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On the truth of nanosc.le for nanobeams based on nonloc.l elastic.stress field theory:equilibrium,governing equation and static.deflec.ion

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Applied Mathematic. and Mec.anic.(English Edition) 2010年第1期31卷 37-54页

作者： c. w. lim Department of Building and c.nstruc.ion City University of Hong Kong

This paper has suc.essfully addressed three c.itic.l but overlooked issues in nonloc.l elastic.stress field theory for nanobeams：（i） w.y does the presenc. of inc.easing nonloc.l effec.s induc. reduc.d nanostruc.ural stiffness in many, but not c.nsistently for all, c.ses of study, i.e., inc.easing static.deflec.ion, dec.easing natural frequenc. and dec.easing buc.ling load, although physic.l intuition ac.ording to the nonloc.l elastic.ty field theory first established by Eringen tells otherw.se？（ii） the intriguing c.nc.usion that nanosc.le effec.s are missing in the solutions in many exemplary c.ses of study, e.g., bending deflec.ion of a c.ntilever nanobeam w.th a point load at its tip; and （iii） the non-existenc. of additional higher-order boundary c.nditions for a higher-order governing differential equation. Applying the nonloc.l elastic.ty field theory in nanomec.anic. and an exac. variational princ.pal approac., w. derive the new.equilibrium c.nditions, do- main governing differential equation and boundary c.nditions for bending of nanobeams. These equations and c.nditions involve essential higher-order differential terms w.ic. are opposite in sign w.th respec. to the previously studies in the static. and dynamic. of nonloc.l nano-struc.ures. The differenc. in higher-order terms results in reverse trends of nanosc.le effec.s w.th respec. to the c.nc.usion of this paper. Effec.ively, this paper reports new.equilibrium c.nditions, governing differential equation and boundary c.ndi- tions and the true basic.static.responses for bending of nanobeams. It is also c.nc.uded that the w.dely ac.epted equilibrium c.nditions of nonloc.l nanostruc.ures are in fac. not in equilibrium, but they c.n be made perfec. should the nonloc.l bending moment be replac.d by an effec.ive nonloc.l bending moment. These c.nc.usions are substantiated, in a general sense, by other approac.es in nanostruc.ural models suc. as strain gradient theory, modified c.uple stress models and experim

关键词： bending effec.ive nonloc.l bending moment nanobeam nanomec.anic.,nanosc.le nonloc.l elastic.stress strain gradient

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Asymptotic.analysis of a vibrating c.ntilever w.th a nonlinear boundary

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Sc.enc. c.ina(Physic.,Mec.anic. & Astronomy) 2009年第9期52卷 1414-1422页

作者： c. w. lim Department of Building and c.nstruc.ion City University of Hong Kong

Nonlinear vibration of a c.ntilever in a c.ntac. atomic.forc. mic.osc.pe is analyzed via an asymptotic.approac.. The asymptotic.solution is sought for a beam equation w.th a nonlinear boundary c.ndition. The steady-state responses are determined in primary resonanc. and subharmonic.resonanc.. The relations betw.en the response amplitudes and the exc.tation frequenc.es and amplitudes are derived from the solvability c.ndition. Multivaluedness oc.urs in the relations as a c.nsequenc. of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predic.s the jumping phenomenon for c.rtain parameters. The c.rves of the response amplitudes c.anging w.th the exc.tation frequenc.es are numeric.lly c.mpared w.th those obtained via the method of multiple sc.les. The c.lc.lation results demonstrate that the tw. methods predic. the same varying tendenc.es w.ile there are small quantitative differenc.s.

关键词： asymptotic analysis vibration nonlinear boundary c.ndition beam c.ntac.

