THE IMPULSE RESPONSE FUNCTION AND SHIP MOTIONS

TLDR

The authors propose two new representations of ship motion equations to address deficiencies in the conventional models. Both representations employ impulse‑response functions and convolution integrals over past force or velocity histories, with the equations extended to six degrees of freedom and linear coupling between modes. The resulting equations feature frequency‑independent coefficients and kernels, are valid for both transient and periodic motions, and the two representations are mathematically related. Author: (Author).

Abstract

Abstract : After a review of the deficiencies of the usual equations of motion for an oscillating ship, two new representations are given. One makes use of the impulse response function and depends only upon the system being linear. The response is given as a convolution integral over th past history of the exciting force with the impulse response funcion appearing as the kernel. The second representation is based upon a hydrodynamic study, and new forms for the equations of motion are exhibited. The equations resemble the usual equations, with the addition of convolution integrals over the past history of the velocity. However, the coefficients in these new equations are independent of frequency, as are the kernel functions in the convolution integrals. Both representations are quite general and apply to transient motions as well as periodic. The relations between the two representations are given. The treatment considers six degrees of freedom, with linear coupling between the various modes. (Author)