Random Excitation of Dynamic Systems with Multiple Internal Resonances

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The purpose of this research project is to develop an approach for analyzing the dynamic behavior of general multi-degree-of- freedom nonlinear systems possessing multiple internal resonances under external random excitation. The research will take the form of combined analytical, numerical and experimental investigations. Multiple internal resonances frequently exist in both continuous and discrete multi-degree-of-freedom systems such as cable systems, plates, coupled beams, aerospace structures, and mechanisms. Systems with multiple internal resonances experimentally exhibit dangerous and complex response characteristics under harmonic excitation, as observed in the laboratory. Under random excitation, we will develop two modes for stochastic bifurcation. These modes will be used to examine the conditions under which catastrophic behavior can be presented in terms of system parameters space and excitation spectral density level. The analytical approach is based on the method of stochastic averaging of the response energy envelope, with some innovations. The advantage of this approach is that it provides useful information pertaining to energy transfer among the interacting modes and their stochastic bifurcation in the neighborhood of multiple internal resonance conditions. The validity of the analytical approach will be verified by Monte Carlo numerical simulations and experimental tests of random excited nonlinear models. All approaches have the common goal of improving our understanding of the mechanisms underlying dangerous nonlinear phenomena. The results of this research will lead to new guidelines for engineers involved in the design of industrial machine components, cable structures, aircraft structures, liquid propellant rockets, and elevated water towers.