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Chaos describes a class of motions of a deterministic system whose time history is sensitive to initial conditions. Because of the sensitivity of initial conditions, the response of a dynamical system may result in instabilities. Hence, a study of nonlinear response of structures under the expected frequencies of excitation becomes important. Chaotic behavior, for example, may be found in the vibration response of large flexible space structures including trusses, booms, and radio antennas. Methods of quantifying chaos have been applied to flexible beams both analytically and experimentally. This research effort investigates the effects of sensors, strain gages and accelerometers, in studying chaotic motions. A long flexible beam is used to model the chaotic behavior, which is also mathematically modeled as Duffing's Equation. Time histories are recorded and analyzed using pseudo-phase space, Fourier spectrums, Poincare sections, Lyapunov exponents and fractal correlation dimensions. Comparison of the two sensors is also performed.

Thesis advisor, Ramesh Kolar

Chaos describes a class of motions of a deterministic system whose time history is sensitive to initial conditions. Because of the sensitivity of initial conditions, the response of a dynamical system may results in instabilities. Hence, a study of nonlinear response of structures under the expected frequencies of excitation becomes important. Chaotic behavior, for example, may be found in the vibration response of large flexible space structures including trusses, booms, and radio antennas. Methods of quantifying chaos have been applied to flexible beams both analytically and experimentally. This research effort investigates the effects of sensors, strain gages and accelerometers, in studying chaotic motions. A long flexible beam is used to model the chaotic behavior, which is also mathematically modeled as Duffing's Equation. Time histories are recorded and analyzed using pseudo-phase space, Fourier spectrums, Poincare sections, Lyapunov exponents and fractal correlation dimensions. Comparison of the two sensors is also performed. (Author)