Oscillations of retaining wall subject to Grob’s swelling pressure
The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob’s swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is es...
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| Published in | Scientific reports Vol. 12; no. 1; pp. 12224 - 10 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Nature Publishing Group UK
18.07.2022
Nature Publishing Group Nature Portfolio |
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| Online Access | Get full text |
| ISSN | 2045-2322 2045-2322 |
| DOI | 10.1038/s41598-022-15591-y |
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| Abstract | The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob’s swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert’s special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations. |
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| AbstractList | The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob’s swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert’s special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations. The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob's swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert's special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations.The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob's swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert's special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations. Abstract The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob’s swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert’s special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations. |
| ArticleNumber | 12224 |
| Author | Kozlov, Maksim Kim, Jong Tulendinova, Aizhan Ellis, Grant Skrzypacz, Piotr |
| Author_xml | – sequence: 1 givenname: Maksim surname: Kozlov fullname: Kozlov, Maksim organization: Center for Preparatory Studies, Nazarbayev University – sequence: 2 givenname: Aizhan surname: Tulendinova fullname: Tulendinova, Aizhan organization: Department of Mathematics, School of Sciences and Humanities, Nazarbayev University – sequence: 3 givenname: Jong surname: Kim fullname: Kim, Jong organization: Department of Civil and Environmental Engineering, School of Engineering and Digital Sciences, Nazarbayev University – sequence: 4 givenname: Grant surname: Ellis fullname: Ellis, Grant organization: Unaffiliated – sequence: 5 givenname: Piotr surname: Skrzypacz fullname: Skrzypacz, Piotr email: piotr.skrzypacz@nu.edu.kz organization: Department of Mathematics, School of Sciences and Humanities, Nazarbayev University |
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| References_xml | – reference: Grob, H. Schwelldruck im Belchentunnel (Swelling pressure in the Belchen tunnel). in Proc. Int. Symp. für Untertagebau(Proceedings of the International Symposium on Underground Mining), Lucerne, Switzerland. 99–119 (1972). – reference: OmarovDNurakhmetovDWeiDSkrzypaczPOn the application of Sturm’s theorem to analysis of dynamic pull-in for a graphene-based MEMS modelAppl. Comput. Mech.201812597210.24132/acm.2018.413 – reference: Brzakala, W., & Baca, M. The measurement and control of building vibrations in course of sheet pile wall and franki pile driving. in Proceedings of the 17th International Multidisciplinary Scientific GeoConference SGEM 2017, 29 June–5 July. 929–936. (2017). – reference: PimentelEExisting methods for swelling tests—A critical reviewEnergy Proc.2015769610510.1016/j.egypro.2015.07.857 – reference: GyselMA contribution to design of a tunnel lining in swelling rockRock Mech.197710557110.1007/BF01261802 – reference: SkrzypaczPWeiDNurakhmetovDKostsovEGSokolovAABegzhigitovMEllisGAnalysis of dynamic pull-in voltage and response time for a micro-electro- mechanical oscillator made of power-law materialsNonlinear Dyn.2021105122724010.1007/s11071-021-06653-3 – reference: XuPJiangGCalculation of natural frequencies of retaining Walls using the transfer matrix methodAdv. Civ. Eng.201921564758 – reference: SkrzypaczSKadyrovSNurakhmetovDWeiDAnalysis of dynamic pull-in voltage of graphene MEMS modelNonlinear Anal. Real World Appl.201945581589385432310.1016/j.nonrwa.2018.07.025 – reference: MezoIBariczAOn the generalization of the Lambert W functionTrans. Am. Math. Soc.20173691179177934369584910.1090/tran/6911 – reference: CorlessRMGonnetGHHareDEGJeffreyDJKnuthDEOn the Lambert W functionAdv. Comput. Math.19965329359141428510.1007/BF02124750 – reference: TimochenkoSVibration Problems in Engineering2015Andesite Press – reference: JuSHFinite element analysis of structure-borne vibration from high-speed trainSoil Dyn. Earthq. Eng.2007273259273234998410.1016/j.soildyn.2006.06.006 – reference: von Wolffersdorff, P.-A. & Fritzsche, S. Laboratory swell tests on overconsolidated clay and diagenetic solidified clay rocks. in Geotechnical Measurements and Modelling: Proceedings of the 8th International Symposium. 