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A Re-Configurable Test Apparatus for Complex Nonlinear Dynamic Systems

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Abstract

This paper reports the results of an analytical and experimental study to design, analyze, construct, test, and evaluate a re-configurable test-bed to allow the convenient performance of sophisticated experiments in a laboratory setting for investigating a broad category of important nonlinear, time-varying phenomena that are widely encountered in the applied mechanics field. The essential elements of the test apparatus include an electro-dynamic exciter that drives an oscillating mass whose restoring force is easily adjustable from one resembling a linear SDOF mass-spring-damper system with constant coefficients, to one that can represent systems with nonlinear elastic forces, to one that models systems possessing hysteretic properties with precisely-controlled time-varying characteristics. The apparatus design is economical to fabricate, convenient to manipulate, and it provides results that can be accurately replicated under repeated test combinations of system parameters and dynamic loads. The utility of the apparatus to provide an investigational tool for studying the dynamic response of systems with time-varying dry-friction forces that give rise to hysteretic phenomena is demonstrated. Sophisticated on-line system-identification techniques are used to estimate the parameters of reduced-order models that capture the dominant features of the physical model. It is shown that the apparatus under discussion is a useful research tool for investigators conducting studies in physics-based models of generic nonlinear dynamic systems.

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References

  1. Ibrahim, R. A. and Pettit, C. L., 'Uncertainties and dynamic problems of bolted joints and other fasteners', in Proceedings of the IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, June 8-13, 2003, Rome, Italy, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  2. Worden, K., 'Data processing and experiment design for the restoring force surface method, part I: Integration and differen-tiation of measured time data', Mechanical Systems and Signal Processing4(4), 1990, 295–319.

    Google Scholar 

  3. Smyth, A. W. and Pei, J. S., 'Integration of response measurements for nonlinear structural health monitoring', in Proceedings of 3rd US-Japan Workshop on Nonlinear System Identification and Structural Health Monitoring, October 20-21, 2000, USC, Los Angeles, California.

  4. Masri, S. F. and Caughey, T. K., 'A nonparametric identification technique for nonlinear dynamic problems', ASME Journal of Applied Mechanics. Presented at the 8th U.S. National Congress of Applied Mechanics, UCLA, 1978 46(2), June 1979, 433–447.

    Google Scholar 

  5. Wen, Y. K., 'Equivalent linearization for hysteretic systems under random excitations', ASME Journal of Applied Mechanics 47, 1980, 150–154.

    Google Scholar 

  6. Vestroni, F. and Noori, M., 'Special issue: Hysteresis in mechanical systems, modelling and dynamic response', International Journal of Non-Linear Mechanics 37(8), 2002, 1261–1459.

    Google Scholar 

  7. Smyth, A. W., Sami, S. F., Kosmatoploulos, E. B., Chassiakos, A. G., and Caughey, T. K., 'Development of adaptive modeling techniques for non-linear hysteretic systems,' International Journal of Non-Linear Mechanics 37(8), 2002, 1435–1451.

    Google Scholar 

  8. Housner, G. W. and Masri, S. F. (eds.), Proceedings of the U.S. National Workshop on Structural Control Research,Vol. 25-26. University of Southern California, Los Angeles, California, USC Publication No. M9013, 1990.

    Google Scholar 

  9. Housner, G. W., Bergman, L. A., Caughey, T. K., Chassiakos, A. G., Claus, R. O., Masri, S. F., Skelton, R. E., Soong, T. T., Spencer, B. F., and Yao, J. T. P., 'Special issue: Structural control: Past, present and future', Mechanics 123(9), 1997, 897–971.

    Google Scholar 

  10. Caughey, T. K., 'Random excitation of a system with bilinear hysteresis', ASME Journal of Applied Mechanics 27, 1960, 649–652.

    Google Scholar 

  11. Caughey, T. K., 'Equivalent linearization techniques', Journal of the Acoustical Society of America 35, 1963, 1706–1711.

    Google Scholar 

  12. Jennings, P. C., 'Periodic response of a general yielding structure', ASCE, Journal of Engineering Mechanics 90(EM2), 1966, 131–166.

    Google Scholar 

  13. Spanos, P. D., 'Stochastic linearization in structural dynamics', ASME Applied Mechanics Review 34(1), 1981.

  14. Andronikou, A. M. and Bekey, G. A., 'Identification of hysteretic systems,' in Proceedings of the 18th IEEE Conference on Decision and Control, 1984, pp. 1072–1073.

  15. Iwan, W. D. and Cifuentes, A. O., 'A model for system identification of degrading structures', Earthquake Engineering and Structural Dynamics 14(6), 1986, 877–890.

    Google Scholar 

  16. Vinogradov, O. and Pivovarov, I., 'Vibrations of system with non-linear hysteresis', Journal of Sound and Vibration 111(1), 1986, 145–152.

    Google Scholar 

  17. Jayakumar, P. and Beck, J. L., 'System identification using non-linear structural models', in Proceedings of the Structural Safety Evaluation Based on System Identification Approaches, Lambracht, Germany, Glp Intl, Germany, 1987, pp. 82–102.

    Google Scholar 

  18. Roberts, J. B., 'Application of averaging methods of randomly excited hysteretic systems', in Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamic Engineering Systems, Innsbruck, Austria, Springer-Verlag, Berlin, 1987, pp. 361–380.

    Google Scholar 

  19. Wen, Y. K. and Ang. A. H. S., 'Inelastic modeling and system identification', in Proceedings of the Structural Safety Evaluation Based on System Identification Approaches, Lambrecht, Germany, Glp Intl, Germany, 1987, pp. 142–160.

