Delay Correlation of Mechanical Hysteresis and Damping
This paper presents a procedure for calculating the effective equivalent structural properties (stiffness and damping) of hysteretic systems from the time histories of their dynamic response. The method is based on the finding that the effective dynamic damping is proportional to the product of the...
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Published in | Journal of structural engineering (New York, N.Y.) Vol. 136; no. 1; pp. 76 - 85 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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American Society of Civil Engineers
01.01.2010
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Abstract | This paper presents a procedure for calculating the effective equivalent structural properties (stiffness and damping) of hysteretic systems from the time histories of their dynamic response. The method is based on the finding that the effective dynamic damping is proportional to the product of the structural natural frequency and the delay between the overall restoring force and the structural displacement. The delay is calculated from the time-shifted cross correlation between the structural force and displacement; and the same procedure also allows us to compute the instantaneous period of the response. It is then shown how, by computing the standard deviations of the force and displacement signals, it is possible to compute both the equivalent damping and the linearized stiffness. By implementing this procedure sequentially through moving windows, it is possible to monitor the nonlinear evolution in time. Some proofs are given for some easily tractable mathematical cases such as for linear simple harmonic and seismic responses, conjecturing that the method can be equally applied for transient forcing functions of nonlinear systems. |
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AbstractList | This paper presents a procedure for calculating the effective equivalent structural properties (stiffness and damping) of hysteretic systems from the time histories of their dynamic response. The method is based on the finding that the effective dynamic damping is proportional to the product of the structural natural frequency and the delay between the overall restoring force and the structural displacement. The delay is calculated from the time-shifted cross correlation between the structural force and displacement; and the same procedure also allows us to compute the instantaneous period of the response. It is then shown how, by computing the standard deviations of the force and displacement signals, it is possible to compute both the equivalent damping and the linearized stiffness. By implementing this procedure sequentially through moving windows, it is possible to monitor the nonlinear evolution in time. Some proofs are given for some easily tractable mathematical cases such as for linear simple harmonic and seismic responses, conjecturing that the method can be equally applied for transient forcing functions of nonlinear systems. |
Author | Gutiérrez, Eugenio Paulotto, Carlo |
Author_xml | – sequence: 1 givenname: Eugenio surname: Gutiérrez fullname: Gutiérrez, Eugenio organization: IPSC-JRC, European Commission European Laboratory for Structural Assessment, , Ispra I-21027, Italy (corresponding author). E-mail – sequence: 2 givenname: Carlo surname: Paulotto fullname: Paulotto, Carlo organization: Acciona Infraestructuras , Calle Valportillo II, Alcobendas, Madrid 8 28108, Spain |
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CitedBy_id | crossref_primary_10_1109_TNS_2013_2294829 |
Cites_doi | 10.1061/(ASCE)0733-9445(2003)129:5(576) 10.1016/j.engstruct.2003.09.014 10.1002/1096-9845(200009)29:9<1261::AID-EQE964>3.0.CO;2-N 10.1061/(ASCE)0733-9445(2005)131:1(160) 10.1109/PROC.1987.13723 10.1061/(ASCE)0733-9399(1995)121:5(596) 10.1002/eqe.513 10.1109/TASSP.1976.1162830 10.1007/978-1-4612-0763-4 |
