and noisy perturbations on the dynamics of a rotating shaft. Hamilton's principle is used to derive the equations of motion and a one mode Galerkin approximation is applied to obtain a two-degree-of-freedom (four dimensional) model. A stochastic averaging method is developed to reduce the dimension of this four dimensional system. Making use of the interaction between the gyroscopic and dissipative forces and the separation of time scales, the original system is reduced to a one dimensional Markov process. Depending on the system parameters, the reduced Markov process takes its values on a line or a graph. For the latter case, the glueing conditions required to complete the description of the problem in the reduced space are derived. This provides a qualitatively accurate and computationally feasible description of the system. Analytical results are obtained for the mean first passage time problem. The stationary probability density is obtained by solving the Fokker Planck Equation(FPE). Finally, the qualitative changes in the stationary density as a result of varying the system parameters are described.

Original languageEnglish (US)
Number of pages10
StatePublished - 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001


Other18th Biennial Conference on Mechanical Vibration and Noise
Country/TerritoryUnited States
CityPittsburgh, PA

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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