(Dr. Jerry Ginsberg, advisor)

"Modal Parameter Extraction Using Mode Isolation"

Abstract

Multiple degree of freedom (MDOF) methods for modal parameter identification in
current use deal with all of the modal parameters in a simultaneous fashion
in the process of matching measured data to analytical forms. In contrast,
the mode isolation algorithm exploits the fact that each mode has unique
characteristics that can be used to isolate it from the contribution of
other modes. The thesis describes how modal parameters are identified
and then refined in a recursive manner. This feature allows the mode isolation
method to offers a simple and consistent modal identification methodology that
is inherently automatic in nature.
 
The present work begins by developing the algorithm in an undamped modal
formulation. A numerical example of the mode isolation method is presented
for a system that was previously studied with the Eigensystem Realization
Algorithm (ERA) and Enhanced ERA.  Eigenvalues and mode shapes are compared
for each algorithm.  The results suggest that the mode isolation method is
more robust in the treatment of noisy data.
 
Development of the algorithm continues by extending it to use state space
modes as the analytical foundation.  This provides the algorithm the ability
to cope with generalized damping.  Prototypical systems are used to
demonstrate that the algorithm is not limited by the presence of modal coupling.
A cantilever beam with three attached spring-mass-damper systems is tuned such
that the bandwidths of two resonances are commensurate with the natural frequency
separation.  In addition, a frame structure is constructed to have flexural
and rotational natural frequencies that are closely spaced.  The addition of
damping elements creates bandwidths that blur the individuality of the
resonance peaks.  Differing levels of noise are imposed on the simulated
time-domain response, which is then transformed to the frequency domain. The
simulated data is used to illustrate the results of the algorithmic steps.
The natural frequencies and damping ratios that result from the procedure
are found to match the analytical system properties, with an error that is
less than the noise level that was added.