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Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments

COMPUTERS & STRUCTURES 2004年第31-32期82卷 2587-2605页

作者： Amabili, M Univ Parma Dipartimento Ingn Quim I-43100 Parma Italy

Large-amplitude (geometrically nonlinear) vibrations of rectangular plates subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The von Karman nonlinear strain-displacement relationships are used. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite plate;geometric imperfections are taken into account. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis. Comparison of calculations to numerical results available in the literature is performed for simply supported plates with immovable and movable edges. Three different boundary conditions are considered and results are compared: (i) simply supported plates with immovable edges;(ii) simply supported plates with movable edges;and (iii) fully clamped plates. An experiment has been specifically performed in laboratory in order to very the accuracy of the present numerical model;a good agreement of theoretical and experimental results has been found for large-amplitude vibrations around the fundamental resonance of the aluminum plate tested. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： plate vibration nonlinear large-amplitude rectangular experiment

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Thermal cracking characteristics of n-decane in the rectangular and circular tubes

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Chinese Journal of Chemical Engineering 2019年第12期27卷 2876-2883页

作者： Zhiliang Lei Bin Liu Qin Huang Kuo He Zewei Bao Quan Zhu Xiangyuan Li School of Chemical Engineering Sichuan UniversityChengdu 610065China

To investigate the effect of regenerative cooling channel geometry on pyrolysis of endothermic hydrocarbon fuel,a series of supercritical pyrolysis experiments of n-decane in the rectangular and circular tubes were ***,sensitivity analysis of production of propylene and methane as well as CFD simulation were also *** results showed that gas yield and conversion in the circular tube with an inner diameter of 2 mm had a similar tendency with the one of 1.5 mm in inner *** conversion in the circular tube was much less than that in the rectangular tube at the same outlet *** heat sink of the rectangular tube at the same outlet temperature was larger than that of circular tubes,but the temperature at the corner of the rectangular tube was relatively *** to the experimental data of the test tubes,a correlation between the conversion and the temperature in the rectangular and circular tubes at the same outlet temperature was fitted,providing a reference for the design of regenerative cooling channels.

关键词： Hydrocarbons Supercritical fluid Pyrolysis rectangular tube Circular tube

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Three-Dimensional Simulation of Detonation Propagation in a rectangular Duct by an Improved CE/SE Scheme

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Chinese Physics Letters 2011年第12期28卷 179-182页

作者： SHEN Hua LIU Kai-Xin ZHANG De-Liang LTCS and College of Engineering Peking UniversityBeijing 100871 Center for Applied Physics and Technology Peking UniversityBeijing 100871 LHD Institute of MechanicsChinese Academy of SciencesBeijing 100080

A genuinely three-dimensional spacetime conservation element and solution element(CE/SE)scheme is built as simple,consistent and straightforward extensions of an improved high resolution 2D CE/SE *** is applied to examine the mechanism of three-dimensional detonation process in rectangular *** simulations clearly show detailed three-dimensional detonation modes,namely a rectangular mode and a diagonal ***,the formation of unreacted pockets with high density and low temperature behind the detonation is observed for the two modes.

关键词： rectangular element straight

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Nonlinear primary resonance analysis for a coupled thermo-piezoelectric-mechanical model of piezoelectric rectangular thin plates

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Applied Mathematics and Mechanics(English Edition) 2019年第8期40卷 1155-1168页

作者： Xun WANG Chunxia XUE Haitao LI Department of Mechanics School of ScienceNorth University of China Taiyuan 030051China Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072China

A model of piezoelectric rectangular thin plates with the consideration of the coupled thermo-piezoelectric-mechanical effect is established. Based on the von Kar- man large deflection theory, the nonlinear vibration governing equation is obtained by using Hamilton’s principle and the Rayleigh-Ritz method. The harmonic balance method (HBM) is used to analyze the first-order approximate response and obtain the frequency response function. The system shows non-linear phenomena such as hardening nonlinear- ity, multiple coexistence solutions, and jumps. The effects of the temperature difference, the damping coefficient, the plate thickness, the excited charge, and the mode on the pri- mary resonance response are theoretically analyzed. With the increase in the temperature difference, the corresponding frequency jumping increases, while the resonant amplitude decreases gradually. Finally, numerical verifications are carried out by the Runge-Kutta method, and the results agree very well with the theoretical results.

