Abstract
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 is 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 extracted parameters 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 backbone curve- fitting technique and a time-domain technique to the second mode of a cantilevered beam. 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.
Similar content being viewed by others
References
Tabaddor, M., 'Nonlinear vibration of a beam and multibeam systems', Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1996.
Masri, S. F., Sassi, H., and Caughey, T. K., 'Nonparametric identification of nearly arbitrary nonlinear systems', Journal of Applied Mechanics 49, 1982, 619–628.
Crawley, E. F. and Aubert, A. C., 'Identification of nonlinear structural elements by force-state mapping', AIAA Journal 24, 1986, 155–162.
Worden, K. and Tomlinson, G. R., 'An experimental study of a number of nonlinear SDOF systems using the resotring force surface method,’ in Proceedings of the 9th International Modal Analysis Conference, Firenze (Florence), Italy, April 15–18, 1991, Vol. 1, pp. 757–764.
Mohammad, K. S., Worden, K., and Tomlinson, G. R., 'Direct parameter estimation for linear and nonlinear structures', Journal of Sound and Vibration 152, 1992, 471–499.
Yasuda, K. and Kamiya, K., 'Experimental identificaiton technique of nonlinear beams in time domain,’ in Proceedings of DETC '97, Santa Barbara, CA, 1997, DETC97/VIB-4114.
Benhafsi, Y., Penny, J. E. T., and Friswell, M. I., 'Identification of damping parameters of vibrating systems with cubic stiffness nonlinearity,’ in Proceedings of the 13th International Modal Analysis Conference, Nashville, TN, February 13–16, 1995, Vol. 1, pp. 623–629.
Fahey, S. O'F. and Nayfeh, A. H., 'Experimental nonlinear indentification of a single structural mode,’ in Proceedings of the 16th International Modal Analysis Conference, Santa Barbra, CA, February 3–5, 1998, pp. 737–745.
Yasuda, K., Kamiya, K., and Komakine, M., 'Experimental identification technique of vibrating structures with geometrical nonlinearity', Journal of Applied Mechanics 64, 1997, 275–280.
Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley, New York, 1981.
Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krauss, R.W., Nayfeh, A.H. Experimental Nonlinear Identification of a Single Mode of a Transversely Excited Beam. Nonlinear Dynamics 18, 69–87 (1999). https://doi.org/10.1023/A:1008355929526
Issue Date:
DOI: https://doi.org/10.1023/A:1008355929526