The variational principles of coupled systems in photoelasticity

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The double mode model of the chaotic motion for a large deflection plate

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电容式微加速度计专用集成电路温度特性

温度是影响微加速度计性能的一个重要的因素。本文在分析微加速度计系统的基础上,设计并实现了电容式微加速度计专用集成电路,通过软件仿真和实际的温度试验,研究了专用集成电路的温度特性,给出了仿真和实测结果,并进行了相应的对比和分析。实测结果表明:在?40~120℃温度范围内,专用集成电路芯片输出随温度的输出变化为68.75μV/℃,即6.875×10-5。     

The practical use of the hole method in photoelasticity

A small circular hole has already been used in plane elasto-static photoelasticity to determine the stress tensor for any general loading situation. Originally the idea required the determination of the stress at four points at the free boundary of the hole, then it was found that more precision would be obtained if the measurements were taken at points located at a distance from the center of the hole equal to twice its radius. Later it was suggested that probably still better results would be obtained from points located at 1.4 times the radius. This paper has three objectives: (1) to improve the precision of the measurements by taking them at any point in the vicinity of the hole, which requires that the expressions giving the principal stresses be presented in a different form, as a function of the normalized variable distance from the center of the hole; (2) to show the consistent application of the method, using the values of the birefringence at various arbitrary radial locations, to plane elasto-static loading problems; and, (3) to present the application of this approach in a concise form so that its application is practical.     

Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.     

Determination of impact parameters by optical measurement of the impactor displacement

In dynamic materials research, high precision impact displacement, velocity and force measurements are often required. In lower velocity testing apparatus, impact force histories are most often obtained through strain gage, piezoelectric force transducer or accelerometer signals. Velocity and displacement histories are then obtained by integration. Non-contact measurement systems have a number of advantages over these more common mechanical contact methods, and can generally be used at higher impact speeds. In this paper a relatively simple optical technique is presented for recording the impactor displacement history, from which the impact velocity and force histories can be readily obtained for a (quasi-) rigid impactor. The technique is based on the relative displacement of two moiré line gratings: one grating attached to the impacting body and the other serving as stationary reference grating. The technique has proven to be useful for impact speeds of a few m/s to well over 200 m/s. Results of transverse impact experiments on composite laminates are presented.     

破碎发射药形状特征量的计算方法

分析了发射药形状特征量与密闭爆发器试验中发射药的燃烧压力曲线之间的关系,提出了估算破碎发射药形状特征量的方法,并给出了确定发射药形状特征量的详细步骤。对通过落锤实验得到的不同破碎程度的发射药进行了密闭爆发器实验,并利用建立的方法计算了该发射药的形状特征量,计算结果与实验结果吻合较好。     

The study on the chaotic motion of a nonlinear dynamic system

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On the use of the rolling-ball viscometer for the measurement of rheological parameters of power law fluids

Summary An attempt has been made to determine the flow curve of fluids obeying the power law rheological model on a rolling ball viscometer. The theoretical analysis is based on the hydrodynamical model developed byLewis in 1956 for the purpose of rolling ball viscometer calibration and extended in 1964 byTurian andBird for the two-parametric power law model. The shear rate variation has been accomplished on varying the tube angle of inclination. Experiments performed on an adapted, commercialHoeppler viscometer with aqueous solutions of carboxymethylcellulose and polyacrylamide reproduced the flow curves obtained simultaneously on rotational and capillary instruments with reasonable accuracy.

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Zusammenfassung Die Möglichkeit der Bestimmung von FließkurvenOstwaldscher Flüssigkeiten in einem Fallkugelviskosimeter wurde überprüft. Die analytische Behandlung des Problems beruht auf dem hydrodynamischen Modell, das 1956Lewis zur Eichung von Fallkugel-viskosimetern entwickelte und das später vonBird undTurian verallgemeinert wurde. Die Änderung der Schergeschwindigkeit wurde durch Neigung des Fallrohrs erzielt. Versuche wurden an einem handelsüblichenHöppler-Viskometer mit wässerigen Lösungen von Karboxymethylzellulose und Polyakrylamid durchgeführt. Vergleiche der gewonnenen Ergebnisse mit Fließkurven, die gleichzeitig an Rotations- und Kapillar-Viskosimetern gemessen wurden, ergaben im Gültigkeitsbereich der Theorie befriedigende Übereinstimmung.