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References | Gutièrrez, E.; Zaldivar, J. M. 2000; 29 Akkar, S. D.; Miranda, E. 2005; 131 Wallace, M. I.; Sieber, J.; Neild, S. A.; Wagg, D. J.; Kraoskopf, B. 2005; 34 Knapp, C. H.; Carter, G. C. 1976; ASSP-24 Kwan, W. P.; Billington, S. L. 2003; 129 Lee, S. H.; Min, K. W.; Hwang, J. S.; Kim, J. 2004; 26 Jacobsen, L. S. 1930; 52 Carter, G. C. 1987; 75 Bousias, S. N.; Verzeletti, G.; Fardis, M. N.; Gutièrrez, E. 1995; 121 e_1_3_3_7_1 e_1_3_3_9_1 e_1_3_3_8_1 Chopra A. K. (e_1_3_3_6_1) 2000 e_1_3_3_14_1 e_1_3_3_13_1 Jacobsen L. S. (e_1_3_3_10_1) 1930; 52 e_1_3_3_15_1 e_1_3_3_3_1 e_1_3_3_2_1 e_1_3_3_5_1 e_1_3_3_12_1 e_1_3_3_4_1 e_1_3_3_11_1 |
References_xml | – volume: 129 start-page: 576 issn: 0733-9445 year: 2003 end-page: 585 article-title: Influence of hysteretic behaviour on equivalent period and damping of structural systems publication-title: J. Struct. Eng. doi: 10.1061/(ASCE)0733-9445(2003)129:5(576) contributor: fullname: Kwan, W. P.; Billington, S. L. – volume: 26 start-page: 335 issn: 0141-0296 year: 2004 end-page: 346 article-title: Evaluation of equivalent damping ratio of a structure with added dampers publication-title: Eng. Struct. doi: 10.1016/j.engstruct.2003.09.014 contributor: fullname: Lee, S. H.; Min, K. W.; Hwang, J. S.; Kim, J. – volume: 29 start-page: 1261 issn: 0098-8847 year: 2000 end-page: 1286 article-title: The application of Karhunen-Loève, or principal components analysis method, to study the non-linear seismic response of structures publication-title: Earthquake Eng. Struct. Dyn. doi: 10.1002/1096-9845(200009)29:9<1261::AID-EQE964>3.0.CO;2-N contributor: fullname: Gutièrrez, E.; Zaldivar, J. M. – volume: 131 start-page: 160 issn: 0733-9445 year: 2005 end-page: 172 article-title: Statistical evaluation of approximate methods for estimating maximum deformation demands on existing structures publication-title: J. Struct. Eng. doi: 10.1061/(ASCE)0733-9445(2005)131:1(160) contributor: fullname: Akkar, S. D.; Miranda, E. – volume: 75 start-page: 236 issn: 0018-9219 year: 1987 end-page: 255 article-title: Coherence and time-delay estimation publication-title: Proc. IEEE doi: 10.1109/PROC.1987.13723 contributor: fullname: Carter, G. C. – volume: 52 start-page: 169 issn: 0097-6822 year: 1930 end-page: 181 article-title: Steady forced vibration as influenced by damping publication-title: Trans. ASME contributor: fullname: Jacobsen, L. S. – volume: 121 start-page: 596 issn: 0733-9399 year: 1995 end-page: 605 article-title: Load-path effects in column biaxial bending with axial force publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1995)121:5(596) contributor: fullname: Bousias, S. N.; Verzeletti, G.; Fardis, M. N.; Gutièrrez, E. – volume: ASSP-24 start-page: 320 issn: 0096-3518 year: 1976 end-page: 327 article-title: The generalized correlation method for estimation of time delay publication-title: IEEE Trans. Acoust., Speech, Signal Process. contributor: fullname: Knapp, C. H.; Carter, G. C. – volume: 34 start-page: 1817 issn: 0098-8847 year: 2005 end-page: 1832 article-title: Stability analysis of real-time dynamic substructuring using delay differential equations publication-title: Earthquake Eng. Struct. Dyn. doi: 10.1002/eqe.513 contributor: fullname: Wallace, M. I.; Sieber, J.; Neild, S. A.; Wagg, D. J.; Kraoskopf, B. – ident: e_1_3_3_3_1 doi: 10.1061/(ASCE)0733-9445(2005)131:1(160) – ident: e_1_3_3_5_1 doi: 10.1109/PROC.1987.13723 – ident: e_1_3_3_4_1 doi: 10.1061/(ASCE)0733-9399(1995)121:5(596) – ident: e_1_3_3_9_1 – ident: e_1_3_3_8_1 doi: 10.1002/1096-9845(200009)29:9<1261::AID-EQE964>3.0.CO;2-N – volume: 52 start-page: 169 year: 1930 ident: e_1_3_3_10_1 article-title: Steady forced vibration as influenced by damping publication-title: Trans. ASME contributor: fullname: Jacobsen L. S. – volume-title: Dynamics of structures: theory and application to earthquake engineering year: 2000 ident: e_1_3_3_6_1 contributor: fullname: Chopra A. K. – ident: e_1_3_3_15_1 doi: 10.1002/eqe.513 – ident: e_1_3_3_7_1 – ident: e_1_3_3_12_1 doi: 10.1109/TASSP.1976.1162830 – ident: e_1_3_3_14_1 doi: 10.1016/j.engstruct.2003.09.014 – ident: e_1_3_3_2_1 doi: 10.1007/978-1-4612-0763-4 – ident: e_1_3_3_11_1 – ident: e_1_3_3_13_1 doi: 10.1061/(ASCE)0733-9445(2003)129:5(576) |
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Title | Delay Correlation of Mechanical Hysteresis and Damping |
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