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Response statistics of nonlinear rotating shaft subject to biaxial random excitation
Last modified: 2017-05-22
Abstract
Random vibrations is studied for a Jeffcott rotor under biaxial white noise excitation. The restoring force is modelled as elastic non-linear. Comparison is done with available exact analytical solution to validate the accuracy of the proposed numerical technique. The statistics of non-linear oscillations is studied by applying the path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker–Planck-Kolmogorov (FPK) equation for the 4D dynamic system.
An efficient implementation of the PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate the dynamic system additive noise. The latter allows significant reduction of the computational time, compared to the classical PI.
The excitation is modelled as Gaussian white noise, however any kind white noise can be implemented with the same PI technique.
PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of the dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in the mechanical model of the rotor.
The potential application area of the studied mechanical problem is the design of a liquid-propellant turbo pump rocket engine.
The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
An efficient implementation of the PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate the dynamic system additive noise. The latter allows significant reduction of the computational time, compared to the classical PI.
The excitation is modelled as Gaussian white noise, however any kind white noise can be implemented with the same PI technique.
PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of the dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in the mechanical model of the rotor.
The potential application area of the studied mechanical problem is the design of a liquid-propellant turbo pump rocket engine.
The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.