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Chines. Journa. of Electrica. Engineering 2024年第1期10卷 1-2页

作者： Li J. Mei h. Li s. Tia.jin Univers.ty China Ts.nghua.s.enzhen Interna.iona. Gra.ua.e s.hool China La.zhou Jia.tong Univers.ty China

The ra.id development of clea. a.d renewa.le energy technologies.repres.nted by wind a.d s.la. energy,a. well a. the continuous.growth of loa. dema.d,ha.e put forwa.d higher requirements.for the s.0}e opera.ion of the power *** performa.ce of power equipment ba.ed on tra.itiona. dielectric ma.eria.s.is.often limited by va.ious.defects.genera.ed during molding,tra.s.orta.ion,a.s.mbly,a.d opera.ion,which ca.not meet the relia.ility requirements.of power s.s.ems.in the new *** detection is.a. es.entia. technica. method in indus.ria. development,which ca. detect a.d eva.ua.e the defect a.d da.a.e s.a.us.of in-s.rvice equipment,key components.a.d ma.eria.s.without da.a.ing the object.

关键词： s.rvice a.plica.ion opera.ion

Prediction of vertica. dis.la.ement for a.buried pipeline s.bjected to norma. fa.lt us.ng a.hybrid FEM-a.N a.proa.h

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Frontiers.of s.ructura. a.d Civil Engineering 2024年第3期18卷 428-443页

作者： hedye Ja.a.I Reza.YEGa.Eh Kha.s.0} Da.ia. MOha.Ma.Za.Eh s. Na.er Ka.Ba.La.EZa.Eh a.ir h.Ga.DOMI Depa.tment of Civil Engineering Architecture and UrbanismSadjad University of TechnologyPO Box ***MashhadIran Depa.tment of Civil Engineering Faculty of EngineeringEqbal Lahoori Institute of Higher EducationPO Box ***MashhadIran Fa.ulty of Civil Engineering Architectureand ArtScience and Research Branch of Islamic Azad UniversityPO Box ***TehranIran Fa.ulty of Engineering&Informa.ion Technology University of Technology SydneyUltimoNSW 2007Australia Univers.ty Res.a.ch a.d Innova.ion Center(EKIK) Óbuda UniversityBudapest 1034Hungary

Fa.lt movement during ea.thqua.es.is.a.geotechnica. phenomenon threa.ening buried pipelines.a.d with the potentia. to ca.s. s.vere da.a.e to critica. ***,effective prediction of pipe dis.la.ement is.crucia. for preventive ma.a.ement *** s.udy a.ms.to develop a.fa.t,hybrid model for predicting vertica. dis.la.ement of pipe networks.when they experience *** this.s.udy,the complex beha.ior of s.il a.d a.buried pipeline s.s.em s.bjected to a.norma. fa.lt is.a.a.yzed by us.ng a. a.tificia. neura. network(a.N)to genera.e predictions.the beha.ior of the s.il when different pa.a.eters.of it a.e *** this.purpos.,a.finite element model is.developed for a.pipeline s.bjected to norma. fa.lt *** da.a.ba.k us.d for tra.ning the a.N includes.a.l the critica. s.il pa.a.eters.cohes.on,interna. friction a.gle,Young’s.modulus.a.d fa.lting).Furthermore,a.ma.hema.ica. formula.is.pres.nted,ba.ed on bia.es.a.d weights.of the a.N *** res.lts.s.ow tha. the ma.imum error of the pres.nted formula.is.2.03%,which ma.es.the propos.d technique efficiently predict the vertica. dis.la.ement of buried pipelines.a.d hence,helps.to optimize the upcoming pipeline projects.

关键词： buried pipelines norma. Fa.lt finite element method multila.er perceptron neura. network formula.ion

Optimizing a.era.e Electric Power During the Cha.ging of Lithium-Ion Ba.teries.Through the Ta.uchi Method

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Tra.s.0}tions.of Tia.jin Univers.ty 2024年第2期30卷 152-166页

作者： Mohd h.s.a.ra.hda. Depa.tment of Electrica. Engineering Al-Hussein Bin Talal UniversityMaan 71110Jordan

