Title page for ETD etd-03242009-040616

Type of Document Master's Thesis
Author Hsu, Tseng-Hsing
URN etd-03242009-040616
Title The parametrically excited pendulum and the criteria for predicting the onset of chaos
Degree Master of Science
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Hendricks, Scott L. Committee Chair
Mook, Dean T. Committee Member
Smith, Charles W. Committee Member
  • Nonlinear mechanics
Date of Defense 1991-11-15
Availability restricted

A pendulum with its supporting point vibrating in both the x and the y direction is analyzed. Numerical simulation by computer is used to analyze the motion of the pendulum. Chaotic motion of the system is observed. Threshold values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The results obtained by simulation and by theoretical criteria are shown to be in good agreement. A brute-force approach is used to supplement the results. It is found that the motion of this simple driven pendulum will have very complicated behavior. Multiple attractors can be shown to coexist.

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