Cyclostationary random vibration of a ship propeller

A special class of nonstationary processes with periodically varying statistics, called cyclostationary (CS), is investigated. This process is encountered in many engineering problems involving rotating machinery, such as turbines, propellers, helicopter rotors, and diesel engines. The objective of this paper is to show that a CS model of the flow-induced excitation on a propeller can describe the physics of the problem more accurately than a traditional stationary model. The mean values of the hydrodynamic forces are calculated using the vortex panel method and the vortex theory of propellers. Considering the randomness in the axial and the tangential components of the wake velocity, we calculate the covariance matrix of the forces. This analysis shows that the hydrodynamic forces acting on the propeller are CS processes. Then we calculate the standard deviation (root mean square [RMS]) of the blade response. We show that the CS model predicts the time-wise variation of the statistics of the excitation and the response (e.g., the RMS), including their peaks. A traditional stationary model cannot provide this information because it assumes constant statistics. Finally, a parametric analysis is performed to demonstrate the effects of the correlation structure of the velocity field behind a ship hull on the RMS of the blade deflection.