关键词： piezoelectric rectangular thin plate thermo-piezoelectric-mechanical coupling harmonic balance method (HBM) primary resonance analysis

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Experimental Investigation of Heat Storage and Heat Transfer Rates during Melting of Nano-Enhanced Phase Change Materials (NePCM) in a Differentially-Heated rectangular Cavity

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Journal of Thermal Science 2020年第2期29卷 503-511页

作者： LI Zirui HU Nan TU Jing FAN Liwu Institute of Thermal Science and Power Systems School of Energy EngineeringZhejiang UniversityHangzhou 310027China State Key Laboratory of Clean Energy Utilization Zhejiang UniversityHangzhou 310027China

In this work, an experimental study of melting heat transfer of nano-enhanced phase change materials(NePCM) in a differentially-heated rectangular cavity was performed. Two height-to-width aspect ratios of the cavity, i.e., 0.9 and 1.5, were investigated. The model Ne PCM samples were prepared by dispersing graphene nanoplatelets(GNP) into 1-tetradecanol, having a nominal melting point of 37℃, at loadings up to 3 wt.%. The viscosity was found to have a more than 10-fold increase at the highest loading of GNP. During the melting experiments, the wall superheat at the heating boundary was set to be 10℃ or 30℃. It was shown that with increasing the loading of GNP, both the heat storage and heat transfer rates during melting decelerate to some extent, at all geometrical and thermal configurations. This suggested that the use of NePCM in such cavity may not be able to enhance the heat storage rate due to the dramatic growth in viscosity, which deteriorates significantly natural convective heat transfer during melting to overweigh the enhanced heat conduction by only a decent increase in thermal conductivity. This also suggested that the numerically predicted melting accelerations and heat transfer enhancements, as a result of the increased thermal conductivity, in the literature are likely overestimated because the negative effects due to viscosity growth are underestimated.

关键词： aspect ratio graphene nanoplatelets latent heat storage melting heat transfer phase change material rectangular cavity

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LAW OF BOUNDARY SHEAR IN OPEN rectangular CHANNELS WITH UNIFORM ROUGHNESS

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Journal of Hydrodynamics 2004年第3期16卷 295-300页

作者： HUXu-yue ZENGGuang-ming XIEGeng-xin HUANGGuo-he LIJian-bing DepartmentofEnvironmentalScienceandEngineering HunanUniversityChangsha410082China

In accordance with the characteristics of the rectangular prismatic channel,the flow in the channel was divided into two parts, the bed part and the wall part. On the basis ofgeneral principles of mechanics, the area relation between the bed part and the wall part was workedout. A formula for determining the shear acting on the bed and the walls in rectangular channelswas derived, which has a simple form and is only related to the ratio of the breadth to the *** difference between the calculated value with the presented formula and the data published wasillustrated to be less than that with other, formulas, which shows that the formula is reasonableand can model the flow in the rectangular prismatic channel with higher accuracy and reliability.

关键词： uniform flow rectangular open channel bed walls boundary shear

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Dynamics analysis and experiment on the fishtailing type of valveless piezoelectric pump with rectangular vibrator

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Science China(Technological Sciences) 2010年第12期53卷 3241-3247页

作者： HUANG Yi1, ZHANG JianHui1, HU XiaoQi1, XIA QiXiao2, HUANG WeiQing1 & ZHAO ChunSheng1 1 Department of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2 Department of Mechanical and Electrical Engineering, Beijing Union University, Beijing 100020, China Department of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing China Department of Mechanical and Electrical Engineering Beijing Union University Beijing China

