Time-Frequency Analysis of Systems with Changing Dynamic Properties

Author: Bradford, Samuel Case, V

Year: 2007

Degree: Dissertation (Ph.D.)

Advisor: Heaton, Thomas H.

Committee Members: Hall, John F.; Beck, James L.; Kohler, Monica D.; Clayton, Robert W.; Heaton, Thomas H.

Option: Civil Engineering; Geophysics

DOI: 10.7907/HMK7-FJ81

Abstract

The Wigner-Ville Distribution, and related refinements, represent a class of advanced time-frequency analysis tools that are distinguished from Fourier and wavelet methods by an increase in resolution in the time frequency plane. Time-frequency analysis provides a set of exploratory tools for analyzing changing frequency content in a signal, which can then be correlated with damage patterns in a structure.

For systems of interest to engineers, investigating the changing properties of a system is typically performed by analyzing vibration data from the system, rather than direct inspection of each component. Nonlinear elastic behavior in the force-displacement relationship can decrease the apparent natural frequencies of the system - these changes typically occur over fractions of a second in moderate to strong excitation and the system gradually recovers to pre-event levels. Structures can also suffer permanent damage (e.g., plastic deformation or fracture), permanently decreasing the observed natural frequencies as the system loses stiffness. Advanced time-frequency representations provide a set of exploratory tools for analyzing changing frequency content in a signal, which can then be correlated with damage patterns in a structure. Modern building instrumentation allows for an unprecedented investigation into the changing dynamic properties of structures: a framework for using time-frequency analysis methods for instantaneous system identification is discussed.

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