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On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory:equilibrium,governing equation and static deflection

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Applied Mathematics and Mechanics(English Edition) 2010年第1期31卷 37-54页

作者： c. W. lim Department of Building and construction City University of Hong Kong

This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams：（i） why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise？（ii） the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and （iii） the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experim

关键词： bending effective nonlocal bending moment nanobeam nanomechanics,nanoscale nonlocal elastic stress strain gradient

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Asymptotic analysis of a vibrating cantilever with a nonlinear boundary

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Science china(Physics,Mechanics & Astronomy) 2009年第9期52卷 1414-1422页

作者： c. W. lim Department of Building and construction City University of Hong Kong

Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.

关键词： asymptotic analysis vibration nonlinear boundary condition beam contact

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Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method

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Science china(Technological Sciences) 2009年第3期52卷 617-621页

作者： c. W. lim Department of Building and construction City University of Hong Kong

The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory. The governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam. The method of multiple scales is applied to the governing equa- tion to evaluate the nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and highlight the contributions of the nonlinear term and nonlocal effect.

关键词： nonlocal elasticity theory nanobeam natural frequency method of multiple scales

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Dynamic Response of composite Materials with 2D Reduced Micromorphic Model

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Acta Mechanica Solida Sinica 2022年第4期35卷 603-615页

作者： A.R.El Dhaba c.W.lim Department of Mathematics Faculty of ScienceDamanhour UniversityDamanhourEgypt Department of Architecture and civil Engineering City University of Hong KongKowloonHong Kong SARChina

In this article,we introduce a complete set of constitutive relations and field equations for the linear reduced micromorphic *** further investigate the internal variables and their relationship in the case of two-dimensional(2D)wave *** dynamic response is investigated for composite materials,which is due to an external wave in two dimensions applied at the boundary of the considered *** solutions for the model are unavailable at this stage due to dependency of the field equations on spatial and time variables in a complicated manner.A finite element approach is adopted to derive approximate solutions for the field equations,and numerical finite element solutions for the internal fields are presented in detail and discussed.

关键词： composite materials Finite element method(FEM) Reduced micromorphic model Wave propagation

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A Novel Application of Multi-Resonant Dissipative Elastic Metahousing for Bearings

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Acta Mechanica Solida Sinica 2021年第4期34卷 449-465页

作者： Muhammad c.W.lim N.S.Vyas Department of Architecture and civil Engineering City University of Hong KongKowloonHong Kong SARChina Department of Mechanical Engineering Indian Institute of Technology KanpurKanpur208016India

Bearing as an important machine element is widely used for industrial and automotive *** certain operational speed,bearings induce disturbing vibrations and noises that affect machine service life,productivity and passenger comfort in case of vehicle *** elastic metamaterials have caught considerable attention of scientific community due to their effective medium properties and peculiar dynamic characteristics including frequency bandgaps that can be effectively applied to attenuate and control undesirable vibration and *** a substantial amount of theoretical work for effective medium characteristics and dynamic properties of acoustic/elastic metamaterials has been reported,the practical design and application of these composite structures for real-life engineering problems still remain *** present study intends to investigate a potential application of dissipative elastic metamaterials in controlling the bearing-generated vibration and noises over an ultrawide frequency *** study is based on a simple analytical model together with rigorous finite element numerical *** has been established that the dissipative characteristic of resonant system caused by larger material mismatch broadens the local resonance bandgaps beyond the bounding resonance frequency at the cost of wave *** order to achieve broadband vibration and noise control,multi-resonant composite structures are embedded inside the bearing housing in five different *** reported results revealed the presence of broadband wave attenuation zone distributed from 3 to 52 kHz with consideration of material *** bearing-generated vibration and noises lying inside the wave attenuation zone will be *** feasibility study provides a new concept for the design and application of acoustic/elastic metamaterials in the bearing industry to improve machine service life and to enhance productivity and passenger comfo

关键词： Bearing metahousing Dissipative elastic metamaterials Frequency Local resonance bandgap Vibration attenuation zone

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Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach

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Acta Mechanica Sinica 2010年第5期26卷 755-765页

作者： c. W. lim c. Li Ji-Lin Yu Department of Building and construction City Universityof Hong Kong Tat Chee Avenue KowloonHong Kong SAR China State Key Laboratory of Structural Analysis for IndustrialEquipment Dalian University of TechnologyDalian 116024 China Department of Modem Mechanics University of Scienceand Technology of China Hefei 230026 China

In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.

