Vibration Control of Structures using Vibro-Impact Nonlinear Energy Sinks
Authors
Abstract
Using Vibro-Impact Nonlinear Energy Sinks (VI NESs) is one of the novel strategies to control structural vibrations and mitigate their seismic response. In this system, a mass is tuned on the structure floor, so that it has a specific distance from an inelastic constraint connected to the floor mass. In case of structure stimulation, the displaced VI NES mass collides with the inelastic constraint and upon impacts, energy is dissipated. In the present work, VI NES is studied when its parameters, including clearance and stiffness ratio, are simultaneously optimized. Harmony search as a recent meta-heuristic algorithm is efficiently specialized and utilized for the aforementioned continuous optimization problem. The optimized attached VI NES is thus shown to be capable of interacting with the primary structure over a wide range of frequencies. The resulting controlled response is then investigated, in a variety of low and medium rise steel moment frames, via nonlinear dynamic time history analyses. Capability of the VI NES to dissipate siesmic input energy of earthquakes and their capabilitiy in reducing response of srtructures effectively, through vibro-impacts between the energy sink’s mass and the floor mass, is discussed by extracting several performance indices and the corresponding Fourier spectra. Results of the numerical simulations done on some structural model examples reveal that the optimized VI NES has caused successive redistribution of energy from low-frequency high-amplitude vibration modes to high-frequency low-amplitude modes, bringing about the desired attenuation of the structural responses.
Keywords
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5. Ogawa, K., Ide, T., and Saitou, T., “Application of Impact Mass Damper to a Cable–Stayed bridge Pylon”, Wind Engineering & Industrial Aerodynamics, Vol. 72(1-3), pp. 301-312, 1997.
6. Peterka, F., “Contribution to the Investigation of Impact Dampers with Free Additional Mass”, Zagadnienia Drgan Nieliniowych/Nonlinear Vibration Problems, pp. 315-325, 1974b.
7. Nigm, M. M., and Shabana, A. A., “Effect of an Impact Damper on a Multi–Degree of Freedom System”, Journal of Sound & Vibration, Vol. 89(4), pp. 541-557, 1983.
8. Li, K., “Experiments on the Effect of an Impact Damper on a Multiple-Degree-of-Freedom System,” Vibration & Control, Vol. 12(5), pp. 445-464, 2006.
9. Gendelman, O. V., “Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of two Oscillators”, Nonlinear Dynamics, Vol. 25, pp. 237-253, 2001.
10. Nucera, F., Vakakis, A. F., McFarland, D. M., Bergman, L. A., and Kerschen, G., “Targeted Energy Transfer in Vibro-Impact Oscillators for Seismic Mitigation”, Nonlinear Dynamics, Vol. 50(3), pp. 651-677, 2007.
11. Quinn, D., and Rand, R. H., “The Dynamics of Resonance Capture”, Nonlinear Dynamics, Vol. 8, pp. 1-20, 1995.
12. Bergman, L. A., “Mitigation Strategies for Systems Subjected to Vibratory, Shock, and Seismic loads”, CISM Courses and Lectures Vol. 518, Springer, Wien NewYork, 2010.
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14. Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J., “Past, Present and Future of Nonlinear System Identification in Structural Dynamics”, Mechanical Systems and Signal Processing, Vol. 20, pp. 505-592, 2006.
15. Spencer Jr. B. F., Christenson, R. E., and Dyke, S. J., “Next Generation Benchmark Control Problem for Seismically Excited Buildings”, Proceedings of 2nd World Conference on Structural Control, New York, Vol. 2, pp. 1135-1360, 1999.
16. Lee, K. S., and Geem, Z. W., “A New Structural Optimization Method Based on the Harmony Search Algorithm”, Computers & Structures, Vol. 82, pp. 781-798, 2004.
17. Nucera, F., Iacono, F. Lo, McFarland, D. M., Bergman, L. A., and Vakakis, A. F., “Application of Broadband Nonlinear Targeted Energy Transfers for Seismic Mitigation of a Shear Frame: Experimental Results”, Journal of Sound & Vibration, Vol. 313, pp. 57-76, 2008.
18. Nucera, F., McFarland, D. M., Bergman, L. A., and Vakakis, A. F., “Application of Broadband Nonlinear Targeted Energy Transfers for Seismic Mitigation of a Shear Frame: Computational Results”, Journal of Sound & Vibration, Vol. 329, pp. 2973-2994, 2010.
19. Kalkan, E., and Kunnath, S. K., “Relevance of Absolute and Relative Energy Content in Seismic Evaluation of Structures”, Advances in Structural Engineering, Vol. 11, No. 1, 2008.
20. Khashaee, P., Mohraz, B., Sadek, F., Lew, H. S., and Gross, J. L., “Distribution of Earthquake Input Energy in Structures”, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, USA, 2003.
21. Gendelman, O. V., “Analytic Treatment of a System with a Vibro-Impact Nonlinear Energy Sink”, Journal of Sound & Vibration, Vol. 331, pp. 4599-4608, 2012.
22. Al-Shudeifat, M. A., Wierschem, N. E., Quinn, D. D., Vakakis, A. F., Bergman, L. A., and Spencer JR., B. F., “Numerical and Experimental Investigation of a Highly Effective Single-Sided Vibro-Impact Nonlinear Energy Sink for Shock Mitigation”, International Journal of Non-Linear Mechanics, Vol. 52, pp. 96-109, 2013.
23. Mollaioli, F, Lucchini, A, Cheng, Y, and Monti, G, “Intensity Measures for the Seismic Response Prediction of Base-Isolated Buildings”, Bulletin of Earthquake Engineering, Vol. 11, pp. 1841-1866, 2013.
