Monograph records
https://feeds.library.caltech.edu/people/Bradford-S-C/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 11 Dec 2023 11:00:40 +0000Time-Frequency Analysis of Systems with Changing Dynamic Properties
https://resolver.caltech.edu/CaltechEERL:EERL-2006-02
Authors: Bradford, Samuel Case
Year: 2006
Time-frequency analysis methods transform a time series into a two-dimensional representation
of frequency content with respect to time. The Fourier Transform identifies
the frequency content of a signal (as a sum of weighted sinusoidal functions) but
does not give useful information regarding changes in the character of the signal, as all
temporal information is encoded in the phase of the transform. A time-frequency representation,
by expressing frequency content at different sections of a record, allows
for analysis of evolving signals. The time-frequency transformation most commonly
encountered in seismology and civil engineering is a windowed Fourier Transform, or
spectrogram; by comparing the frequency content of the first portion of a record with
the last portion of the record, it is straightforward to identify the changes between
the two segments. Extending this concept to a sliding window gives the spectrogram,
where the Fourier transforms of successive portions of the record are assembled into a
time-frequency representation of the signal. The spectrogram is subject to an inherent
resolution limitation, in accordance with the uncertainty principle, that precludes
a perfect representation of instantaneous frequency content. The wavelet transform
was introduced to overcome some of the shortcomings of Fourier analysis, though
wavelet methods are themselves unsuitable for many commonly encountered signals.
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. I introduce several
time-frequency representations and apply them to various synthetic signals as well as
signals from instrumented buildings.
vi
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 forcedisplacement
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.https://authors.library.caltech.edu/records/n1zsj-yj341Results of Millikan Library Forced Vibration Testing
https://resolver.caltech.edu/CaltechEERL:EERL-2004-03
Authors: Bradford, Samuel Case; Clinton, John F.; Favela, J.; Heaton, T. H.
Year: 2008
This report documents an investigation into the dynamic properties of Millikan Library under forced excitation. On July 10, 2002, we performed frequency sweeps from 1 Hz to 9.7 Hz in both the East-West (E-W) and North-South (N-S) directions using a roof level vibration generator. Natural frequencies were identified at 1.14 Hz (E-W fundamental mode), 1.67 Hz (N-S fundamental mode), 2.38 Hz (Torsional fundamental mode), 4.93 Hz (1st E-Wovertone), 6.57 Hz (1st Torsional overtone), 7.22 Hz (1st N-S overtone), and at 7.83 Hz (2nd E-Wovertone). The damping was estimated at 2.28% for the fundamental E-W mode and 2.39% for the N-S fundamental mode. On August 28, 2002, a modal analysis of each natural frequency was performed using the dense instrumentation network located in the building. For both the E-W and N-S fundamental modes, we observe a nearly linear increase in displacement with height, except at the ground floor which appears to act as a hinge. We observed little basement movement for the E-W mode, while in the N-S mode 30% of the roof displacement was due to basement rocking and translation. Both the E-W and N-S fundamental modes are best modeled by the first mode of a theoretical bending beam. The higher modes are more complex and not well represented by a simple structural system.https://authors.library.caltech.edu/records/0tkwf-dq711