RANDOM-EXCITATION OF COUPLED OSCILLATORS WITH SINGLE AND SIMULTANEOUSINTERNAL RESONANCES

The primary objective of this paper is to examine the random response characteristics of coupled nonlinear oscillators in the presence of si ngle and simultaneous internal resonances. A model of two coupled beam s with nonlinear inertia interaction is considered. The primary beam i s directly excited by a random support motion, while the coupled beam is indirectly excited through autoparametric coupling and parametric e xcitation. For a single one to-two internal resonance, we used Gaussia n and non Gaussian closures, Monte Carlo simulation, and experimental testing to predict and measure response statistics and stochastic bifu rcation in the mean square. The mean square stability boundaries of th e coupled beam equilibrium position are obtained by a Gaussian closure scheme. The stochastic bifurcation of the coupled beam is predicted t heoretically and experimentally. The stochastic bifurcation predicted by non-Gaussian closure is found to take place at a lower excitation l evel than the one predicted by Gaussian closure and Monte Carlo simula tion. It is also found that above a certain excitation level, the solu tion obtained by non-Gaussian closure reveals numerical instability at much lower excitation levels than those obtained by Gaussian and Mont e Carlo approaches. The experimental observations reveal that the coup led beam does not reach a stationary state, as reflected by the time e volution of the mean square response. For the case of simultaneous int ernal resonances, both Gaussian and non-Gaussian closures fail to pred ict useful results, and attention is focused on Monte Carlo simulation and experimental testing. The effects of nonlinear coupling parameter s, internal detuning ratios, and excitation spectral density level are considered in both investigations. It is found that both studies reve al common nonlinear features such as bifurcations in the mean square r esponses of the coupled beam and modal interaction in the neighborhood of internal resonances. Furthermore, there is an upper limit for the excitation level above which the system experiences unbounded response in the neighborhood of simultaneous internal resonances.