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Nonlinear vibrations of nano-beams ac.ounting for nonloc.l effec. using a multiple sc.le method

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Sc.enc. c.ina(Tec.nologic.l Sc.enc.s) 2009年第3期52卷 617-621页

作者： c. w. lim Department of Building and c.nstruc.ion City University of Hong Kong

The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonloc.l elastic.ty theory. The governing equation is proposed by c.nsidering geometric.nonlinearity due to finite stretc.ing of the beam. The method of multiple sc.les is applied to the governing equa- tion to evaluate the nonlinear natural frequenc.es. Numeric.l examples are presented to demonstrate the analytic.l results and highlight the c.ntributions of the nonlinear term and nonloc.l effec..

关键词： nonloc.l elastic.ty theory nanobeam natural frequenc. method of multiple sc.les

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Dynamic.behaviour of axially moving nanobeams based on nonloc.l elastic.ty approac.

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Ac.a Mec.anic. Sinic. 2010年第5期26卷 755-765页

作者： c. w. lim c. Li Ji-Lin Yu Department of Building and c.nstruc.ion City Universityof Hong Kong Tat Chee Avenue KowloonHong Kong SAR China State Key Laboratory of Struc.ural Analysis for IndustrialEquipment Dalian University of TechnologyDalian 116024 China Department of Modem Mec.anic. University of Scienceand Technology of China Hefei 230026 China

In this artic.e, transverse free vibrations of axially moving nanobeams subjec.ed to axial tension are studied based on nonloc.l stress elastic.ty theory. A new.higher-order differential equation of motion is derived from the variational princ.ple w.th c.rresponding higher-order, non-c.assic.l boundary c.nditions. Tw. supporting c.nditions are investigated, i.e. simple supports and c.amped supports. Effec.s of nonloc.l nanosc.le, dimensionless axial veloc.ty, density and axial tension on natural frequenc.es are presented and disc.ssed through numeric.l examples. It is found that these fac.ors have great influenc. on the dynamic.behaviour of an axially moving nanobeam. In partic.lar, the nonloc.l effec. tends to induc. higher vibration frequenc.es as c.mpared to the results obtained from c.assic.l vibration theory. Analytic.l solutions for c.itic.l veloc.ty of these nanobeams w.en the frequenc. vanishes are also derived and the influenc.s of nonloc.l nanosc.le and axial tension on the c.itic.l veloc.ty are disc.ssed.

关键词： Axially moving nanobeams c.itic.l veloc.ty Free vibration Natural frequenc. Nonloc.l elastic.ty

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Energetic. and c.nserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

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Ac.a Mec.anic. Sinic. 2008年第2期24卷 215-221页

作者： Liqun c.en c. w. lim Hu Ding Department of Mec.anic. Shanghai University Shanghai 200444 China Department of c.nstruc.ion and Building City University of Hong Kong Hong Kong China Shanghai Institute of Applied Mathematic. and Mec.anic. Shanghai 200072 China

Nonlinear three-dimensional vibration of axially moving strings is investigated in the view.of energetic.. The governing equation is derived from the Eulerian equation of motion of a c.ntinuum for axially ac.elerating strings. The time-rate of the total mec.anic.l energy assoc.ated w.th the vibration is c.lc.lated for the string w.th its ends moving in a presc.ibed w.y. For a string moving in a c.nstant axial speed and c.nstrained by tw. fixed ends, a c.nserved quantity is proved to remain unc.anged during three-dimensional vibration, w.ile the string energy is not c.nserved. An approximate c.nserved quantity is derived from the c.nserved quantity in the neighborhood of the straight equilibrium c.nfiguration. The approximate c.nserved quantity is applied to verify the Lyapunov stability of the straight equilibrium c.nfiguration. Numeric.l simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mec.anic.l energy and the invarianc. of the c.nserved quantity.

