Novel Criterion for Evaluation of Stationarity in Nonlinear Structural Dynamics
Publication: Journal of Aerospace Engineering
Volume 33, Issue 4
Abstract
The evaluation of stationarity, such as the widely used steady-state response assessment in stepped-sine testing, is a critical issue in structural dynamics. Stepped-sine excitation is a crucial testing method for nonlinear structures. This method can provide high signal-to-noise measurement data but requires a long measurement time. The disadvantage of lengthy measurements stems mainly from the prolonged time for a structure to reach a steady-state response in each frequency step. Although stepped-sine testing has been applied in numerous studies, there is still no uniform criterion to exactly indicate the moment when the response of a testing structure begins to achieve a steady state. In this study, a precise and novel criterion for evaluating stationarity in nonlinear structural dynamics based on the trend of the squared 2-norm of sinusoidal fitting residual vectors is proposed. Three numerical examples show that the steady-state response determined periodically by the criterion is in good agreement with the results of the theoretical analysis, which demonstrates that the presented criterion not only can assist engineers and researchers in accurately checking steady-state response but also can reduce the unnecessary and redundant waiting time during stepped-sine testing; therefore, the comprehensive performance of stepped-sine testing applied in nonlinear structures can be improved.
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Data Availability Statement
The data used in the three numerical examples are available from the corresponding author by request. Namely, the data used in the first example are used to draw Figs. 5–8; the data used in the second example are used to draw Figs. 9–11; and the data used in the third example are used to draw Figs. 13 and 14, respectively.
Acknowledgments
This work was supported by the National Program on Key Basic Research Project (973 Project) [Grant No. 2015CB057704], the National Natural Science Foundation of China [Grant No. 51578107, 51778103], the Science Fund for Creative Research Groups of the National Natural Science Foundation of China [Grant No. 51121005], the Fundamental Research Funds for the Central Universities [Grant No. DUT18LAB07], and the STU Scientific Research Foundation for Talents [Grant No. NTF18012].
References
Al-Hadid, M. A., and J. R. Wright. 1989. “Development in the force-state mapping technique for non-linear systems and the extension to the location of non-linear elements in a lumped-parameter system.” Mech. Syst. Signal Proc. 3 (3): 269–290. https://doi.org/10.1016/0888-3270(89)90053-8.
Bendat, J. S., and A. G. Piersol. 2010. Random data: Analysis and measurement procedures. 4th ed. Hoboken, NJ: Wiley.
Carrella, A., and D. J. Ewins. 2011. “Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions.” Mech. Syst. Signal Proc. 25 (3): 1011–1027. https://doi.org/10.1016/j.ymssp.2010.09.011.
Catalfamo, S., S. A. Smith, F. Morlock, M. R. W. Brake, P. Reuß, C. W. Schwingshackl, and W. D. Zhu. 2016. “Effects of experimental methods on the measurements of a nonlinear structure.” In Proc. 34th IMAC Conf. and Exposition on Structural Dynamics, 491–500. Basel, Switzerland: Springer.
Chopra, A. K. 2012. Dynamics of structures: Theory and applications to earthquake engineering. London: Pearson Education.
Ewins, D. J. 1984. Modal testing: Theory and practice. Letchworth, UK: Research Studies Press.
Friswell, M. I., and J. E. T. Penny. 1993. “Stepped sine testing using recursive estimation.” Mech. Syst. Signal Proc. 7 (6): 477–491. https://doi.org/10.1006/mssp.1993.1028.
Heylen, W., S. Lammens, and P. Sas. 1999. Modal analysis theory and testing. Belgium: Dept. Werktuigkunde, Katholieke Universteit Leuven.
Huo, L. S., F. R. Wang, H. N. Li, and G. B. Song. 2017. “A fractal contact theory based model for bolted connection looseness monitoring using piezoceramic transducers.” Smart Mater. Struct. 26 (10): 104010. https://doi.org/10.1088/1361-665X/aa6e93.
Inman, D. J. 2006. Vibration with control. West Sussex, UK: Wiley.
ISO. 1991. Shewhart control charts. ISO 8258. Geneva: ISO.
Kang, M. J., and H. J. Kim. 2017. “A method of frequeney response analysis of mechanical system combining swept-sine and stepped-sine excitation.” In Proc., 2017 IEEE Int. Conf. on Real-time Computing and Robotics, 704–708. Okinawa, Japan.