24. Taflampas, I. M., Spyrakos, C. C., and Maniatakis, Ch. A., “A New Definition of Strong Motion Duration and Related Parameters Affecting the Response of Medium-Long period Structures”, 14th World Conference on Earthquake Engineering, China, 2008.
2. 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, “Structural Control: Past, Present and Future”, ASCE Engineering Mechanics, Vol. 123(9), pp. 897-971, 1997.
3. Lieber, P., and Jensen, D. P., “An Acceleration Damper: Development and Design, and some Applications”, Transactions of American Society of Mechanical Engineers (ASME), Vol. 67, pp. 523-530, 1945.
4. Engleder, T., Vielsack, P., and Spiess, H., “Damping by Impacts, an Application of Non- Smooth dynamics”, In: Proceedings of the Conference on Nonlinear Oscillations in Mechanical Systems, St. Petersburg, Russia, pp. 134-144, 1998.
5. Ogawa, K., Ide, T., and Saitou, T., “Application of Impact Mass Damper to a Cable–Stayed bridge Pylon”, Wind Engineering & Industrial Aerodynamics, Vol. 72(1-3), pp. 301-312, 1997.
6. Peterka, F., “Contribution to the Investigation of Impact Dampers with Free Additional Mass”, Zagadnienia Drgan Nieliniowych/Nonlinear Vibration Problems, pp. 315-325, 1974b.
7. Nigm, M. M., and Shabana, A. A., “Effect of an Impact Damper on a Multi–Degree of Freedom System”, Journal of Sound & Vibration, Vol. 89(4), pp. 541-557, 1983.
8. Li, K., “Experiments on the Effect of an Impact Damper on a Multiple-Degree-of-Freedom System,” Vibration & Control, Vol. 12(5), pp. 445-464, 2006.
9. Gendelman, O. V., “Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of two Oscillators”, Nonlinear Dynamics, Vol. 25, pp. 237-253, 2001.
10. Nucera, F., Vakakis, A. F., McFarland, D. M., Bergman, L. A., and Kerschen, G., “Targeted Energy Transfer in Vibro-Impact Oscillators for Seismic Mitigation”, Nonlinear Dynamics, Vol. 50(3), pp. 651-677, 2007.
11. Quinn, D., and Rand, R. H., “The Dynamics of Resonance Capture”, Nonlinear Dynamics, Vol. 8, pp. 1-20, 1995.
12. Bergman, L. A., “Mitigation Strategies for Systems Subjected to Vibratory, Shock, and Seismic loads”, CISM Courses and Lectures Vol. 518, Springer, Wien NewYork, 2010.
13. Vakakis, A. F., Gendelman, O. V., Bergman, L. A., McFarland, D. M., Kerschen, G., and Lee, Y. S., “Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems”, Springer, The Netherlands, 2008.
14. Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J., “Past, Present and Future of Nonlinear System Identification in Structural Dynamics”, Mechanical Systems and Signal Processing, Vol. 20, pp. 505-592, 2006.
15. Spencer Jr. B. F., Christenson, R. E., and Dyke, S. J., “Next Generation Benchmark Control Problem for Seismically Excited Buildings”, Proceedings of 2nd World Conference on Structural Control, New York, Vol. 2, pp. 1135-1360, 1999.
16. Lee, K. S., and Geem, Z. W., “A New Structural Optimization Method Based on the Harmony Search Algorithm”, Computers & Structures, Vol. 82, pp. 781-798, 2004.
17. Nucera, F., Iacono, F. Lo, McFarland, D. M., Bergman, L. A., and Vakakis, A. F., “Application of Broadband Nonlinear Targeted Energy Transfers for Seismic Mitigation of a Shear Frame: Experimental Results”, Journal of Sound & Vibration, Vol. 313, pp. 57-76, 2008.
18. Nucera, F., McFarland, D. M., Bergman, L. A., and Vakakis, A. F., “Application of Broadband Nonlinear Targeted Energy Transfers for Seismic Mitigation of a Shear Frame: Computational Results”, Journal of Sound & Vibration, Vol. 329, pp. 2973-2994, 2010.
19. Kalkan, E., and Kunnath, S. K., “Relevance of Absolute and Relative Energy Content in Seismic Evaluation of Structures”, Advances in Structural Engineering, Vol. 11, No. 1, 2008.
20. Khashaee, P., Mohraz, B., Sadek, F., Lew, H. S., and Gross, J. L., “Distribution of Earthquake Input Energy in Structures”, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, USA, 2003.
21. Gendelman, O. V., “Analytic Treatment of a System with a Vibro-Impact Nonlinear Energy Sink”, Journal of Sound & Vibration, Vol. 331, pp. 4599-4608, 2012.
22. Al-Shudeifat, M. A., Wierschem, N. E., Quinn, D. D., Vakakis, A. F., Bergman, L. A., and Spencer JR., B. F., “Numerical and Experimental Investigation of a Highly Effective Single-Sided Vibro-Impact Nonlinear Energy Sink for Shock Mitigation”, International Journal of Non-Linear Mechanics, Vol. 52, pp. 96-109, 2013.
23. Mollaioli, F, Lucchini, A, Cheng, Y, and Monti, G, “Intensity Measures for the Seismic Response Prediction of Base-Isolated Buildings”, Bulletin of Earthquake Engineering, Vol. 11, pp. 1841-1866, 2013.
24. Taflampas, I. M., Spyrakos, C. C., and Maniatakis, Ch. A., “A New Definition of Strong Motion Duration and Related Parameters Affecting the Response of Medium-Long period Structures”, 14th World Conference on Earthquake Engineering, China, 2008.
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