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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

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

ROBUSTNESS ANALYSIS OF LEADER-FOLLOWER CONSENSUS

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Journal of systems science & {2.ity 2009年第2期22卷 186-206页

作者： Jinzhi WANG Ying TAN · Iven MAREELS state key {2. for turbulence and complex System and department of mechanics and Aerospace engi-neering College of Engineering Peking University Beijing 100871 China. Departmen~ of Electrical and Electronic engineering University of Melbourne Melbourne VIC. 3010 Aus-tralia.

In this paper,robustness properties of the leader-follower consensus are *** of presentation,the attention is focused on a group of continuous-time first-order dynamicagents with a time-invariant communication topology in the presence of communication *** orderto evaluate the robustness of leader-follower consensus,two robustness measures are proposed:the L_2.ain of the error vector to the state of the network and the worst case L_2.gain at a *** L_2.gain of the error vector to the state of the network is widely used in robust control design andanalysis,the worst case L_2.gain at a node is less conservative with respect to the number of nodes inthe *** is thus suggested that the worst case L_2.gain at a node is used when the robustnessof consensus is *** analysis and simulation results show that these two measuresare sensitive to the communication *** general,the 'optimal' communication topology thatcan achieve most robust performance with respect to either of the proposed robustness measures isdifficult to characterize and/or *** the in-degree of each follower is one,it is shown thatboth measures reach a minimum when the leader can communicate to each node in the network.

关键词： Communication errors leader-follower consensus robustness.

Theorem of turbulent intensity and macroscopic mechanism of the turbulence development

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science china Earth sciences 2007年第5期50卷 789-800页

作者： HU YinQiao1,2. CHEN JinBei3,4 & ZUO HongChao2.1 Gansu Province key laboratory of Arid Climatic Change and Reducing Disaster, Cold and Arid Regions Environment and {2.- neering Institute, Chinese Academy of sciences, Lanzhou 730000, china 2.state key laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry (LAPC), beijing 10002., china 3 Atmospheric science College, Lanzhou {12., Lanzhou 730000, china 4 Resource Environment department, Lanzhou Agriculture {12., Lanzhou 730060, china Gansu Province key laboratory of Arid Climatic Change and Reducing Disaster Cold and Arid Regions Environment and Engineering Institute Chinese Academy of Sciences Lanzhou 730000 China state key {2. of Atmospheric Boundary Layer Physics and Atmospheric Chemistry(LAPC) Beijing 100029China Atmospheric science College Lanzhou University Lanzhou 730000 China Resource Environment department Lanzhou Agriculture University Lanzhou 730060 China state key {2. of Atmospheric Boundary Layer Physics and Atmospheric Chemistry LAPC Beijing 100029 China

turbulence is one of the most common nature phenomena in everyday experience, but that is not adequately understood yet. This article reviews the history and present state of development of the turbulence theory and indicates the necessity to probe into the turbulent features and mechanism with the different methods at different levels. Therefore this article proves a theorem of turbulent transpor- tation and a theorem of turbulent intensity by using the theory of the nonequilibrium thermodynamics, and that the Reynolds turbulence and the Rayleigh-Bénard turbulence are united in the theorems of the turbulent intensity and the turbulent transportation. The macroscopic cause of the development of fluid turbulence is a result from shearing effect of the velocity together with the temperature, which is also the macroscopic cause of the stretch and fold of trajectory in the phase space of turbulent field. And it is proved by the observed data of atmosphere that the phenomenological coefficient of turbulent in- tensity is not only a function of the velocity shear but also a function of temperature shear, viz the sta- bility of temperature stratification, in the atmosphere. Accordingly, authenticity of the theorem, which is proved by the theory of nonequilibrium thermodynamics, of turbulent intensity is testified by the facts of observational experiment.

关键词： turbulence nonequilibrium thermodynamics linear thermodynamics atmosphere boundary layer Reynolds turbulence Rayleigh-Bénard turbulence