The response of a parametrically-excited system to a deterministic nonstationary excitation is studied. The system, which has a cubic nonlinearity, has one focus and two saddle points and can be used as a simple model of a ship in the head or follower seas. The method of multiple scales is applied to the governing equation to derive equations for the amplitude and phase of the response. These equations are used to find the stationary response of the system to stationary excitation. The stability of the stationary response is examined. The stability of stationary periodic solutions to the original governing equation is examined through a Floquet analysis. The response to a nonstationary excitation having (a) a frequency that varies linearly with time, or (b) an amplitude that varies linearly with time, is studied. The response is computed from digital computer integration of the equations found from the method of multiple scales and of the original governing equation. The response to nonstationary excitation has several unique characteristics, including penetration, jump-up, oscillation, and convergence to the stationary solution. The agreement between solutions found from the original governing equation and the method-of-multiple-scales equations is good. For some sweeps of the excitation frequency or amplitude, the response to nonstationary excitation found from the original governing equation exhibits behavior which is analogous to symmetry-breaking bifurcations, period-doubling bifurcations, chaos, and unboundedness in the stationary solution. The maximum response amplitude and the excitation frequency or amplitude at which the response goes unbounded is found as a function of sweep rate. The effect of initial conditions and noise on the response to nonstationary excitation is considered. The results of the digital-computer simulations are verified with an analog computer. / Master of Science

A modeling approach suitable for simulating solid-state-controlled machine systems, including component failures within either the electronics or machine(s), is presented in detail. The capability of modeling unbalanced-machine operation is included in the modeling approach. The approach is directly amenable to computer implementation. Computer implementation of the modeling approach was performed and the simulated results were compared with actual oscillograms, obtained from the performance tests of an Electric Vehicle Propulsion Unit, in order to verify the proposed modeling approach. Excellent correlation between the simulated waveforms and the oscillograms existed in all the simulated cases. The modeling approach was used also to simulate the electrical behavior of a brushless-excitation system used for large turbine generators. The simulations consisted of normal steady-state operation as well as a scenario of fault conditions occurring within the rotating rectifier assembly of the brushless exciter. The simulated results are displayed and a discussion of intrinsic features of these results needed to identify the specific fault is presented. Fault detection schemes are warranted for such expensive systems. Actual voltage and/or current waveforms could be telemetered to an controller for fault detection and classification. The elements of this modeling approach which allow inexpensive computer simulation of such systems, that can contain nonlinearities and/or spontaneous faults in any of its components, are listed as follows: 1. The capability of automatically generating the systems' governing state equations, from a minimal set of topological data and component values, at any point within the simulation run; 2. Inclusion of unbalanced machine operation is a result of having no topological restrictions placed upon the mutual coupling. 3. Using piece-wise linear I-V characteristics of the solid-state switching components decreases the computation time needed for a given simulation run since iteration for the status of the equivalent resistance values for each switch is only required at their threshold (I-V) points. 4. Employment of an implicit (predictor-corrector) integration algorithm designed specifically for solving stiff differential equations, typically associated with solid-state controlled machine systems, allows realistic modeling of the solid-state switches' equivalent resistance values. Also, implicit algorithms (like the one employed in this work) result in a drastic reduction of computer execution time and an increase in accuracy, when compared to explicit algorithms, systems. for simulating these types of stiff systems. / Ph. D.

published_or_final_version / Electrical Engineering / Master / Master of Philosophy

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