Experimental Identification of Nonlinear Systems
A procedure is presented for using a primary resonance excitation in experimentally identifying the nonlinear parameters of a model approximating the response of a cantilevered beam by a single mode. The model accounts for cubic inertia and stiffness nonlinearities and quadratic damping. The...
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Virginia Tech
2014
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| Online Access: | http://hdl.handle.net/10919/36912 http://scholar.lib.vt.edu/theses/available/etd-71898-14457/ |
| Summary: | A procedure is presented for using a primary resonance excitation in
experimentally identifying the nonlinear parameters of a model approximating the
response of a cantilevered beam by a single mode. The model accounts for cubic
inertia and stiffness nonlinearities and quadratic damping. The method of
multiple scales is used to determine the frequency-response function for the
system. Experimental frequency- and amplitude-sweep data are compared with the
prediction of the frequency-response function in a least-squares curve-fitting
algorithm. The algorithm is improved by making use of experimentally known
information about the location of the bifurcation points. The method is
validated by using the parameters extracted to predict the force-response curves
at other nearby frequencies.
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We then compare this technique with two other techniques
that have been presented in
the literature. In addition to the amplitude- and frequency-sweep technique
presented, we apply a second frequency-domain technique and a time-domain
technique to the second mode of a cantilevered beam. We apply the
restoring-force surface method assuming no a priori knowledge of the system and
use the shape of the surface to guide us in assuming a form for the equation of
motion. This equation is used in applying the frequency-domain techniques: a
backbone curve-fitting technique based on the describing-function method and the
amplitude- and frequency-sweep technique based on the method of multiple scales.
We derive the equation of motion from a Lagrangian and discover that the form
assumed based on the restoring-force surface is incorrect. All of the methods
are reapplied with the new form for the equation of motion. Differences in the
parameter estimates are discussed. We conclude by discussing the limitations
encountered for each technique. These include the inability to separate the
nonlinear curvature and inertia effects and problems in estimating the
coefficients of small terms with the time-domain technique.
<p> === Master of Science |
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