RANDOM-EXCITATION OF NONLINEAR ELASTIC STRUCTURES WITH INTERNAL RESONANCES

The influence of random vibration on the design of mechanical componen ts has been restricted to the linear theory of small oscillations. How ever, this theory is inadequate and fails to predict the complex respo nse characteristics which may be observed experimentally and can only be predicted by employing the nonlinear theory. This paper presents a brief overview of the basic nonlinear phenomena associated with nonlin ear random vibration. An example of a clamped-clamped beam under filte red white noise excitation in the neighbourhood of 1:1 internal resona nce condition is considered. Three approaches are employed to examine the response and stochastic bifurcation of the beam coupled modes. The se are the Fokker-Planck equation together with closure schemes, Monte Carlo simulation, and experimental testing. The analytical results ar e compared with those determined by Monte Carlo simulation. It is foun d that above a critical static buckling load the analytical results fa il to predict the snap-through phenomenon, while both Monte Carlo simu lation and experimental results reveal the occurrence of snap-through. The bifurcation of second mode is studied in terms of excitation leve l, internal detuning and damping ratios. It is found that below the cr itical load parameter, the response statistics do not significantly de viate from normality. Above the critical value, where snap-through tak es place, the response is strongly non-Gaussian.