Title page for ETD etd-71898-14457

Type of Document Master's Thesis
Author Krauss, Ryan
Author's Email Address rkrauss@vt.edu
URN etd-71898-14457
Title Experimental Identification of Nonlinear Systems
Degree Master of Science
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Nayfeh, Ali H. Committee Chair
Hendricks, Scott L. Committee Member
Mook, Dean T. Committee Member
  • experimental identification
  • nonlinear beam
  • perturbation methods
  • time-domain techniques
  • frequency-domain techniques
Date of Defense 1998-08-04
Availability unrestricted
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.

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.

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  bibliography.pdf 27.80 Kb 00:00:07 00:00:03 00:00:03 00:00:01 < 00:00:01
  chapter1.pdf 75.86 Kb 00:00:21 00:00:10 00:00:09 00:00:04 < 00:00:01
  chapter2.pdf 57.82 Kb 00:00:16 00:00:08 00:00:07 00:00:03 < 00:00:01
  chapter3.pdf 207.99 Kb 00:00:57 00:00:29 00:00:25 00:00:12 00:00:01
  chapter4.pdf 422.24 Kb 00:01:57 00:01:00 00:00:52 00:00:26 00:00:02
  cover.pdf 13.53 Kb 00:00:03 00:00:01 00:00:01 < 00:00:01 < 00:00:01
  vita.pdf 13.26 Kb 00:00:03 00:00:01 00:00:01 < 00:00:01 < 00:00:01

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