关键词： Nonlinear free vibration Axial movingstring Energetic. c.nserved quantity Stability

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Free vibration of pre-tensioned nanobeams based on nonloc.l stress theory

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Journal of Zhejiang University-Sc.enc. A(Applied Physic. & Engineering) 2010年第1期11卷 34-42页

作者： c. w. lim c.eng LI Ji-lin YU Department of Building and c.nstruc.ion City University of Hong Kong Kowloon Hong Kong SAR China Department of Modern Mec.anic. University of Science and Technology of China Hefei 230026 China

The transverse free vibration of nanobeams subjec.ed to an initial axial tension based on nonloc.l stress theory is presented. It c.nsiders the effec.s of nonloc.l stress field on the natural frequenc.es and vibration modes. The effec.s of a small sc.le parameter at molec.lar level unavailable in c.assic.l mac.o-beams are investigated for three different types of boundary c.nditions:simple supports,c.amped supports and elastic.lly-c.nstrained supports. Analytic.l solutions for transverse deforma-tion and vibration modes are derived. Through numeric.l examples,effec.s of the dimensionless nanosc.le parameter and pre-tension on natural frequenc.es are presented and disc.ssed.

关键词： Nanobeam Natural frequenc. Nonloc.l stress Pre-tensioned Vibration mode

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3D thermoelastic.ty solutions for func.ionally graded thic. plates

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Journal of Zhejiang University-Sc.enc. A(Applied Physic. & Engineering) 2009年第3期10卷 327-336页

作者： Ji YING c.ao-feng LU c. w. lim Department of Mec.anic.l Engineering Zhejiang University Hangzhou 310027 China Department of c.vil Engineering Zhejiang University Hangzhou 310058 China Department of Building and c.nstruc.ion City University of Hong Kong Hong Kong China

Thermal-mec.anic.l behavior of func.ionally graded thic. plates, w.th one pair of opposite edges simply supported, is investigated based on 3D thermoelastic.ty. As for the arbitrary boundary c.nditions, a semi-analytic.l solution is presented via a hybrid approac. c.mbining the state spac. method and the tec.nique of differential quadrature. The temperature field in the plate is determined ac.ording to the steady-state 3D thermal c.nduc.ion. The Mori-Tanaka method w.th a pow.r-law.volume frac.ion profile is used to predic. the effec.ive material properties inc.uding the bulk and shear moduli, w.ile the effec.ive c.effic.ent of thermal expansion and the thermal c.nduc.ivity are estimated using other mic.omec.anic.-based models. To fac.litate the im-plementation of state spac. analysis through the thic.ness direc.ion, the approximate laminate model is employed to reduc. the inhomogeneous plate into a homogeneous laminate that delivers a state equation w.th c.nstant c.effic.ents. The present solutions are validated by c.mparisons w.th the exac. ones for both thin and thic. plates. Effec.s of gradient indic.s, volume frac.ion of c.ramic., and boundary c.nditions on the thermomec.anic.l behavior of func.ionally graded plates are disc.ssed.

关键词： Func.ionally graded plates Semi-analytic.l solutions 3D thermoelastic.ty Mori-Tanaka method

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Experimental and FEM Modal Analysis of a Deployable-Retrac.able w.ng

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Modern Mec.anic.l Engineering 2014年第4期4卷 183-197页

作者： P. Jia S. K. Lai w. Zhang c. w. lim Department of Arc.itec.ure and c.vil Engineering City University of Hong Kong Hong Kong China Shenzhen Researc. Institute City University of Hong Kong Shenzhen China c.llege of Mec.anic.l Engineering Beijing University of Technology Beijing China Meinhardt (M & E) Ltd Hong Kong China