关键词： Axially moving nanobeams critical velocity Free vibration Natural frequency Nonlocal elasticity

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Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第11期8卷 1740-1745页

作者： LU chao-feng lim c.W. XU Feng Department of civil Engineering Zhejiang University Hangzhou 310027 China） Department of Building and construction City University of Hong Kong Kowloon Hong Kong China Zhejiang Tiandi Environmental Protection Engineering co. Ltd. Hangzhou 310012 China

Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed.

关键词： Semi-analytical elasticity solution State-space-based differential quadrature method (SSDQM) Angle-ply laminates cylindrical bending

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Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

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Acta Mechanica Sinica 2008年第2期24卷 215-221页

作者： Liqun chen c. W. lim Hu Ding Department of Mechanics Shanghai University Shanghai 200444 China Department of construction and Building City University of Hong Kong Hong Kong China Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.

关键词： Nonlinear free vibration Axial movingstring Energetics conserved quantity Stability

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Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

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Applied Mathematics and Mechanics(English Edition) 2022年第12期43卷 1821-1840页

作者： cheng LI chengxiu ZHU c.W.lim Shuang LI School of Automotive Engineering Changzhou Institute of TechnologyChangzhou 213032Jiangsu ProvinceChina School of Rail Transportation Soochow UniversitySuzhou 215131Jiangsu ProvinceChina Department of Architecture and civil Engineering City University of Hong KongTat Chee AveKowloonHong Kong Special Administrative RegionChina

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite(FG-cNTRc)shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is *** arches with thickness-graded material properties,four different distribution patterns of carbon nanotubes(cNTs)are *** classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field,and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual *** critical geometric parameters are introduced to determine the criteria for buckling mode *** studies are carried out to demonstrate the effects of temperature variations,material parameters,geometric parameters,and elastic constraints on the stability of the *** is found that increasing the volume fraction of cNTs and distributing cNTs away from the neutral axis significantly enhance the bending stiffness of the *** addition,the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.

关键词： functional gradient carbon nanotube(cNT)reinforcement buckling in-plane instability nonlinear

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Development of an Internally circulating Fluidized Bed Membrane Reactor for Hydrogen Production from Natural Gas

Development of an Internally Circulating Fluidized Bed Membr...

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第七届全国氢能学术会议

作者： GRAcE John R lim c.jim Membrane Reactor Technologies Ltd 1800-200 Granville StreetVancouverCanada V6C 1S4 Department of Chemical and Biological EngineeringUniversity of British Columbia2360 East MallVancouverCanada V6T 1Z3 Membrane Reactor Technologies Ltd 1800-200 Granville StreetVancouverCanada V6C 1S4 Department of Chemical and Biological EngineeringUniversity of British Columbia2360 East MallVancouverCanada V6T 1Z3

＜正＞An innovative Internally circulating Fluidized Bed Membrane Reactor （IcFBMR） was designed and operated for ultra-pure hydrogen production from natural gas. The reactor includes internal catalyst solids circulation for conveying heat between a reforming zone and an oxidation zone. In the reforming zone, catalyst particles are transported upwards by reactant gas where steam reforming reactions are taking place and hydrogen is permeating through the membrane surfaces. Air is injected into the oxidation zone to generate heat which is carried by catalyst particles to the reforming zone supporting the endothermic steam reforming reaction. The technology development process is introduced: cold model test, pilot plant and industrial demonstration unit. The process flow diagram and key components of each unit are described. The IcFBMR process has the potential to provide improved performance relative to conventional SMR fixed-bed tubular reactors.

关键词： hydrogen fluidization membrane reforming

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