    Google Scholar 

  20. Yar, M. and Hammond, J. K., 'Modelling and response of bilinear hysteretic systems', ASCE Journal of Engineering Mechanics 113, 1987, 1000–1013.

    Google Scholar 

  21. Yar, M. and Hammond, J. K., 'Parameter estimation for hysteretic systems', Journal of Sound and Vibration 117(1), 1987, 161–172.

    Google Scholar 

  22. Worden, K. and Tomlinson, G. R., 'Identification of linear nonlinear restoring force surfaces in single-and multi-mode systems', in Proceedings of the Third International Conference on Recent Advances in Structural Dynamics, Institute of Sound and Vibration Research, Southampton, UK, 1988, pp. 299–308.

    Google Scholar 

  23. Sues, R. H., Mau, S. T., and Wen, Y. K., 'System identification of degrading hysteretic restoring forces,' ASCE Journal of Engineering Mechanics 114, 1988, 833–846.

    Google Scholar 

  24. Roberts, J. B. and Spanos, P. D., Random Vibration and Statistical Linearization,Wiley, New York, 1990.

    Google Scholar 

  25. Masri, S. F., Miller, R. K, Traina, M. I., and Caughey, T. K., 'Development of bearing friction models from experimental measurements', Journal of Sound and Vibration 149(3), 1991, 159–167.

    Google Scholar 

  26. Capecchi, D., 'Accurate solutions and stability criterion for periodic oscillations in hysteretic systems,' Meccanica 25, 1990,159–167.

    Google Scholar 

  27. Peng, C. Y. and Iwan, W. D., 'An identification methodology for a class of hysteretic structures,' Earthquake Engineering and Structural Dynamics 21, 1992, 695–712.

    Google Scholar 

  28. Loh, C. and Chung, S., 'A three-stage identification approach for hysteretic systems', Earthquake Engineering and Structural Dynamics 22, 1993, 129–150.

    Google Scholar 

  29. Chassiakos, A. G., Masri, S. F., Smyth, A. W., and Anderson, J. C., 'Adaptive methods for identification of hysteretic structures', in Proceedings of the 1995 American Control Conference, Seattle, Washington, 21-23 June, IEEE Service Center, Piscataway, New Jersey, 1995.

    Google Scholar 

  30. Benedettini, F., Capecchi, D., and Vestroni, F., 'Identification of hysteretic oscillators under earthquake loading by nonpara-metric models', ASCE Journal of Engineering Mechanics 121, 1995, 606–612.

    Google Scholar 

  31. Iwan, W. D. 'A distributed-element model for hysteresis and its steady-state dynamic response', ASME Journal of Applied Mechanics 33(4), 1966, 893–900.

    Google Scholar 

  32. Ni, Y. Q., Ko, J. M., and Wong, C. W., 'Nonparametric identification of nonlinear hysteretic systems', ASCE Journal of Engineering Mechanics 125(2), 1999, 206–215.

    Google Scholar 

  33. Sato, T. and Qi, K., 'Adaptive h∞ filter: its applications to structural identification', ASCE Journal of Engineering Mechanics 124(11), 1998, 1233–1240.

    Google Scholar 

  34. Smyth, A. W., Kosmatopoulos, E. B., Masri, S. F., and Chassiakos, A. G., 'Adaptive identification of nonlinear hysteretic structural systems', 2001 ASME International Mechanical Engineering Congress and Exposition,November 11-16, New York, ASME, 2001.

  35. Worden, K. and Tomlinson, G. R., Nonlinearity in Structural Dynamics: Detection, Identification and Modelling, Institute of Physics Publication, London, 2001.

    Google Scholar 

  36. Lin, J. W., Betti, R., Smyth, A. W., and Longman, R. W., 'On-line identification of nonlinear hysteretic structural systems using a variable trace approach', Earthquake Engineering & Structural Dynamics 30, 2001, 1279–1303.

    Google Scholar 

  37. Bouc, R., 'Forced vibration of mechanical systems with hysteresis, abstract', in Proceedings of the Fourth Conference on Nonlinear Oscillation, Prague, Czechoslovakia, 1967, p. 315.

    Google Scholar 

  38. Wen, Y. K. 'Method for random vibration of hysteretic systems', ASCE Journal of Engineering Mechanics 102, 1976, 249–263.

    Google Scholar 

  39. Ioannou, P. A. and Sun, J., Robust Adaptive Control, Prentice-Hall, Upper Saddle River, New Jersey, 1996.

    Google Scholar 

  40. Ioannou, P. A. and Datta, A., 'Robust adaptive control: A unified approach', Proceedings of the IEEE 79(12), 1991, 1736–1768.

    Google Scholar 

  41. Chassiakos, A. G., Masri, S. F., Smyth, A. W., and Caughey, T. K., 'On-line identification of hysteretic systems', ASME Journal of Applied Mechanics 65(1), 1998, 194–203.

    Google Scholar 

  42. Smyth, A. W., Masri, S. F., and Chassiakos, A. G., 'On-line parametric identification of mdof nonlinear hysteretic systems', ASCE Journal of Engineering Mechanics 125(2), 1999, 133–142.

    Google Scholar 

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Caffrey, J.P., Masri, S.F., Tasbihgoo, F. et al. A Re-Configurable Test Apparatus for Complex Nonlinear Dynamic Systems. Nonlinear Dynamics 36, 181–201 (2004). https://doi.org/10.1023/B:NODY.0000045507.10048.e1

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