Abstract
Cubic dynamical systems are of great interest in marine technology. The state of the art concerning ship rolling and vessel mooring is described. Time-domain simulation is an indirect and unreliable way to determine harmonic response characteristics of nonlinear systems; frequency-domain analysis is therefore preferable. Numerical methods for deterministic and random oscillations are approximate. In order to establish a general sophisticated method, the well-known harmonic balance method is extended to polyharmonic excitation and improved to operate completely in the frequency domain. Special recurrent and simultaneous algorithms are given for the case of monoharmonic and polyharmonic excitation and multi-and single-valued response respectively. Subharmonic oscillations are analyzed using the general method. Random oscillations are treated as a set of periodic responses caused by the same excitation spectrum and different phase angles. Illustrative examples are chosen from marine technology practice. Principal, superharmonic and subharmonic response spectra are analyzed. The importance of further research which would cover other nonlinear effects by harmonic analysis is pointed out.
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