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Vibr.tion analysis of multi-walled car.on nanotubes embedded in elastic medium

Fr.ntier. of Str.ctur.l and Civil Engineer.ng 2014年第2期8卷 151-159页

作者： pattabhi r. budarapu Sudhir.Sastr. YB Br.hmanandam JAVVAJI D. r.y MAHAPATr. Institute of Str.ctur.l Mechanics Bauhaus University of Weimar Weimar 99423 Germany Deptar.ent of Aer.nautical Engineer.ng Institute of Aeronautical Engineering Hyderabad 500043 India Depar.ment of Aer.space Engineer.ng Indian Institute of Science Bangalore 560012 India

We pr.pose a method to estimate the natur.l fr.quencies of the multi-walled car.on nanotubes （MWCNTs） embedded in an elastic medium. Each of the nested tubes is tr.ated as an individual bar.inter.cting with the adjacent nanotubes thr.ugh the inter.tube Van der.Waals for.es. The effect of the elastic medium is intr.duced thr.ugh an elastic model. The mathematical model is finally r.duced to an eigen value pr.blem and the eigen value pr.blem is solved to ar.ive at the inter.tube r.sonances of the MWCNTs. Var.ation of the natur.l fr.quencies with differ.nt par.meter. ar. studied. The estimated r.sults fr.m the pr.sent method ar. compar.d with the liter.tur. and r.sults ar. obser.ed to be in close agr.ement.

关键词： natur.l fr.quencies multi-walled car.on nanotubes (MWCNTS) elastic medium

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An ar.ificial neur.l networ. based deep collocation method for.the solution of tr.nsient linear.and nonlinear.par.ial differ.ntial equations

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Fr.ntier. of Str.ctur.l and Civil Engineer.ng 2024年第8期18卷 1296-1310页

作者： Abhishek MISHr. Cosmin ANITESCU pattabhi r.maiah budarapu Sundar.r.jan NATAr.JAN Pandu r.ng VUNDAVILLI Timon r.BCZUK School of Mechanical Sciences Indian Institute of TechnologyBhubaneswar 752050India Institute of Str.ctur.l Mechanics Bauhaus University of WeimarWeimar 99423Germany Depar.ment of Mechanical Engineer.ng Indian Institute of Technology MadrasChennai 600036India

A combined deep machine lear.ing(DML)and collocation based appr.ach to solve the par.ial differ.ntial equations using ar.ificial neur.l networ.s is *** developed method is applied to solve pr.blems gover.ed by the Sine–Gor.on equation(SGE),the scalar.wave equation and *** methods ar. studied:one is a space-time for.ulation and the other.is a semi-discr.te method based on an implicit r.nge–Kutta(r.)time *** methodology is implemented using the Tensor.low fr.mewor. and it is tested on sever.l numer.cal *** on the r.sults,the r.lative nor.alized er.or.was obser.ed to be less than 5%in all cases.

关键词： collocation method ar.ificial neur.l networ.s deep machine lear.ing Sine-Gor.on equation tr.nsient wave equation dynamic scalar.and elasto-dynamic equation r.nge-Kutta method

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Physics-infor.ed neur.l networ.s for.estimating str.ss tr.nsfer.mechanics in single lap joints

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Jour.al of Zhejiang Univer.ity-Science A(Applied Physics & Engineer.ng) 2021年第8期22卷 621-631页

作者： Shivam SHAr.A r.jneesh AWASTHI Yedlabala Sudhir.SASTr. pattabhi r.maiah budarapu School of Mechanical Sciences Indian Institute of TechnologyBhubaneswar 752050India Depar.ment of Aer.nautical Engineer.ng Institute of Aeronautical EngineeringHyderabad 500043India

With the explosive gr.wth of computational r.sour.es and data gener.tion,deep machine lear.ing has been successfully employed in var.ous *** impor.ant and emer.ing scientific application of deep lear.ing involves solving differ.ntial ***,physics-infor.ed neur.l networ.s(PINNs)ar. developed to solve the differ.ntial equations associated with a specific scientific *** such,algor.thms for.solving the differ.ntial equations by embedding their.initial and boundar. conditions in the cost function of the ar.ificial neur.l networ.s using algor.thmic differ.ntiation must also be *** this study,var.ous PINNs ar. adopted to estimate the str.sses in the tablets and the inter.hase of a single lap *** pr.posed model is r.pr.sented by two four.h-or.er.non-homogeneous coupled par.ial differ.ntial equations,with the axial str.sses in the upper.and lower.tablets adopted as the dependent *** axial str.sses ar. a function of the tablet length,which pr.sents the independent ***,the axial str.sses in the tablets ar. estimated by solving the coupled par.ial differ.ntial equations when subjected to the boundar. conditions,wher.as the r.maining str.ss components ar. expr.ssed in ter.s of axial *** r.sults obtained using the developed methodology ar. validated using the r.sults obtained via MAPLE softwar..

关键词： Physics-infor.ed neur.l networ.s(PINNs) Algor.thmic differ.ntiation Ar.ificial neur.l networ.s Loss function Single lap joint

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