Integration algorithm for covariance nonstationary dynamic analysis using equivalent stochastic linearization
Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearizati...
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| Published in: | Mathematics and computers in simulation Vol. 125; pp. 70 - 82 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.07.2016
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| ISSN: | 0378-4754, 1872-7166 |
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| Abstract | Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearization. It is a simple approach from the theoretical point of view, but needs numerical techniques whose computational complexity increases in case of nonstationary excitations. In this paper a procedure to solve covariance analysis of stochastic linearized systems in the case of nonstationary excitation is proposed. The nonstationary Lyapunov differential matrix covariance equation for the linearized system is solved using a numerical algorithm which updates linearized system coefficient matrix at each step. The technique used is a predictor–corrector procedure based on backward Euler method. Accuracy and computational costs are analysed showing the efficiency of the proposed procedure. |
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| AbstractList | Deterministic mechanical systems subject to stochastic dynamic actions, such as wind or earthquakes, have to be properly evaluated using a stochastic approach. For nonlinear mechanical systems it is necessary to approximate solutions using mathematical tools, as the stochastic equivalent linearization. It is a simple approach from the theoretical point of view, but needs numerical techniques whose computational complexity increases in case of nonstationary excitations. In this paper a procedure to solve covariance analysis of stochastic linearized systems in the case of nonstationary excitation is proposed. The nonstationary Lyapunov differential matrix covariance equation for the linearized system is solved using a numerical algorithm which updates linearized system coefficient matrix at each step. The technique used is a predictor–corrector procedure based on backward Euler method. Accuracy and computational costs are analysed showing the efficiency of the proposed procedure. |
| Author | Marano, Giuseppe C. Abrescia, Angelamaria Di Modugno, Filomena Acciani, Giuseppe |
| Author_xml | – sequence: 1 givenname: Giuseppe surname: Acciani fullname: Acciani, Giuseppe email: giuseppe.acciani@poliba.it organization: Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy – sequence: 2 givenname: Filomena orcidid: 0000-0001-8376-8098 surname: Di Modugno fullname: Di Modugno, Filomena email: filomena.dimodugno@poliba.it organization: Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy – sequence: 3 givenname: Angelamaria surname: Abrescia fullname: Abrescia, Angelamaria email: angelamaria.abrescia@poliba.it organization: Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy – sequence: 4 givenname: Giuseppe C. surname: Marano fullname: Marano, Giuseppe C. email: giuseppecarlo.marano@poliba.it organization: Dipartimento dell’Ingegneria Civile e Architettura, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy |
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| CitedBy_id | crossref_primary_10_1142_S0219455426501981 crossref_primary_10_1016_j_probengmech_2018_05_002 crossref_primary_10_1016_j_engstruct_2018_04_008 crossref_primary_10_1007_s10957_020_01778_8 crossref_primary_10_1007_s11071_018_4078_4 crossref_primary_10_1061__ASCE_EM_1943_7889_0001682 |
| Cites_doi | 10.1007/BF00052451 10.1002/stc.4300080203 10.1016/0266-8920(94)90025-6 10.1016/S0965-9978(98)00111-2 10.1002/eqe.4290040408 10.1142/S0219876207001072 10.1109/ACC.2001.945634 10.1061/JMCEA3.0002768 10.1109/ACC.2003.1243496 10.4236/ijg.2013.42027 10.1115/1.1668082 10.1155/2014/401469 10.1109/TCT.1954.6373354 10.1007/s11071-011-9976-7 10.1002/eqe.4290060403 10.1023/A:1008304408643 10.3130/aijs.80.551 10.1007/s11071-009-9532-x 10.1016/j.soildyn.2007.12.003 10.1016/j.soildyn.2013.05.001 10.1016/0266-8920(90)90018-F |
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| Keywords | Bouc–Wen mechanical model Stochastic dynamics Covariance analysis Lyapunov equation Equivalent linearization |
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| SubjectTerms | Bouc–Wen mechanical model Covariance analysis Equivalent linearization Lyapunov equation Stochastic dynamics |
| Title | Integration algorithm for covariance nonstationary dynamic analysis using equivalent stochastic linearization |
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