In recent years, the research and development of piezoelectric pumps have become an increasingly popular topic. Minimization, structure simplification and stronger output become the focus of piezoelectric pumps’ research due to its possible application in MEMS technology. The valveless fishtailing piezoelectric pump, neither a volumetric nor a rotating pump, was invented according to the bionics of fish swimming. With assumption that the head of the fish is fixed while its tail is swinging, fluid would flow toward the end of the tail, achieving the function of a valveless pump. This type of pumps creates a new branch for the piezoelectric pump research, which is proposed for the first time in this paper. The relationship between the flow rates and vibrating frequencies was derived from the interaction between the vibrator and fluid. Numerical simulations with FEM software were conducted to study the first and second vibration modes of the piezoelectric vibrator. The results showed that the maximum amplitude of the vibrator was 0.9 mm at the frequency of 76 Hz for the first vibration mode, while the maximum amplitude of the vibrator was 0.22 mm at the frequency of 781 Hz for the second vibration mode. Experiments were conducted with the Doppler laser vibration measurement system, and the results were compared to those of the FEM simulation. It was shown that in the first vibration mode the piezoelectric vibrator reached its maximum amplitude of about 0.9 mm at the driving frequency of 49 Hz, which gives the flow rate of 2.0 mL/min, in the second vibration mode, the maximum amplitude was about 0.25 mm at the frequency of 460 Hz with the flow rate being 6.4 mL/min.

关键词： piezoelectric pump valveless fishtailing rectangular vibrator dynamics analysis experiment

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2-PHASE FLOW PATTERNS AND TRANSITIONS IN A SMALL, HORIZONTAL, rectangular CHANNEL

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INTERNATIONAL JOURNAL OF MULTIPHASE FLOW 1991年第3期17卷 327-342页

作者： WAMBSGANSS, MW JENDRZEJCZYK, JA FRANCE, DM UNIV ILLINOIS DEPT MECH ENGNCHICAGOIL 60680

Horizontal two-phase flow was studied in a small cross-sectional-area (19.05 x 3.18 mm) rectangular channel with both the short and long sides forming the base, resulting in aspect ratios of 6 and 1/6, respectively. Adiabatic flows of air/water mixtures were tested over a large mass flux range (50-2000 kg/m2s). The full quality range was considered whenever experimentally achievable. Flow patterns were established and both mean and dynamic pressure measurements were used to accurately establish the plug/bubble-to-slug flow transition. This result, together with visual observations and supplemented with photographic data, was used to develop flow pattern maps. A comparison of existing flow pattern maps for circular pipes, capillary tubes and larger rectangular channels led to the conclusion that, while qualitative agreement exists, these maps are not generally applicable to the subject small rectangular channel on the quantitative basis.

关键词： 2-PHASE FLOW HORIZONTAL rectangular FLOW PATTERNS TRANSITIONS

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Flow frictional characteristics of microencapsulated phase change material suspensions flowing through rectangular minichannels

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Science China(Technological Sciences) 2006年第4期49卷 445-456页

作者： Frank Dammel Peter Stephan Chair of Technical Thermodynamics Darmstadt University of Technology Germany

An experimental investigation was conducted on the laminar flow frictional characteristics of suspensions with microencapsulated phase change material (MEPCM) in water flowing through rectangular copper minichannels. The MEPCM was provided at an average particle size of 4.97 μm, and was mixed with distilled water to form suspen- sions with various mass concentrations ranging from 0 to 20%. The experiment was per- formed to explore the effect of MEPCM mass concentration on friction factor and pressure drop in the minichannels. The Reynolds number ranged from 200 to 2000 to provide laminar and transitional flows. It was found that the experimental data for the suspensions with 0 and 5% concentration agree well with the existing theoretical data for an incom- pressible, fully developed, laminar Newtonian flow. For the suspensions with mass con- centrations higher than 10%, there is an obvious increase in friction factor and pressure drop in comparison with laminar Newtonian flow.

关键词： microencapsulated phase change material suspension, friction factor, rectangular minichannel.

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Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

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Science China(Physics,Mechanics & Astronomy) 2009年第12期52卷 1989-2000页

作者： ZHANG Wei GAO MeiJuan YAO MingHui YAO ZhiGang College of Mechanical Engineering Beijing University of TechnologyBeijing 100124China

The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimen-sional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly,the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then,the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bi-furcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally,numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.

关键词： composite laminated piezoelectric rectangular plate normal form energy-phase method numerical simulation jumping orbits chaotic motion

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