Response statistics of nonlinear systems with fractional derivative elements subject to nonstationary excitations
In this paper nonlinear systems/structures endowed with fractional derivative elements are analyzed. The excitation considered can be either stationary or nonstationary, and either white or non-white. As an analysis tool, the stochastic averaging technique involving a widely-used approximation of fr...
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| Veröffentlicht in: | Nonlinear dynamics Jg. 113; H. 25; S. 34371 - 34388 |
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| Abstract | In this paper nonlinear systems/structures endowed with fractional derivative elements are analyzed. The excitation considered can be either stationary or nonstationary, and either white or non-white. As an analysis tool, the stochastic averaging technique involving a widely-used approximation of fractional derivatives is employed. This leads to a one-dimensional integer-order stochastic differential equation governing the evolution of the response amplitude. Further, the derived averaged Fokker–Planck-Kolmogorov equation is tackled by two techniques: the Galerkin technique and numerical path integration. Notably, significant modifications are needed to extend the Galerkin scheme to systems under nonstationary and nonwhite excitation with inseparable power spectral density. Numerical examples including a Van der Pol system, and a Duffing system are considered. The reliability and accuracy of the proposed scheme are demonstrated by juxtaposing the results derived by the proposed approaches with pertinent Monte Carlo simulation results. |
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| AbstractList | In this paper nonlinear systems/structures endowed with fractional derivative elements are analyzed. The excitation considered can be either stationary or nonstationary, and either white or non-white. As an analysis tool, the stochastic averaging technique involving a widely-used approximation of fractional derivatives is employed. This leads to a one-dimensional integer-order stochastic differential equation governing the evolution of the response amplitude. Further, the derived averaged Fokker–Planck-Kolmogorov equation is tackled by two techniques: the Galerkin technique and numerical path integration. Notably, significant modifications are needed to extend the Galerkin scheme to systems under nonstationary and nonwhite excitation with inseparable power spectral density. Numerical examples including a Van der Pol system, and a Duffing system are considered. The reliability and accuracy of the proposed scheme are demonstrated by juxtaposing the results derived by the proposed approaches with pertinent Monte Carlo simulation results. |
| Author | Spanos, Pol D. Luo, Yi |
| Author_xml | – sequence: 1 givenname: Yi surname: Luo fullname: Luo, Yi – sequence: 2 givenname: Pol D. surname: Spanos fullname: Spanos, Pol D. |
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| Cites_doi | 10.1061/AJRUA6.RUENG-1167 10.1007/978-1-84996-335-0 10.1137/1111038 10.1115/1.3167616 10.1016/0020-7462(86)90025-9 10.1016/j.ymssp.2023.111043 10.1016/j.ijnonlinmec.2022.104247 10.1007/s11071-015-2482-6 10.1007/s11071-019-05124-0 10.1109/ICFDA.2014.6967364 10.1016/j.strusafe.2020.101975 10.1007/BF00045338 10.1016/j.ijnonlinmec.2015.02.002 10.1016/j.ijnonlinmec.2022.104170 10.1002/9780470824269 10.1007/978-3-031-57863-2 10.1016/S0022-460X(87)80062-7 10.1016/j.jsv.2008.06.026 10.1007/s11071-021-07014-w 10.1115/1.4056946 10.1007/978-3-642-61544-3 10.1115/1.2198253 10.1007/BF00120671 10.1016/j.ijnonlinmec.2015.11.010 10.1016/j.strusafe.2024.102525 10.1109/9.739144 10.1007/978-3-662-05389-8 10.1016/j.probengmech.2022.103411 10.1016/S0020-7462(96)00096-0 10.1006/jsvi.2001.3682 10.1016/j.ress.2025.111056 10.1016/j.cnsns.2011.11.024 10.1016/j.probengmech.2017.10.001 10.1016/j.taml.2023.100436 10.1016/j.probengmech.2014.07.001 