SECOND-ORDER HYDRODYNAMIC FORCES DUE TO STOCHASTIC EXCITATION.

This paper treats the problems of synthesizing and predicting second-order forces in hydrodynamic systems excited by stochastic forcing functions. Immediate applications are to second-order forces on naval vessels operating in or beneath an irregular wave system. The concept of transfer functions for nonlinear hydrodynamic systems is outlined. An analytical technique is developed for identifying the transfer function from wave and force time histories. The relative merits of the identification technique are discussed, and application to digitally simulated ship-wave systems is shown. The probability density function for hydrodynamic forces is derived to second-order under the assumption that the wave excitation is a stationary Gaussian stochastic process. Statistical properties of the resulting hydrodynamic forces are given in terms of physical characteristics of the input wave field. The notions of slowly varying and rapidly varying components of the total second-order hydrodynamic force are introduced and the methodology required for their synthesis and prediction is discussed.