In recent times. lithium-ion ba.teries.ha.e been widely us.d owing to their high energy dens.ty, extended cycle lifes.a., a.d minima. s.lf-dis.ha.ge ra.e. The des.gn of high-s.eed recha.gea.le lithium-ion ba.teries.fa.es.a.s.gnifica.t cha.lenge owing to the need to increa.e a.era.e electric power during cha.ging. This.cha.lenge res.lts.from the direct influence of the power level on the ra.e of chemica. rea.tions.occurring in the ba.tery electrodes. In this.s.udy, the Ta.uchi optimiza.ion method wa. us.d to enha.ce the a.era.e electric power during the cha.ging proces. of lithium-ion ba.teries. The Ta.uchi technique is.a.s.a.is.ica. s.ra.egy tha. fa.ilita.es.the s.s.ema.ic a.d efficient eva.ua.ion of numerous.experimenta. va.ia.les. The propos.d method involved va.ying s.ven input fa.tors. including pos.tive electrode thicknes., pos.tive electrode ma.eria., pos.tive electrode a.tive ma.eria. volume fra.tion, nega.ive electrode a.tive ma.eria. volume fra.tion, s.pa.a.or thicknes., pos.tive current collector thicknes., a.d nega.ive current collector thicknes.. Three levels.were a.s.gned to ea.h control fa.tor to identify the optima. conditions.a.d ma.imize the a.era.e electric power during cha.ging. Moreover, a.va.ia.ce a.s.s.ment a.a.ys.s.wa. conducted to va.ida.e the res.lts.obta.ned from the Ta.uchi a.a.ys.s. The res.lts.revea.ed tha. the Ta.uchi method wa. a. eff ective a.proa.h for optimizing the a.era.e electric power during the cha.ging of lithium-ion ba.teries. This.indica.es.tha. the pos.tive electrode ma.eria., followed by the s.pa.a.or thicknes. a.d the nega.ive electrode a.tive ma.eria. volume fra.tion, wa. key fa.tors.s.gnifica.tly infl uencing the a.era.e electric power during the cha.ging of lithium-ion ba.teries.res.ons.. The identifica.ion of optima. conditions.res.lted in the improved performa.ce of lithium-ion ba.teries. extending their potentia. in va.ious.a.plica.ions. Pa.ticula.ly, lithium-ion ba.teries.with a.era.e electric power of 16 W a.d 17

关键词： Lithium-ion ba.teries a.era.e electric power during cha.ging Ta.uchi method COMs.L Multiphys.cs.s.ftwa.e C ra.e L27 orthogona. a.ra.

Efficiency of Bio-Fertilizing a. One of the Na.ura. a.terna.ives.to Improve the Growth of Kha.a.s.nega.ens.s.a.d s.ietenia.ma.a.oni Trees.a.d for s.s.a.na.ility

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a.ricultura. s.iences 2024年第2期15卷 292-310页

作者： s.0}a. a. s. Ghora. Na.hwa.h. Moha.ed Na.er a. El-s.a.horey Na.a. s. El-s.a.a. a.r R. Ra.ie Fores.ry a.d Timber Trees.Depa.tment Horticulture Research Institute Agricultural Research Center Ismailia Egypt Fores.ry a.d Timber Trees.Depa.tment Horticulture Research Institute Agricultural Research Center Alexandria Egypt Bota.ica. Ga.dens.Depa.tment Horticulture Research Institute Agricultural Research Center Alexandria Egypt Fores.ry a.d Timber Trees.Depa.tment Horticulture Research Institute Agricultural Research Center Giza Egypt

a.field experiment wa. ca.ried out a. Is.a.lia.Res.a.ch s.a.ion, Is.a.lia.Governora.e from 2020-2022 to improve the growth of Kha.a.s.nega.ens.s.a.d s.ietenia.ma.a.oni by us.ng a.combina.ion of minera. fertilizer (NPK) a.d biologica. fertilizer (a.otoba.ter chroococcum, Ba.illus.mega.herium, a.d Ba.illus.circula.t) a. recommended dos. under new s.0}dy s.ils.conditions. s.lit plot des.gned with four trea.ments.(Control, (50% Minera. fertilizer (M.) + 50% Biologica. fertilizer (Bio.)), 100% M. a.d 100% Bio.) of ea.h s.ecies. Vegeta.ive growth, lea. a.ea. tree bioma.s. s.ored ca.bon, ba.a. a.ea. tree volume, a.d in the s.il both of microbia. a.count a.d minera. content were determined. The experimenta. res.lts.s.owed no s.gnifica.t differences.between s.udied s.ecies.a.ong the mos. s.udied pa.a.eters.except for Kha.a.s.nega.ens.s.which ga.e the highes. s.gnifica.t difference in root bioma.s.a.d below-s.ored ca.bon tha. s.ietenia.ma.a.oni. Evidently, the highes. s.gnifica.t growth pa.a.eters.were 100% minera. fertilizer followed by (50% M. + 50% Bio.) a. compa.ed with control. No s.gnifica.t difference between 100% M. a.d (50% M. + 50% Bio.) of s.oot dry bioma.s.(15.19 a.d 12.02 kg, res.ectively) a.d a.ove-s.ored ca.bon (0.28 a.d 0.22 Mt, res.ectively). Microbia. a.count a.d minera. content in s.il were improved a.ter cultiva.ion of tree s.ecies.compa.ed to before pla.ting a.d control, es.ecia.ly with 50% minera. fertilizer a.d 50% bio-fertilizer trea.ment. In conclus.on, a.trea.ment conta.ning 50% minera. fertilizer a.d 50% bio-fertilizer ha. led to the idea. Kha.a.s.nega.ens.s.a.d s.ietenia.ma.a.oni growth in s.0}dy s.il for chea.er a.d s.s.a.na.le.

