Dynamical behaviour of the planar non-linear mechanical system - Part I: Theoretical modelling

A non-linear planar centrifugally excited oscillatory system was studied in its steady-state domain. The dynamic behaviour in phase space was analysed by a model based on the numerical integration of non-linear equations of motion. The integral of the correlation dimension and Lyapunov exponents were used as a quantitative measure to describe the motion of the model. The estimates of the correlation dimension for the values in real phase space and for those obtained by embedding numerical time histories show good agreement. In addition, the visualization procedure, as a qualitative measure, shows good agreement with the results of Lyapunov exponents and the correlation dimension of the model. Power spectral and bispectral analyses have further been used to analyze the behaviour of the model in the frequency domain. The dominance of the first mode was found, while other modes have significantly lower power. In the calculated bicoherences a "wall" of values can be seen, which is attributed to the bicoherence's estimated sensitivity to the division by small number. This sensitivity resulted with an increase in the number of bicoherence peaks. A new approach to reduce the number of divisions by small number is proposed and its advantage over those found in the literature is given. (C) 1999 Academic Press.