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The refined theory of deep rectangular beams based on general solutions of elasticity

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science china(Physics,{2. & Astronomy) 2006年第3期49卷 291-303页

作者： GAO Yang1 & WANG Minzhong2.1. College of science, china Agricultural {2., beijing 100083, china 2. State key laboratory for turbulence and complex Systems and Department of mechanics and Engi- neering science, peking university,{{12., china College of science China Agricultural University Beijing 100083 China State key laboratory for {2. complex Systems Department of mechanics engineering science Peking University Beijing 100871 China

The problem of deducing one-dimensional theory from two-dimensional the- ory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the re- fined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two ex- amples, it is shown that the new theory provides better results than Levinson’s beam the- ory when compared with those obtained from the linear theory of elasticity.

关键词： deep rectangular beams,the refined theory,Papkovich-Neuber solution,Lur'e method,governing equation

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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science china(Physics,{2. & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2.1. Institute of Applied Mathematics, School of Math & System science, Shandong university, Jinan 2.0100,{2. 2. State key laboratory of turbulence and complex Systems & Department of mechanics and engineering science, peking university, beijing 100871,{2. 1. Institute of Applied Mathematics School of Math & System Science Shandong University Jinan 250100 China 2. State key laboratory of {2. and complex Systems & Department of mechanics and engineering science Peking University Beijing 100871 China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

The refined theory of deep rectangular beams for symmetrical deformation

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science china(Physics,{2. & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2.1 College of science, china Agricultural {2., beijing 100083, china 2.State key laboratory for turbulence and complex Systems and Department of mechanics and Aerospace engineering, peking university,{{12., china College of science China Agricultural University Beijing 100083 China State key laboratory for {2. and complex Systems and Department of mechanics and Aerospace engineering Peking University Beijing 100871 China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method

SURFACE-ENHANCED CANTILEVER SENSORS WITH NANO-POROUS FILMS

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Acta Mechanica Solida Sinica 2010年第1期23卷 1-12页

作者： Huiling Duan(State key laboratory for {2. and complex System,CAPT and Department of mechanics and Aerospace engineering,College of engineering,peking university,beijing 100871,china) [a] State key laboratory for {2. complex System CAPT Department of mechanics Aerospace engineering College of Engineering Peking University Beijing 100871 China

Developing surface-enhanced microcantilevers with improved sensitivities is of longstanding interest. In this paper, the design of surface-enhanced cantilever sensors using nano- （micro-） porous films as surface layers is proposed. The static deformation and resonance frequencies of these surface-enhanced sensors with the simultaneous effects of the eigenstrain, the surface stress and the adsorption mass are analyzed. It is shown that the sensitivities of these novel cantilever sensors for the static deformation and resonance frequencies can be tuned by the porosity, the size of the pores and the structure of the porous films. For the three kinds of cantilever consisting of solid films, films with aligned cylindrical micro-scale pores, and those with nano-scale pores, the nano-porous one has the highest static and dynamic sensitivities, whereas the solid one has the lowest.

关键词： cantilever sensors nano- (micro-) porous films surface stress curvature resonance frequency

The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms

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science china(Physics,{2. & Astronomy) 2009年第6期52卷 909-918页

作者： SHEN Fang1 & WU WangYi2.1 State key laboratory for Space Weather, Center for Space {2. and Applied Research, Chinese Academy of {2.s, beijing 100190, china 2.State key laboratory of turbulence and complex Systems & Department of mechanics and engineering {2.,{13., beijing 100871, china 1. State key laboratory for Space Weather Center for Space Science and Applied Research Chinese Academy of Sciences Beijing 100190 China 2. State key laboratory of {2. and complex Systems & Department of mechanics and engineering science Peking University Beijing 100871 China

Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.

关键词： basic function unstructured grid aneurysm viscous incompressible flow artificial compressibility flux splitting

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

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Acta Mechanica Sinica 2009年第3期25卷 279-294页

作者： Zhen-Su She Zhi-Xiong Zhang State key laboratory for {2. and complex Systems, College of engineering, peking university, 100871 beijing, china State key laboratory for {2. and complex Systems College of Engineering Peking University 100871 Beijing China

Scaling is an important measure of multi-scale fluctuation systems. turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque （SL） hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.

关键词： turbulence. Scaling law. She-Leveque modelHierarchical symmetry Self-organization - turbulenceensemble

Structural ensemble dynamics based closure model for wall-bounded turbulent flow

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Acta Mechanica Sinica 2009年第5期25卷 731-736页

作者： Zhen-Su She Ning Hu You Wu State key laboratory for {2. and complex Systems and Dept Mechanical and Aerospace engineering,College of engineering, peking university,100871 beijing, china State key laboratory for {2. and complex Systems and Dept Mechanical and Aerospace engineering College of Engineering Peking University 100871 Beijing China

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

关键词： turbulence Closure equation Channel flow Structural ensemble dynamics

On the dynamics in a transitional boundary layer

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Communications in Nonlinear science and Numerical Simulation 2001年第3期6卷 111-171页

作者： C. B. LEE and R. LEE Department of mechanics and engineering {2./State key laboratory for Studies of turbulence and complex Systems, peking university, beijing 100871, china Department of engineering mechanics, Tsinghua {{12., {13. 100084, Chi Department of mechanics and engineering {2. / State key laboratory for Studies of turbulence and complex Systems Peking University Beijing 100871 China Department of engineering mechanics Tsinghua University Beijing 100084 China

A model is presented to describe the dynamic physical processes that occur in a transitional boundary layer flow. The CS-solitons, the closed vortex, the secondary closed vortex and the chain of ring-like vortices are postulated to be the basic flow structures of the transitional boundary layer as well as the turbulent boundary layer. It is argued that the central features of transitional and developed turbulent boundary layer flows can be explained in terms of how the series vortices interact with each other, and with the CS-solitons. The physical process that leads to the regeneration of the new closed vortex along the border of the CS-soliton, as well as the processes of evolution of the vortices to high frequency vortices, is described. The model is supported by the important developments in a number of "kernel" experiments, which illustrate both transitional and developed turbulent boundary layer. An important aspect of the model is that it has been formulated to be consistent with accepted rational mechanics concepts that are known to provide a proper physical description of other flows.

关键词： boundary layer transition dynamic processes onset of turbulence

Constructions of Some Exact VortexSuperposition Solutions

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Communications in Nonlinear science and Numerical Simulation 1999年第4期4卷 3-5页

作者： Xin HU Yonghan HUANG(Department of mechanics and engineering {2., State key laboratory for turbulenceResearch, peking university, beijing 100871, china) Department of mechanics and engineering {2. State Key Laboratory for Turbulence Research Peking University Beijing 100871 China

IntroductionOneofthemostusefulmethodstosolvetheN-Sequationistodecomposethevelocity（l）(z)where.（'）--acNow,***3=w3（t）,wewillthengetco3=coear(jb（t）dt).Ifwetakeg=--M（axl+fixs）+ac,T=--M（Axf+Bx;）+cohere,goandcos... 详细信息

关键词： exact solution Stokes-Helmholtz decomposition vorticity equation