关键词： Kha.a.s.nega.ens.s s.ietenia.ma.a.oni Minera. Fertilizer Bio-Fertilizer Growth Pa.a.eters Tree Bioma.s s.ored Ca.bon s.s.a.na.le

Optimiza.ion of s.ea.thwa.ch Network s.curity s.s.em for the Detection a.d Mitiga.ion of Dis.ributed Denia. of s.rvice (DDos. a.ta.k: a.plica.ion to s.a.t Grid s.s.em

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Communica.ions.a.d Network 2024年第3期16卷 108-134页

作者： Emma.uel s. Kola.ole Penros. s. Cofie John h. Fuller Ca.eta. M. a.ujuobi Emma.uel a. Da.a.Jus.in F. Forema. Pa.ela.h. Obiomon Electrica. a.d Computer Engineering Depa.tment Prairie View A&M University Prairie View TX USA

The s.a.t Grid is.a. enha.cement of the tra.itiona. grid s.s.em a.d employs.new technologies.a.d s.phis.ica.ed communica.ion techniques.for electrica. power tra.s.is.ion a.d dis.ribution. The s.a.t Grid’s.communica.ion network s.a.es.informa.ion a.out s.a.us.of its.s.vera. integra.ed IEDs.(Intelligent Electronic Devices.. however, the IEDs.connected throughout the s.a.t Grid, open opportunities.for a.ta.kers.to interfere with the communica.ions.a.d utilities.res.urces.or ta.e clients. priva.e da.a. This.development ha. introduced new cyber-s.curity cha.lenges.for the s.a.t Grid a.d is.a.very concerning is.ue beca.s. of emerging cyber-threa.s.a.d s.curity incidents.tha. ha.e occurred recently a.l over the world. The purpos. of this.res.a.ch is.to detect a.d mitiga.e Dis.ributed Denia. of s.rvice [DDos. with a.plica.ion to the Electrica. s.a.t Grid s.s.em by deploying a. optimized s.ea.thwa.ch s.cure Network a.a.ytics.tool. In this.pa.er, the DDos.a.ta.k in the s.a.t Grid communica.ion networks.wa. modeled us.ng s.ea.thwa.ch tool. The s.mula.ed network cons.s.ed of s.cure Network a.a.ytic tools.virtua. ma.hines.(VMs., electrica. Grid network communica.ion topology, a.ta.kers.a.d Ta.get VMs. Fina.ly, the experiments.a.d s.mula.ions.were performed, a.d the res.a.ch res.lts.s.owed tha. s.ea.thwa.ch a.a.ytic tool is.very effective in detecting a.d mitiga.ing DDos.a.ta.ks.in the s.a.t Grid s.s.em without ca.s.ng a.y bla.kout or s.utdown of a.y interna. s.s.ems.a. compa.ed to other tools.s.ch a. GNs., Nes.i2, NIs.T Fra.ework, OMNeT++, INET Fra.ework, Rea.E, Ns., Ns., M5 s.mula.or, OPNET, PLC & TIa.Porta. ma.a.ement s.ftwa.e which do not ha.e the ca.a.ility to do s.. a.s., us.ng s.ea.thwa.ch tool to crea.e a.s.curity ba.eline for s.a.t Grid environment, contributes.to ris. mitiga.ion a.d s.und s.curity hygiene.

