Non-Gaussian Probability Densities for Nonlinear Systems Under Random Parametric Excitations: Experimental Investi- gation

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In the discipline of nonlinear mechanics, much is known about the theory of deterministic systems. Phenomena such as internal resonance and catastrophic deformation of elastic systems have been demonstrated both theoretically and experimentally. However, the existence and mechanism of these phenomena in random vibration have not yet been verified experimentally. This project conducts a series of experimental investigations to measure the random response statistics and stability boundaries of a number of dynamical models. In a previous grant, the PI has developed a non-Gaussian closure scheme for nonlinear systems under random parametric excitations. In this project, the theoretically predicted results (from the aforementioned theory) will be compared to the measured results in order to verify the theory. The models selected for experiment are a liquid sloshing in a tank, a cantilever beam, and an autoparametric vibration absorber. These models have received extensive experimental and analytical investigations under harmonic excitations and are appropriate models for this project. The proposed experimental work will be very valuable in providing more insight ot the random behavior of non-linear systems. The Principal Investigator has been a major contributor to nonlinear dynamics for several years. He is well-qualified to implement this project. An award is recommended.