The aim of this paper is to c.nduc. experimental modal analysis and numeric.l simulation to verify the struc.ural c.arac.eristic. of a deployable-retrac.able w.ng for airc.aft and spac.c.aft. A modal impac. test w.s c.nduc.ed in order to determine the free vibration c.arac.eristic.. Natural frequenc.es and vibration mode shapes w.re obtained via measurement in LMS Test. Lab. The frequenc. response func.ions w.re identified and c.mputed by forc. and ac.eleration signals, and then mode shapes of this morphing w.ng struc.ure w.re subsequently identified by PolyMAX modal parameter estimation method. FEM modal analysis w.s also implemented and its numeric.l results c.nvinc.ngly presented the mode shape and natural frequenc. c.arac.eristic. w.re in good agreement w.th those obtained from experimental modal analysis. Experimental study in this paper foc.ses on the transverse response of morphing w.ng as its moveable part is deploying or retreating. Vibration response to different rotation speeds have been c.llec.ed, managed and analyzed through the use of c.mparison methodology w.th eac. other. Evident phenomena have been disc.vered inc.uding the resonanc. on w.ic. most analysis is foc.sed bec.use of its potential use to generate large amplitude vibration of spec.fic.frequenc. or to avoid suc. resonant frequenc.es from a w.de spec.rum of response. Manufac.ured deployable-retrac.able w.ngs are studied in stage of experimental modal analysis, in w.ic. some nonlinear vibration resulted should be partic.larly noted bec.use suc. w.ng struc.ure displays a low.resonant frequenc. w.ic. is alw.ys optimal to be avoided for struc.ural safety and stability.

关键词： Deployable-Retrac.able w.ng Experimental Modal Analysis FEM Mode Shapes Natural Frequenc. LMS Test. Lab

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电动力学中衰减机械系统的非线性振荡方法

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力学季刊 2005年第4期26卷 534-538页

作者：林志华黎绍佳梁以德香港城市大学建筑系

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式,而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法(线性谐波平衡法)而产生色散关系,再把平均法应用在弱非线性的耗散... 详细信息

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式,而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法(线性谐波平衡法)而产生色散关系,再把平均法应用在弱非线性的耗散系统中得到非常准确的瞬变反应。在此提出的方法不仅考虑能量耗散, 而且利用简单的线性代数等式关系来代替冗长及复杂的分析近似解。

关键词：谐波平衡法非线性振荡电动力学

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Novel N-doped multic.annel c.rbon nanofiber arc.itec.ure w.th porous c.S nanoprisms for high-performanc. potassium-ion batteries

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Rare Metals 2024年第3期43卷 971-983页

作者： Jae Bong lim Seung-Keun Park Department of Advanc.d Materials Engineering Chung-Ang UniversityGyeonggi-do17546Republic of Korea Department of Intelligenc. Energy and Industry Chung-Ang UniversitySeoul06974Republic of Korea w.stern Seoul c.nter Korea Basic Science InstituteSeoul03759Republic of Korea

Potassium-ion batteries(PIBs)have gained signific.nt attention as an alternative to lithium-ion batteries(LIBs)due to the abundanc. of potassium(K)and low.***,the diffic.lty in finding appropriate elec.rode materials that c.n effic.ently store the larger K ions has hindered their prac.ic.l ***,w. report a novel anode material,N-doped multic.annel c.rbon nanofibers embedded w.th porous c.S nanoprisms(c.P@NMc.F),for high-performanc. *** c.P@NMc.F w.s synthesized using a tw.-step strategy c.mprising of the elec.rospinning of c. ac.tate hydroxide nanoprism/binary polymer blend and a subsequent heat *** porous c.S nanoprisms w.th an anisotropic.morphology w.re w.ll aligned along the length axis of the N-doped multic.annel c.rbon nanofibers,thus ensuring their struc.ural stability during the repeated c.arge-disc.arge *** addition,numerous pores fac.litated the transport of elec.rons and ***,the c.P@NMc.F anode exhibited exc.llent elec.roc.emic.l performanc.,delivering a high spec.fic.c.pac.ty of 368 mAh·g^(-1)at 0.5 A·g^(-1)after 200 c.c.es and exc.llent rate c.pability(232 mAh·g^(-1)at 2.0 A·g^(-1)).

关键词： K-ion batteries c.balt sulfide Multic.annel struc.ured c.mposite Elec.rospinning Nanoprism Porous struc.ure

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