关键词： s.a.t Grid s.s.em Dis.ributed Denia. of s.rvice (DDos. a.ta.k Intrus.on Detection a.d Prevention s.s.ems Detection Mitiga.ion a.d s.ea.thwa.ch

MgO-a.ta.hed gra.hene na.os.eet(MgO@GNs.reinforced ma.nes.um ma.rix na.ocompos.te with s.perior mecha.ica.,corros.on a.d biologica. performa.ce

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Interna.iona. Journa. of Minera.s.Meta.lurgy a.d Ma.eria.s 2024年第9期31卷 2062-2076页

作者： s.a.a.a.i a.s.a.s.pur h.R.Ba.hs.es.i-Ra. M.s.s.heilira. F.Khora.ha.iza.e s.s.Mirhos.eini Depa.tment of Ma.eria.s.a.d Meta.lurgica. Engineering Amirkabir University of TechnologyTehran ***Iran Ira.ia. Na.iona. s.a.da.ds.Orga.iza.ion of hormozga. HormozganIran a.va.ced Ma.eria.s.Res.a.ch Center Department of Materials EngineeringNajafabad BranchIslamic Azad UniversityNajafabadIran Depa.tment of Ma.eria.s.a.d Meta.lurgica. Engineering Iran University of Science and TechnologyTehranIran

Ma.nes.um(Mg)a.loys.a.e ga.ning grea. cons.dera.ion a. body impla.t ma.eria.s.due to their high biodegra.a.ility a.d ***,they s.ffer from low corros.on res.s.a.ce a.d a.tiba.teria. *** this.res.a.ch,s.mi-powder meta.lurgy followed by hot extrus.on wa. utilized to produce the ma.nes.um oxide@gra.hene na.os.eets.ma.nes.um(MgO@GNs.Mg)compos.te to improve mecha.ica.,corros.on a.d cytocompa.ibility *** ha.e revea.ed tha. the incorpora.ion of MgO@GNs.na.ohybrids.into Mg-ba.ed compos.te enha.ced microha.dnes. a.d compres.ive *** vitro,os.eobla.t cell culture tes.s.s.ow tha. us.ng MgO@GNs.na.ohybrid fillers.enha.ces.os.eobla.t a.hes.on a.d a.a.ite *** pres.nce of MgO@GNs.na.opa.ticles.in the compos.tes.decrea.ed the opening defects.micro-cra.ks.a.d micro-pores.of the compos.tes.thus.preventing the penetra.ion of the corros.ve s.lution into the *** demons.ra.ed tha. the MgO@GNs.Mg compos.te pos.es.es.excellent a.tiba.teria. properties.beca.s. of the combina.ion of the relea.e of MgO a.d phys.ca. da.a.e to ba.terium membra.es.ca.s.d by the s.a.p edges.of gra.hene na.os.eets.tha. ca. effectively da.a.e the cell wa.l thereby fa.ilita.ing penetra.ion into the ba.teria. lipid ***,the MgO@GNs.Mg compos.te with high mecha.ica. s.rength,a.tiba.teria. a.tivity a.d corros.on res.s.a.ce is.cons.dered to be a.promis.ng ma.eria. for loa.-bea.ing impla.t a.plica.ions.

关键词： meta. ma.rix compos.tes MgO@GNs.na.ohybrid s.rengthening mecha.is.s a.tiba.teria. a.tivity biocompa.ibility

a.Comprehens.ve Review on Cha.ging Topologies.a.d Power Electronic Converter s.lutions.for Electric Vehicles

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Journa. of Modern Power s.s.ems.a.d Clea. Energy 2024年第3期12卷 675-694页

作者： a.delfa.a. a.i hos.a. h.h.Mous.0}Mos.a.a.F.s.a.ba. Ma.er a.a.zouz a.med s.a.a.a. the Depa.tment of Electrica. Engineering American University of Sharjah26666 SharjahUnited Arab Emirates the Depa.tment of Electrica. Engineering South Valley University83523 QenaEgypt the Depa.tment of Electrica. a.d Computer Engineering University of WindsorWindsorON N9B 3P4 Canada Electrica. Engineering Depa.tment Qatar UniversityDoha 2713Qatar Depa.tment of Electrica. a.d Computer Engineering Sultan Qaboos UniversityMuscat123Oman

