Cyclostationary Random Vibration of a Ship Propeller and a Road Vehicle

Abstract

A special class of nonstationary processes with periodically varying statistics, called cyclostationary (CS), is investigated. These processes are encountered in many engineering problems involving rotating machinery such as turbines, propellers, helicopter rotors, and diesel engines. We analyze a cyclostationary process model in order to show its advantages compared to a traditional stationary process model and present a methodology for calculating the statistics of the response of a linear system subjected to CS excitations. We demonstrate that a CS model estimates the statistics of the response of a linear dynamic system subjected to CS excitations more accurately by considering (1) a vehicle traveling on a rough road and (2) a propeller rotating in the wake of a ship in the presence of turbulence. In the case of the vehicle, the road consists of concrete plates of fixed length. We model the road excitation using a CS process and calculate the standard deviation (root mean square) of the vehicle response. In the case of the ship propeller, we calculate the hydrodynamic forces acting on the propeller using the vortex panel method and the vortex theory of propeller. Considering the randomness in the axial and the tangential components of velocity, we calculate the mean and the covariance of the forces. This analysis shows that the hydrodynamic forces acting on the propeller are CS processes. Then we perform finite element analysis of the propeller and calculate the mean and the standard deviation of the blade response. We do the parametric analysis to demonstrate the effects of some physical quantities such as the standard deviation, the correlation coefficient, the decorrelation time, and the scale of turbulence of the axial and the tangential components of the wake velocity on the standard deviation of the blade deflection. We found that the CS model yields the time-wise variation of the statistics of the excitation and the response (e.g., the root mean square) and their peaks correctly. This is important information for the calculation of probability of failure of the propeller. A traditional stationary model cannot provide this information.