Stochastic response of flexible rotor-bearing system to seismic excitations

Abstract

Random vibration analysis of flexible rotor-bearing systems subjected to six-component nonstationary earthquake ground accelerations is carried out. The rotor system consists of several rigid disks and a flexible shaft that is modelled as a Timoshenko beam. The governing equations of motion involve both inhomogeneous random excitations and random parametric excitations. Analytically, the Markov vector approach using the Ito equation and Stratonovich averaging procedures is employed to determine the response statistics. Unfortunately, the second moments of the response quantities thus obtained involve a great discrepancy when compared with the results of Monte Carlo simulation. The difficulty involved in analytically solving such a complicated problem is pointed out. Currently, the method of Monte Carlo simulation appears to be the only practical approach for such a problem. The significant influence of the seismic base rotations and the flexibility of the rotor-bearing system on the overall dynamic structural response is demonstrated by a numerical example.