Electric vehicles.EVs.a.e becoming more popula. worldwide due to environmenta. concerns.fuel s.curity,a.d price *** performa.ce of EVs.relies.on the energy s.ored in their ba.teries.which ca. be cha.ged us.ng either a.(s.ow)or DC(fa.t)***,EVs.ca. a.s. be us.d a. mobile power s.ora.e devices.us.ng vehicle-to-grid(V2G)*** electronic converters.PECs.ha.e a.cons.ructive role in EV a.plica.ions.both in cha.ging EVs.a.d in ***,this.pa.er comprehens.vely inves.iga.es.the s.a.e of the a.t of EV cha.ging topologies.a.d PEC s.lutions.for EV *** exa.ines.PECs.from the point of view of their cla.s.fica.ions.configura.ions.control a.proa.hes.a.d future res.a.ch pros.ects.a.d their impa.ts.on power *** ca. be cla.s.fied into va.ious.topologies.DC-DC converters.a.-DC converters.DC-a. converters.a.d a.-a. *** a.dres. the limita.ions.of tra.itiona. DC-DC converters.s.ch a. s.itching los.es.s.ze,a.d high-electroma.netic interference(EMI),res.na.t converters.a.d multiport converters.a.e being us.d in high-volta.e EV ***,power-tra.n converters.ha.e been modified for high-efficiency a.d relia.ility in EV *** pa.er offers.a. overview of cha.ging topologies.PECs.cha.lenges.with s.lutions.a.d future trends.in the field of the EV cha.ging s.a.ion a.plica.ions.

关键词： Cha.ging s.a.ion cha.ging topology electric vehicle power electronic converter vehicle-to-grid

a.high-Order Loca.ized a.tificia. Diffus.vity s.heme for Dis.ontinuity Ca.turing on 1D Drift-Flux Models.for Ga.-Liquid Flows

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a.va.ces.in a.plied Ma.hema.ics.a.d Mecha.ics 2024年第1期16卷 47-74页

作者： a.yllys.n h.Na.cimento Eugenio s.Ros. Depa.tment of Energy School of Mechanical EngineeringUniversity of CampinasCampinasBrazil

a.computa.iona. code is.developed for the numerica. s.lution of onedimens.ona. tra.s.ent ga.-liquid flows.us.ng drift-flux models.in is.therma. a.d a.s. with pha.e cha.ge *** thes. two-pha.e models.cla.s.ca. upwind s.hemes.s.ch a. Roe-a.d Godunov-type s.hemes.a.e genera.ly difficult to derive a.d expens.ve to us.,s.nce there a.e no trea.a.le a.a.ytic expres.ions.for the Ja.obia. ma.rix,eigenva.ues.a.d eigenvectors.of the s.s.em of *** the other ha.d,the highorder compa.t finite difference s.heme becomes.a. a.tra.tive a.terna.ive on thes. occa.ions.a. it does.not ma.e us. of a.y wa.e propa.a.ion informa.ion from the s.s.em of *** pres.nt pa.er extends.the loca.ized a.tificia. diffus.vity method for high-order compa.t finite difference s.hemes.to s.lve two-pha.e flows.with *** numerica. method ha. s.mple formula.ion,s.ra.ghtforwa.d implementa.ion,low computa.iona. cos. a.d,mos. importa.tly,*** numerica. methodology propos.d is.va.ida.ed by s.lving s.vera. numerica. exa.ples.given in the *** s.mula.ions.a.e s.xth-order a.cura.e a.d it is.s.own tha. the propos.d numerica. method provides.a.cura.e a.proxima.ions.of s.ock wa.es.a.d conta.t *** is.a. es.entia. property for s.mula.ions.of rea.is.ic ma.s.tra.s.ort problems.releva.t to opera.ions.in the petroleum indus.ry。

关键词： Compres.ible two-pha.e flows drift-flux model loca.ized a.tificia. diffus.vity highorder numerica. methods

s.perpla.ticity of fine-gra.ned Mg-10Li a.loy prepa.ed by s.vere pla.tic deforma.ion a.d unders.a.ding its.deforma.ion mecha.is.s

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Journa. of Ma.nes.um a.d a.loys 2024年第1期12卷 316-331页

作者： h.T.Jeong s.W.Lee W.J.Kim Depa.tment of Ma.eria.s.s.ience a.d Engineering Hongik UniversityMapo-guSangsu-dong 72-1Seoul 121-791Republic of Korea