10.1016/j.apm.2021.03.032 10.1007/s11071-009-9543-7 10.1115/1.4047882 10.1140/epjst/e2011-01383-5 10.1016/j.jcp.2020.109525 10.1016/j.soildyn.2010.01.013 10.1016/j.mechmat.2011.08.016 10.1016/j.ymssp.2021.108024 10.1111/j.1365-246X.1967.tb02303.x 10.1002/zamm.19950750820 10.1023/A:1016595107471 10.1016/0020-7683(78)90076-8 10.2514/3.8142 10.1016/j.ijnonlinmec.2022.104178 10.1016/0020-7225(65)90045-5 10.1016/j.engstruct.2024.118844 10.1016/j.engstruct.2006.01.006 10.1115/1.4034460 10.1016/j.probengmech.2021.103156 10.1061/JMCEA3.0002579 10.1016/j.mechatronics.2016.06.005 10.1016/j.ymssp.2015.11.016 10.1016/j.probengmech.2022.103410 10.1016/j.probengmech.2023.103471 |
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| References | PD Spanos (11648_CR53) 1980; 106 ZL Huang (11648_CR20) 2009; 319 11648_CR13 S Kempfle (11648_CR24) 2002; 29 RC Koeller (11648_CR26) 1984; 51 F Kong (11648_CR27) 2022; 107 11648_CR51 VC Fragkoulis (11648_CR16) 2019; 97 Y Zhang (11648_CR71) 2023; 71 A Gemant (11648_CR19) 1936; 7 K Itô (11648_CR22) 1944; 20 ZL Huang (11648_CR21) 2010; 59 11648_CR18 IA Kougioumtzoglou (11648_CR33) 2024 PD Spanos (11648_CR54) 1983; 109 A Naess (11648_CR40) 1994; 5 JS Yu (11648_CR67) 1997; 32 KR dos Santos (11648_CR15) 2020; 86 PD Spanos (11648_CR60) 2022; 146 W Zhang (11648_CR70) 2023; 90 P Ni (11648_CR41) 2024; 111 W Li (11648_CR35) 2015; 71 11648_CR62 JB Chen (11648_CR7) 2020; 415 DJ Jerez (11648_CR23) 2024; 208 F Kong (11648_CR28) 2022; 162 RL Bagley (11648_CR2) 1983; 21 JB Roberts (11648_CR46) 1986; 21 F Kong (11648_CR29) 2024; 10 I Podlubny (11648_CR43) 1999; 44 P Shah (11648_CR48) 2016; 38 PD Spanos (11648_CR59) 2018; 144 Y Shen (11648_CR49) 2012; 17 Y Zhang (11648_CR68) 2021; 97 M Caputo (11648_CR5) 1967; 13 J Li (11648_CR34) 2009 PD Spanos (11648_CR52) 1978; 14 Y Luo (11648_CR36) 2022 F Rüdinger (11648_CR47) 2006; 28 PD Spanos (11648_CR58) 2016; 83 J Xu (11648_CR64) 2016; 72 H Beyer (11648_CR3) 1995; 75 RW Clough (11648_CR8) 1993 M Di Paola (11648_CR14) 2020; 6 WQ Zhu (11648_CR72) 1987; 117 11648_CR30 Y Luo (11648_CR37) 2023; 13 H Risken (11648_CR45) 1996 E Wong (11648_CR63) 1965; 3 11648_CR39 B Pomaro (11648_CR44) 2023 A Di Matteo (11648_CR10) 2014; 38 B Bonilla (11648_CR4) 2007; 187 M Di Paola (11648_CR12) 2011; 43 IA Kougioumtzoglou (11648_CR32) 2022; 146 I Podlubny (11648_CR42) 1999 PD Spanos (11648_CR55) 1997; 123 PD Spanos (11648_CR57) 2010; 30 RZ Khas’minskii (11648_CR25) 1966; 11 Y Xu (11648_CR65) 2016; 83 LC Chen (11648_CR6) 2011; 193 Y Xu (11648_CR66) 2024; 319 OP Agrawal (11648_CR1) 2001; 247 PD Spanos (11648_CR56) 2007; 74 Y Luo (11648_CR38) 2025 E Simiu (11648_CR50) 1996 Y Zhang (11648_CR69) 2021; 66 A Di Matteo (11648_CR11) 2018; 54 VC Fragkoulis (11648_CR17) 2023; 71 IA Kougioumtzoglou (11648_CR31) 2016; 80 JP Conte (11648_CR9) 1997; 123 BF Spencer (11648_CR61) 1993; 4 |
| References_xml | – volume: 10 start-page: 04023048 issue: 1 year: 2024 ident: 11648_CR29 publication-title: ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A: Civ. Eng. doi: 10.1061/AJRUA6.RUENG-1167 – ident: 11648_CR39 doi: 10.1007/978-1-84996-335-0 – volume: 11 start-page: 390 issue: 3 year: 1966 ident: 11648_CR25 publication-title: Theory Probab. Appl. doi: 10.1137/1111038 – volume: 51 start-page: 299 issue: 2 year: 1984 ident: 11648_CR26 publication-title: J. Appl. Mech. doi: 10.1115/1.3167616 – volume: 21 start-page: 111 issue: 2 year: 1986 ident: 11648_CR46 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/0020-7462(86)90025-9 – volume: 187 start-page: 68 issue: 1 year: 2007 ident: 11648_CR4 publication-title: Appl. Math. Comput. – ident: 11648_CR30 – volume: 208 start-page: 111043 year: 2024 ident: 11648_CR23 publication-title: Mech. Syst. Signal Process. doi: 10.1016/j.ymssp.2023.111043 – year: 2022 ident: 11648_CR36 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2022.104247 – volume: 83 start-page: 2311 year: 2016 ident: 11648_CR65 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-015-2482-6 – volume: 97 start-page: 2291 year: 2019 ident: 11648_CR16 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-019-05124-0 – ident: 11648_CR13 doi: 10.1109/ICFDA.2014.6967364 – volume: 86 start-page: 101975 year: 2020 ident: 11648_CR15 publication-title: Struct. Saf. doi: 10.1016/j.strusafe.2020.101975 – volume: 144 start-page: 04017173 issue: 2 year: 2018 ident: 11648_CR59 publication-title: J. Eng. Mech. – volume: 5 start-page: 287 year: 1994 ident: 11648_CR40 publication-title: Nonlinear Dyn. doi: 10.1007/BF00045338 – volume: 71 start-page: 83 year: 2015 ident: 11648_CR35 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2015.02.002 – volume: 146 start-page: 104170 year: 2022 ident: 11648_CR60 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2022.104170 – volume-title: Stochastic dynamics of structures year: 2009 ident: 11648_CR34 doi: 10.1002/9780470824269 – volume-title: Path integrals in stochastic engineering dynamics year: 2024 ident: 11648_CR33 doi: 10.1007/978-3-031-57863-2 – ident: 11648_CR62 – volume: 117 start-page: 421 issue: 3 year: 1987 ident: 11648_CR72 publication-title: J. Sound Vib. doi: 10.1016/S0022-460X(87)80062-7 – volume: 319 start-page: 1121 issue: 3–5 year: 2009 ident: 11648_CR20 publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2008.06.026 – volume: 107 start-page: 375 year: 2022 ident: 11648_CR27 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-021-07014-w – volume: 90 start-page: 061011 issue: 6 year: 2023 ident: 11648_CR70 publication-title: ASME J. Appl. Mech. doi: 10.1115/1.4056946 – volume-title: The Fokker-Planck Equation: Methods of Solution and Applications year: 1996 ident: 11648_CR45 doi: 10.1007/978-3-642-61544-3 – volume: 74 start-page: 315 issue: 2 year: 2007 ident: 11648_CR56 publication-title: J. Appl. Mech. doi: 10.1115/1.2198253 – volume: 4 start-page: 357 year: 1993 ident: 11648_CR61 publication-title: Nonlinear Dyn. doi: 10.1007/BF00120671 – volume: 80 start-page: 66 year: 2016 ident: 11648_CR31 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2015.11.010 – volume: 111 start-page: 102525 year: 2024 ident: 11648_CR41 publication-title: Struct. Saf. doi: 10.1016/j.strusafe.2024.102525 – volume: 123 start-page: 290 issue: 3 year: 1997 ident: 11648_CR55 publication-title: J. Eng. Mech. – volume: 44 start-page: 208 issue: 1 year: 1999 ident: 11648_CR43 publication-title: IEEE Trans. Autom. Control doi: 10.1109/9.739144 – ident: 11648_CR18 doi: 10.1007/978-3-662-05389-8 – volume: 71 start-page: 103411 year: 2023 ident: 11648_CR17 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2022.103411 – volume: 32 start-page: 759 issue: 4 year: 1997 ident: 11648_CR67 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/S0020-7462(96)00096-0 – volume: 109 start-page: 1134 issue: 4 year: 1983 ident: 11648_CR54 publication-title: J. Eng. Mech. – volume: 247 start-page: 927 issue: 5 year: 2001 ident: 11648_CR1 publication-title: J. Sound Vib. doi: 10.1006/jsvi.2001.3682 – year: 2025 ident: 11648_CR38 publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2025.111056 – volume: 17 start-page: 3092 issue: 7 year: 2012 ident: 11648_CR49 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2011.11.024 – volume: 7 start-page: 311 issue: 8 year: 1936 ident: 11648_CR19 publication-title: J. Appl. Phys. – volume: 54 start-page: 138 year: 2018 ident: 11648_CR11 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2017.10.001 – volume: 13 start-page: 100436 issue: 3 year: 2023 ident: 11648_CR37 publication-title: Theor. Appl. Mech. Lett. doi: 10.1016/j.taml.2023.100436 – ident: 11648_CR51 – volume: 38 start-page: 127 year: 2014 ident: 11648_CR10 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2014.07.001 – volume: 97 start-page: 268 year: 2021 ident: 11648_CR68 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2021.03.032 – volume: 20 start-page: 519 issue: 8 year: 1944 ident: 11648_CR22 publication-title: Proceed. Imperial Academy – volume: 59 start-page: 339 year: 2010 ident: 11648_CR21 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-009-9543-7 – volume: 6 start-page: 040801 issue: 4 year: 2020 ident: 11648_CR14 publication-title: ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B: Mech. Eng. doi: 10.1115/1.4047882 – volume: 193 start-page: 81 issue: 1 year: 2011 ident: 11648_CR6 publication-title: Eur. Phys. J. Spec. Top. doi: 10.1140/epjst/e2011-01383-5 – volume: 415 start-page: 109525 year: 2020 ident: 11648_CR7 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2020.109525 – volume: 30 start-page: 811 issue: 9 year: 2010 ident: 11648_CR57 publication-title: Soil Dyn. Earthquake Eng. doi: 10.1016/j.soildyn.2010.01.013 – volume: 43 start-page: 799 issue: 12 year: 2011 ident: 11648_CR12 publication-title: Mech. Mater. doi: 10.1016/j.mechmat.2011.08.016 – volume-title: Dynamics of Structures year: 1993 ident: 11648_CR8 – volume-title: Wind effects on structures: fundamentals and applications to design year: 1996 ident: 11648_CR50 – volume: 162 start-page: 108024 year: 2022 ident: 11648_CR28 publication-title: Mech. Syst. Signal Process. doi: 10.1016/j.ymssp.2021.108024 – volume: 13 start-page: 529 issue: 5 year: 1967 ident: 11648_CR5 publication-title: Geophys. J. Int. doi: 10.1111/j.1365-246X.1967.tb02303.x – volume: 123 start-page: 15 issue: 1 year: 1997 ident: 11648_CR9 publication-title: J. Eng. Mech. – volume: 75 start-page: 623 issue: 8 year: 1995 ident: 11648_CR3 publication-title: ZAMM-J. Appl. Math. Mech. doi: 10.1002/zamm.19950750820 – volume: 29 start-page: 99 issue: 1 year: 2002 ident: 11648_CR24 publication-title: Nonlinear Dyn. doi: 10.1023/A:1016595107471 – volume: 14 start-page: 861 issue: 10 year: 1978 ident: 11648_CR52 publication-title: Int. J. Solids Struct. doi: 10.1016/0020-7683(78)90076-8 – volume: 21 start-page: 741 issue: 5 year: 1983 ident: 11648_CR2 publication-title: AIAA J. doi: 10.2514/3.8142 – volume-title: Fractional differential equations, Mathematics in Science and Engineering, year: 1999 ident: 11648_CR42 – volume: 146 start-page: 104178 year: 2022 ident: 11648_CR32 publication-title: Int. J. Non-Linear Mech. doi: 10.1016/j.ijnonlinmec.2022.104178 – volume: 3 start-page: 213 issue: 2 year: 1965 ident: 11648_CR63 publication-title: Int. J. Eng. Sci. doi: 10.1016/0020-7225(65)90045-5 – volume: 319 start-page: 118844 year: 2024 ident: 11648_CR66 publication-title: Eng. Struct. doi: 10.1016/j.engstruct.2024.118844 – volume: 28 start-page: 1774 issue: 13 year: 2006 ident: 11648_CR47 publication-title: Eng. Struct. doi: 10.1016/j.engstruct.2006.01.006 – volume: 83 start-page: 121003 issue: 12 year: 2016 ident: 11648_CR58 publication-title: ASME J. Appl. Mech. doi: 10.1115/1.4034460 – volume: 66 start-page: 103156 year: 2021 ident: 11648_CR69 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2021.103156 – volume: 106 start-page: 213 issue: 2 year: 1980 ident: 11648_CR53 publication-title: J. Eng. Mech. Division doi: 10.1061/JMCEA3.0002579 – volume: 38 start-page: 29 year: 2016 ident: 11648_CR48 publication-title: Mechatronics doi: 10.1016/j.mechatronics.2016.06.005 – volume: 72 start-page: 865 year: 2016 ident: 11648_CR64 publication-title: Mech. Syst. Signal Process. doi: 10.1016/j.ymssp.2015.11.016 – volume: 71 start-page: 103410 year: 2023 ident: 11648_CR71 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2022.103410 – year: 2023 ident: 11648_CR44 publication-title: Probabilistic Eng. Mech. doi: 10.1016/j.probengmech.2023.103471 |
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| SubjectTerms | Approximation Derivatives Differential equations Excitation Galerkin method Mathematical analysis Monte Carlo simulation Nonlinear systems Power spectral density Random vibration |
| Title | Response statistics of nonlinear systems with fractional derivative elements subject to nonstationary excitations |
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