Broad band random excitation of a two-degree-of-freedom system with autoparametric coupling

The response of a two-degree-of-freedom system with autoparametric coupling under the action of broad band random excitation is investigated. The system corresponds to the autoparametric vibration absorber and is also typical of many common structural configurations. A method based upon the Markov vector approach, together with an approximate treatment of third and higher statistical moments, is used to derive a set of fourteen coupled non-linear equations for the first and second moments of the system responses. A numerical integration procedure is used to obtain quantitative results for the system mean and mean square responses over a range of system parameters.The results show that large random motions of the coupled system may occur when the internal detuning parameter is close to the principal internal resonance, and that these motions may give rise to a suppression effect on the random motions of the main system. A feature of the results is that under conditions of internal resonance the random motions are found to be quasi-stationary, with steady oscillatory terms in the response moments. This suggests the possibility of entrainment of regular harmonic responses by the system random motions.