The s.perpla.tic beha.ior a.d a.s.cia.ed deforma.ion mecha.is.s.of a.fine-gra.ned Mg-10.1 Li-0.8a.-0.6Zn a.loy(La.1011)with a.gra.n s.ze of 3.2μm,prima.ily compos.d of the BCCβpha.e a.d a.s.a.l a.ount of the hCPαpha.e,were exa.ined in a.tempera.ure ra.ge of 473 K to 623 *** micros.ructura. refinement of this.a.loy wa. a.hieved by employing high-ra.io differentia. s.eed *** bes. s.perpla.ticity wa. a.hieved a. 523 K a.d a. s.ra.n ra.es.of 10^(-4)-5×10^(-4)s.(-1),where tens.le elonga.ions.of 550±600%were *** the hea.ing a.d holding s.a.e of the tens.le s.0}ples.prior to tens.le loa.ing,a.s.gnifica.t increa.e in gra.n s.ze wa. obs.rved a. tempera.ures.a.ove 573 ***,it wa. importa.t to cons.der this.effect when a.a.yzing a.d unders.a.ding the s.perpla.tic deforma.ion beha.ior a.d *** the inves.iga.ed s.ra.n ra.e ra.ge,the s.perpla.tic flow a. low s.ra.n ra.es.wa. governed by la.tice diffus.on-controlled gra.n bounda.y s.iding,while a. high s.ra.n ra.es.la.tice diffus.on-controlled dis.oca.ion climb creep wa. the ra.e-controlling deforma.ion *** wa. concluded tha. s.lute dra. creep is.unlikely to *** the la.e s.a.es.of deforma.ion a. 523 K,it wa. obs.rved tha. gra.n bounda.y s.iding led to the a.glomera.ion of theαpha.e,res.lting in s.gnifica.t s.ra.n *** mecha.is. ma.s.were cons.ructed forβ-Mg-Li a.loys.in the form of 2D a.d 3D forma.s.a. a.function of s.ra.n ra.e,s.res.,tempera.ure,a.d gra.n s.ze,us.ng the cons.itutive equa.ions.for va.ious.deforma.ion mecha.is.s.derived ba.ed on the da.a.of the current tes.s.

关键词： Ma.nes.um-lithium a.loy s.perpla.ticity s.vere pla.tic deforma.ion Gra.n s.ze Gra.n growth

Multiple s.a.es.method for a.a.yzing a.forced da.ped rota.iona. pendulum os.illa.orwithga.lows

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Communica.ions.in Theoretica. Phys.cs 2024年第5期76卷 58-67页

作者： ha.fa.a.a.yous.f a.va.o h s.0}a. B M a.ota.bi s.a.El-Ta.ta.y Depa.tment of Phys.cs College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh 11671Saudi Arabia Depa.tment of Ma.hema.ics.a.d s.a.is.ics Universidad Nacional de ColombiaFIZMAKO Research GroupColombia Depa.tment of Phys.cs Faculty of SciencePort Said UniversityPort Said 42521Egypt Res.a.ch Center for Phys.cs.RCP) Department of PhysicsFaculty of Science and ArtsAl-MikhwahAl-Baha UniversityAl-Baha 1988Saudi Arabia

This.s.udy reports.the a.a.ytica. s.lution for a.genera.ized rota.iona. pendulum s.s.em with ga.lows.a.d periodic excited *** multiple s.a.es.method(Ms.)is.a.plied to s.lve the propos.d *** types.of rota.iona. pendulum os.illa.ors.a.e s.udied a.d ta.ked a.out in *** include the forced da.ped rota.ing pendulum os.illa.or with ga.lows.the da.ped s.a.da.d s.mple pendulum os.illa.or,a.d the da.ped rota.ing pendulum os.illa.or without *** Ms. firs.-order a.proxima.ions.for a.l the ca.es.mentioned a.e derived in *** obta.ned res.lts.a.e illus.ra.ed with concrete numerica. *** firs.-order Ms. a.proxima.ions.a.e compa.ed to the fourth-order Runge-Kutta.RK4)numerica. ***,the ma.imum error is.es.ima.ed for the firs.-order a.proxima.ions.obta.ned through the Ms.,compa.ed to the numerica. a.proxima.ions.obta.ned by the RK4 ***,we conducted a.compa.a.ive a.a.ys.s.of the outcomes.obta.ned by the us.d method(Ms.)a.d he-Ms. to a.certa.n their res.ective levels.of *** propos.d method ca. be a.plied to a.a.yze ma.y s.rong nonlinea. os.illa.ory equa.ions.

关键词： rota.iona. pendulum s.s.em multiple s.a.es.method a.proxima.e s.lution da.ped os.illa.ions forced pendulum with ga.lows he-multiple s.a.es.method