Abstract
Engineered structures are becoming increasingly lightweight and flexible, and as such more likely to achieve large amplitude and nonlinear vibratory responses. This leads to a demand for new methods and experimental test structures to see how in practice nonlinearity can be handled. In previous work, the authors studied a continuous modal structure with a local nonlinearity. The structure has been designed to have transparent underlying physics, and easily adjustable natural frequencies, and this leads to the ability to investigate an approximately 3:1 internal resonance between the 1st and 2nd modal frequencies. Therefore the structure exhibits complex responses to harmonic excitation, including isolated regions of the frequency response and quasiperiodic behaviour. In the present work we discuss a rapid means of identifying the structure with the minimum requirements of test data and time. A particular aim is to characterise the underlying linear system using data that is strongly influenced by nonlinearity. A harmonic balance procedure is used to identify a nonlinear discrete spring-mass system, that is modally equivalent to the structure under test. It is found that the inclusion of harmonic components in the test data and the presence of internal resonance leads to surprising amounts of information about modes that are not directly excited by the fundamental stepped-sine excitation.
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References
Wagg, D.J., Neild, S.A.: Nonlinear Vibration with Control. Springer, New York (2009)
Amabili, M.: Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press, Cambridge (2008)
Ogden, R.W.: Non-linear Elastic Deformations. Courier Corporation (1997)
Rebeiz, G.M.: RF MEMS: Theory, Design, and Technology. Wiley, New York (2004)
Carrella, A.: Passive Vibration Isolators with High-Static-Low-Dynamic-Stiffness. VDM Verlag Dr. Muller (2010)
Daqaq, M.F., Masana, R., Erturk, A., Quinn, D.D.: On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. Appl. Mech. Rev. 66(4), 040801 (2014)
Ewins, D.: Modal Testing: Theory, Practice, and Application. Mechanical Engineering Research Studies: Engineering Dynamics Series. Research Studies Press (2000)
Worden, K., Tomlinson, G.R.: Nonlinearity in Structural Dynamics. Institute of Physics, Bristol (2001)
Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.-C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process 20(3), 505–592 (2006)
Thouverez, F.: Presentation of the ECL benchmark. Mech. Syst. Signal Process. 17(1), 195–202 (2003)
Demarie, G.V., Ceravolo, R., Sabia, D., Argoul, P.: Experimental identification of beams with localized nonlinearities. J. Vib. Control 17(11), 1721–1732 (2011)
Peeters, M., Kerschen, G., Golinval, J.: Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech. Syst. Signal Process. 25(4), 1227–1247 (2011)
Kuether, R.J., Renson, L., Detroux, T., Grappasonni, C., Kerschen, G., Allen, M.S.: Nonlinear normal modes, modal interactions and isolated resonance curves. J. Sound Vib. 351, 299–310 (2015)
Detroux, T., Noël, J.P., Masset, L., Kerschen, G., Virgin, L.N.: Numerical study of the intrinsic features of isolas in 2-DOF nonlinear system. In: Proceedings of International Conferences on Structural Engineering Dynamics (ICEDyn) (2015)
Shaw, A.D., Hill, T.L., Neild, S.A., Friswell, M.I.: Periodic responses of a structure with 3:1 internal resonance (manuscript submitted for publication)
LabVIEW System Design Software
Yasuda, K., Kawamura, S., Watanabe, K.: Identification of nonlinear multi-degree-of-freedom systems. Presentation of an identification technique. JSME Int. J. Ser. III, Vib. Control Eng. Eng. Ind. 31(1), 8–14 (1988)
Acknowledgements
The research leading to these results has received funding from EPSRC programme grant Engineering Nonlinearity (EP/G036772/1). In addition, Simon Neild and Tom Hill are supported by an EPSRC Fellowship (EP/K005375/1).
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Shaw, A.D., Hill, T.L., Neild, S.A., Friswell, M.I. (2016). Experimental Identification of a Structure with Internal Resonance. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29739-2_5
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DOI: https://doi.org/10.1007/978-3-319-29739-2_5
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