Rotating shaft's non-linear response statistics under biaxial random excitation, by path integration

The response of rotating shaft to random excitations is of practical concern for various rotor type engine design applications, with high level of potential external forces of stochastic nature. Authors have studied extreme value statistics of random vibrations of a Jeffcott type rotor, modeled as multidimensional dynamic system with non-linear restoring forces, under biaxial white noise excitation. The latter type of dynamic system is of wide use in stability studies of rotating machinery - from automotive to rocket turbo engine design. In particular, the design of liquid-propellant turbo pump rocket engines may be a potential application area of the studied system, due to the biaxial nature of the mechanical excitation, caused by surrounding liquid turbulent pressure field. In this paper, the extreme statistics of the rotor's non-linear oscillations has been studied by applying an enhanced implementation of the numerical path integration method, benchmarked by a known analytical solution. The obtained response probability distributions can serve as input for a wide range of system reliability issues, for example in extreme response study of turbo-pumps for liquid-propellant rocket engines. Predicting extreme transverse random vibrations of shafts in rotating machinery is of importance for applications with high environmental dynamic loads on Jeffcott type rotor supports. The major advantage of using path integration technique rather than direct Monte Carlo simulation is ability to estimate the probability distribution tail with high accuracy. The latter is of critical importance for extreme value statistics and first passage probability calculations. The main contribution of this paper is a reliable and independent confirmation of the path integration technique as a tool for assessing the dynamics of the kind of stochastic mechanical models considered in this paper. By the latter authors mean application of a unique and nontrivial analytical solution, that yields exact dynamic system response distribution, therefore it provides absolutely reliable reference to be compared to. The potential for providing a good qualitative understanding of the behavior of such systems is therefore available.