An Analysis of the Quadratic Frequency Response for Added Resistance

Abstract

The objective of the present work was to extend existing hydrodynamic theory for ship resistance added by waves to include time-dependent fluctuations, so that the so-called "quadratic frequency response function" for added resistance could be computed and compared with previously obtained experimental estimates. The concept of a quadratic frequency response function follows from the (nonphysical) theory for the general functional polynomial input-output model which was utilized in the previous experimental work. It was hoped that the present work, by providing a physical model, would either lend credibility to the previous work or expose its shortcomings. In the event, the present work appears to have accomplished both. Analytical and experimental estimates of the quadratic frequency response function are in good qualitative agreement, and in fair quantitative agreement. Most of those experimental estimates which appeared in the previous work to be of at least slightly dubious statistical merit have been discredited. Since it was these marginal experimental estimates which gave rise to the speculation that the quadratic frequency response function was inordinately complicated, the present work indicates that the function is merely, moderately complicated. There seems reasonable evidence that it is feasible to make hydrodynamic estimates of the quadratic frequency response function required for prediction of nonlinear fluctuations of resistance in random seas.