Kerschen, G., K. Worden, A. F. Vakakis, and J. C. Golinval. 2006. “Past, present and future of nonlinear system identification in structural dynamics.” Mech. Syst. Signal Proc. 20 (3): 505–592. https://doi.org/10.1016/j.ymssp.2005.04.008.
Kovacic, I., and M. J. Brennan. 2011. The Duffing equation: Nonlinear oscillators and their behaviour. Chichester, UK: Wiley.
Kurt, M., K. J. Moore, M. Eriten, D. M. McFarland, L. A. Bergman, and A. F. Vakakis. 2017. “Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system.” Mech. Syst. Signal Proc. 88 (May): 111–122. https://doi.org/10.1016/j.ymssp.2016.10.016.
Londono, J. M., S. A. Neild, and J. E. Cooper. 2015. “Identification of backbone curves of nonlinear systems from resonance decay responses.” J. Sound Vib. 348 (Jul): 224–238. https://doi.org/10.1016/j.jsv.2015.03.015.
Mituletu, I. C., G. R. Gillich, and N. M. M. Maia. 2019. “A method for an accurate estimation of natural frequencies using swept-sine acoustic excitation.” Mech. Syst. Signal Proc. 116 (Feb): 693–709. https://doi.org/10.1016/j.ymssp.2018.07.018.
Moler, B. C. 2008. Numerical computing with MATLAB: Revised Reprint. Philadelphia: Society for Industrial and Applied Mathematics.
Peeters, M., G. Kerschen, and J. C. Golinval. 2011. “Dynamic testing of nonlinear vibrating structures using nonlinear normal modes.” J. Sound Vib. 330 (3): 486–509. https://doi.org/10.1016/j.jsv.2010.08.028.
Ruan, J. B., S. C. M. Ho, D. Patil, M. Li, and G. B. Song. 2014. “Wind turbine blade damage detection using an active sensing approach.” Smart Mater. Struct. 23 (10): 105005. https://doi.org/10.1088/0964-1726/23/10/105005.
Tiso, P., and J. P. Noël. 2017. “A new, challenging benchmark for nonlinear system identification.” Mech. Syst. Signal Proc. 84 (Part B): 185–193. https://doi.org/10.1016/j.ymssp.2016.08.008.
van der Auweraer, H., P. Vanherck, P. Sas, and R. Snoeys. 1987. “Accurate modal analysis measurements with programmed sine wave excitation.” Mech. Syst. Signal Proc. 1 (3): 301–313. https://doi.org/10.1016/0888-3270(87)90107-5.
Vuojolainen, J., N. Nevaranta, R. Jastrzebski, and O. Pyrhonen. 2017. “Comparison of excitation signals in active magnetic bearing system identification.” Model. Ident. Control. 38 (3): 123–133. https://doi.org/10.4173/mic.2017.3.2.
Wang, H., and G. B. Song. 2014. “Innovative NARX recurrent neural network model for ultra-thin shape memory alloy wire.” Neurocomputing 134 (Jun): 289–295. https://doi.org/10.1016/j.neucom.2013.09.050.
Wang, X., T. L. Hill, S. A. Neild, A. D. Shaw, H. H. Khodaparast, and M. I. Friswell. 2018a. “Model updating strategy for structures with localised nonlinearities using frequency response measurements.” Mech. Syst. Signal Proc. 100 (Feb): 940–961. https://doi.org/10.1016/j.ymssp.2017.08.004.
Wang, X., H. H. Khodaparast, A. D. Shaw, M. I. Friswell, and G. T. Zheng. 2018b. “Localisation of local nonlinearities in structural dynamics using spatially incomplete measured data.” Mech. Syst. Signal Proc. 99 (Jan): 364–383. https://doi.org/10.1016/j.ymssp.2017.06.021.
Wang, X., and G. T. Zheng. 2016. “Equivalent dynamic stiffness mapping technique for identifying nonlinear structural elements from frequency response functions.” Mech. Syst. Signal Proc. 68-69 (Feb): 394–415. https://doi.org/10.1016/j.ymssp.2015.07.011.
Worden, K., and G. R. Tomlinson. 2001. Nonlinearity in structural dynamics: Detection, identification and modeling. Boca Raton: CRC Press.
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Published In
Journal of Aerospace Engineering
Volume 33 • Issue 4 • July 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jan 15, 2019
Accepted: Jan 2, 2020
Published online: Mar 31, 2020
Published in print: Jul 1, 2020
Discussion open until: Aug 31, 2020
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