Communications Project

Document Type:Master's Thesis
Name:Ryan Krauss
Title:Experimental Identification of Nonlinear Systems
Degree:Master of Science
Department:Engineering Science and Mechanics
Committee Chair: Ali H. Nayfeh
Committee Members:Dean T. Mook
Scott L. Hendricks
Keywords:experimental identification, nonlinear beam, perturbation methods, time-domain techniques, frequency-domain techniques
Date of defense:August 4, 1998
Availability:Release the entire work immediately worldwide.


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.

List of Attached Files

bibliography.pdf chapter1.pdf chapter2.pdf
chapter3.pdf chapter4.pdf cover.pdf

The author grants to Virginia Tech or its agents the right to archive and display their thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. The author retains all proprietary rights, such as patent rights. The author also retains the right to use in future works (such as articles or books) all or part of this thesis or dissertation.