Summary
In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned in a 1∶1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature. Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM) is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant attenuation in the response.
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Anderson, J.G.;Bertero, V.: Uncertainties in establishing design earthquake. J Struct Eng 113 (1986) 1709–1724
Chopra, A.K.: Dynamics of structures, theory and applications to earthquake engineering. Prentice-Hall, New Jersey, 1995
Hall, J.F.;Heaton, T.H.;Halling, M.W.;Wald, D.J.: Near-source ground motions and effects on flexible buildings. Earthquake Spectra 11 (1995) 569–605
He, W.: Smart energy dissipation systems for protection of civil infrastructures from near-field earthquakes. PhD thesis, The City University of New York, 2003
Iwan, W.D.; Chen, X.D.: Important near-field ground motion data from the landers earthquake. In: Proceedings of 10 th European conference of earthquake engineering, Vienna, (1994) Austria
Iwan, W.D.: Drift Spectrum: measure of demand for earthquake ground motions. J Struct Eng 123 (4) (1997) 397–404
Iwan, W.D.: Personal communication with one of the authors (YW) during the international conference on advances and new challenges in earthquake engineering research. Harbin, (2002) China
Jiang, X.: Theoretical and experimental studies of steady-state nonlinear localization and energy pumping in systems of coupled oscillators. PhD thesis, University of Illinois at Urbana-Champaign 2002
Kelly, J.M.: Earthquake-resistant design with rubber, 2nd edn. Springer-Verlag Berlin, 1997
Ma, X.;Nayfeh, T.A.;Vakakis, A.F.;Bergman, L.: Experimental verification of shock reduction achieved through nonlinear localization. J Sound Vib 230(5) (2000) 1177–1184
Malhotra, P.K.: Dynamics of seismic impacts in base-isolated buildings. Earthquake Eng Struct Dyn 26 (1997) 797–813
Makris, N.;Chang, Shih-Po.: Effect of damping mechanisms on the response of seismically isolated structures. PEER Report 1998/06, Pacific Earthquake Engineering Research Center, University of California, Berkeley, 1998
Masri S.F.: Steady-state response of a multidegree system with an impact damper. J Appl Mech 40 (1973) 127–132
McFarland, D.M.;Wang, Y.;Vakakis, A.F.;Bergman L.A.: A parametric analysis of a novel shock isolation system. In: Proceedings of the 15th ASCE engineering mechanics conference EM 2002. Columbia University, New York, 2002a
McFarland, D.M.;Wang, Y.;Vakakis, A.F.;Bergman, L.A.: Model testing of a nonlinear base isolation concept. In: Proceedings of the 15th ASCE engineering mechanics conference EM 2002. Columbia University, New York, 2002b
Manevitch, L.I.: Description of localized normal modes in the chain of nonlinear coupled oscillators using complex variables. Nonlin Dyn 25 (2001) 95–109
Nashif, A.D.;Jones, D.I.G.;Henderson, J.P.: Vibration damping Wiley, New York, 1985
Nayfeh, A.H.;Mook, D.: Nonlinear oscillations, Wiley Interscience, New York, 1985
Nayfeh, S.A.;Nayfeh, A.H.: Energy transfer from high- to low-frequency modes in a flexible structure via modulation. J Vib Acoust 116 (1994) 203–207
Nayfeh, T.A.;Emaci, E.;Vakakis, A.F.: Application of nonlinear localization to the optimization of a vibration isolation system. AIAA J 35(8) (1997) 1378–1386
Rosenberg, R.M.: Normal modes of nonlinear dual-mode systems. J Appl Mech 27 (1960) 263–368
Rosenberg, R.M.: The Ateb(h)-functions and their properties. Q J Appl Math 21 (1) (1963) 37–47
Vakakis, A.F.;Manevitch, L.I.;Mikhlin, Y.V.;Pilipchuk, V.N.;Zevin, A.A.: Normal modes and localization in nonlinear systems. Wiley, New York, 1996
Vakakis, A.F.;Kounadis, A.N.;Raftoyiannis I.G.. Use of nonlinear localization for isolating structures from earthquake-induced motions. Earthquake Eng Struct Dyn 28 (1999) 21–36
Wang, Y.; McFarland, D.M.; Vakakis, A.F.; Bergman, L.A.: Efficacy of a nonlinear base isolation system subjected to near-field earthquake motions. Proceedings of International Conference on Advances and New Challenges in Earthquake Engineering Research, Harbin, (2002) China
Wang, Y.: Seismic base isolation by means of nonlinear mode localization. MS thesis, University of Illinois at Urbana-Champaign, 2003
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This work was supported in part by the National Science Foundation Grant CMS 00-00060. The authors are grateful for this support.
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Wang, Y., McFarland, D.M., Vakakis, A.F. et al. Seismic base isolation by nonlinear mode localization. Arch. Appl. Mech. 74, 387–414 (2005). https://doi.org/10.1007/BF02637038
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DOI: https://doi.org/10.1007/BF02637038