407–412. (2003). – reference: KlymenkovPATrofymchukAOKhavkinKABerchunIAExperimental diagnostics and mathematical modelling of stress-strain state of a railway retaining wallBull. Belarusian-Russ. Univ.2016150140148 – reference: BilirMESwelling problems and triaxial swelling behavior of claystone: A case study in Tire, TurkeySci. Res. Essays20116511061116 – reference: JohnFWissFASCE, construction vibrations: State-of-the-artJ. Geotech. Eng. Div.1981107216710.1061/AJGEB6.0001095 – reference: Nayfeh A.H., & Mook D.T. Nonlinear Oscillations. (Wiley, 1995). – reference: SkrzypaczPBountisANurakhmetovDKimJAnalysis of the lumped mass model for the cantilever beam subject to Grob’s swelling pressureCommun. Nonlinear Sci. Numer. Simulat.202085407034610.1016/j.cnsns.2020.105230 – reference: Mezo, I. The Lambert W Function Its Generalizations and Applications. 1st Edn. (Chapman and Hall/CRC, 2022). – reference: ParsapourDFahimifarASemi-analytical solution for time-dependent deformations in swelling rocks around circular tunnelsGeosci. J.201620451752810.1007/s12303-015-0050-12016GescJ..20..517P – reference: RjeilyYEAKhouriMFLongitudinal stress analysis of buried pipes under expansive soilsInt. J. Sci. Res. (IJSR)201231125922599 – reference: WrightEMSolution of the equation zez = aBull. Am. Math. Soc.195965899310.1090/S0002-9904-1959-10290-1 – reference: NayfehAHPaiPFLinear and Nonlinear Structural Mechanics2004Wiley-VCH Verlag GmbH & Co10.1002/9783527617562 – reference: Ghosh, P. Seismic active earth pressure behind a nonvertical retaining wall using pseudo-dynamic analysis. Can. Geotech. J. (2008). – reference: VeberičDLambert W function for applications in physicsComput. Phys. Commun.201218326222628297036610.1016/j.cpc.2012.07.0082012CoPhC.183.2622V – ident: 15591_CR25 doi: 10.1002/9783527617586 – volume: 27 start-page: 259 issue: 3 year: 2007 ident: 15591_CR5 publication-title: Soil Dyn. Earthq. Eng. doi: 10.1016/j.soildyn.2006.06.006 – volume: 183 start-page: 2622 year: 2012 ident: 15591_CR24 publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2012.07.008 – ident: 15591_CR23 doi: 10.1201/9781003168102 – volume-title: Vibration Problems in Engineering year: 2015 ident: 15591_CR16 – ident: 15591_CR8 doi: 10.5593/sgem2017/12/S02.118 – volume: 1 start-page: 140 issue: 50 year: 2016 ident: 15591_CR10 publication-title: Bull. Belarusian-Russ. Univ. – volume: 5 start-page: 329 year: 1996 ident: 15591_CR22 publication-title: Adv. Comput. Math. doi: 10.1007/BF02124750 – volume-title: Linear and Nonlinear Structural Mechanics year: 2004 ident: 15591_CR15 doi: 10.1002/9783527617562 – volume: 3 start-page: 2592 issue: 11 year: 2012 ident: 15591_CR2 publication-title: Int. J. Sci. Res. (IJSR) – volume: 12 start-page: 59 year: 2018 ident: 15591_CR18 publication-title: Appl. Comput. Mech. doi: 10.24132/acm.2018.413 – volume: 107 start-page: 167 issue: 2 year: 1981 ident: 15591_CR7 publication-title: J. Geotech. Eng. Div. doi: 10.1061/AJGEB6.0001095 – volume: 369 start-page: 7917 issue: 11 year: 2017 ident: 15591_CR20 publication-title: Trans. Am. Math. Soc. doi: 10.1090/tran/6911 – volume: 65 start-page: 89 year: 1959 ident: 15591_CR21 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1959-10290-1 – ident: 15591_CR1 – ident: 15591_CR6 doi: 10.1139/T07-071 – ident: 15591_CR11 – volume: 105 start-page: 227 issue: 1 year: 2021 ident: 15591_CR19 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-021-06653-3 – volume: 20 start-page: 517 issue: 4 year: 2016 ident: 15591_CR14 publication-title: Geosci. J. doi: 10.1007/s12303-015-0050-1 – volume: 10 start-page: 55 year: 1977 ident: 15591_CR3 publication-title: Rock Mech. doi: 10.1007/BF01261802 – volume: 2156475 start-page: 8 year: 2019 ident: 15591_CR9 publication-title: Adv. Civ. Eng. – volume: 85 year: 2020 ident: 15591_CR4 publication-title: Commun. Nonlinear Sci. Numer. Simulat. doi: 10.1016/j.cnsns.2020.105230 – volume: 45 start-page: 581 year: 2019 ident: 15591_CR17 publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2018.07.025 – volume: 6 start-page: 1106 issue: 5 year: 2011 ident: 15591_CR13 publication-title: Sci. Res. Essays – volume: 76 start-page: 96 year: 2015 ident: 15591_CR12 publication-title: Energy Proc. doi: 10.1016/j.egypro.2015.07.857 |
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| Snippet | The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to... Abstract The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and... |
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| SubjectTerms | 639/166 639/166/986 Approximation Boundary conditions Civil engineering Earthquakes Humanities and Social Sciences Mathematical models multidisciplinary Oscillations Science Science (multidisciplinary) Seismic engineering |
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| Title | Oscillations of retaining wall subject to Grob’s swelling pressure |
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