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Nomenclature d ball diameter - D tube diameter - f function ofz defined in eq. [16] - F function ofn defined in eq. [30] - g gravity acceleration - H clearance between the ball and tube - I definite integral defined in eq. [17] - J _L = 3/4J(1) definite integral defined in [4] - J (n) definite integral defined in eq. [21] - K instrument constant defined forNewtonian fluids in eq. [1] - L distance marked on the viscometer tube - m consistency parameter - n flow behaviour index - p pressure - r radial variable - S area - t time - T temperature - u _z velocity component - U velocity of the ball - V flow rate - y, z spatial rate - tube angle of inclination - shear rate - gamma function - azimuthal variable - µ dynamic viscosity - fluid density - _s ball density - shear stress - dimensionless variable defined in eq. [9] - — denotes mean value - w denotes conditions at the solid surface With 9 figures and 2 tables     

The use of images in fluid mechanics

Still images, photographs and drawings, as well as movies are widely used in fluid mechanics and this has been true since the very early developments of this discipline. The intrinsic geometrical complexity of fluid flows, in particular when they are turbulent, explains this necessity of using visual representations to gain a physical understanding of the phenomena involved. The aesthetic appeal of images in fluid mechanics research is another reason why their use is more prevalent than in other fields of the physical sciences.     

基于ANN的定向井有杆抽油系统悬点示功图特征参数的计算

有杆抽油系统悬点示功图的特征参数是合理选择地面机电设备的主要依据.由于井下工况的复杂性和部分参数难以确定,使得基于求解高维时变非线性方程的传统方法的计算结果存在偏差.本文将传统方法和神经网络相结合,给出了一种能比较精确地确定定向井有杆抽油系统悬点示功图特征参数的方法,避免了建立和求解复杂的非线性动力学方程.首先依据传统方法,计算出简化悬点示功图的特征参数.然后考虑抽油杆柱弹性振动、抽油杆与油管之问的库仑和粘性摩擦、气体和供液能力等因素的影响,利用BP神经网络和RBF神经网络建立了不同工况下悬点示功图特征参数的计算模型.利用现场实测数据对建立的神经网络进行了训练和测试.测试结果表明了本文方法的正确性和有效性.     

The general properties of the spherical vortices (SV) ofn-TH order and the chaotic phenomena and of the ordered structures of the SV of 3RD order

The general properties of the spherical vortices (SV) of n-th order are discussed in this paper. Numerical calculations are carried out in the case of n=3. We find out some interesting phenomena concerning the chaotic regions and ordered islands on the Poincaré sections. Interpretations of these phenomena are also given. Project supported by the National Basic Research (Nonlinear Science) Foundation of China     

The concept of minimized integrated exponential error for low dispersion and low dissipation schemes

We devise two novel techniques to optimize parameters which regulate dispersion and dissipation effects in numerical methods using the notion that dissipation neutralizes dispersion. These techniques are baptized as the minimized integrated error for low dispersion and low dissipation (MIELDLD) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD) . These two techniques of optimization have an advantage over the concept of minimized integrated square difference error (MISDE) , especially in the case when more than one optimal cfl is obtained, out of which only one of these values satisfy the shift condition. For instance, when MISDE is applied to the 1‐D Fromm's scheme, we have obtained two optimal cfl numbers: 0.28 and 1.0. However, it is known that Fromm's scheme satisfies shift condition only at r=1.0. Using MIELDLD and MIEELDLD , the optimal cfl of Fromm's scheme is computed as 1.0. We show that like the MISDE concept, both the techniques MIELDLD and MIEELDLD are effective to control dissipation and dispersion. The condition ν²>4µ is satisfied for all these three techniques of optimization, where ν and µ are parameters present in the Korteweg‐de‐Vries‐Burgers equation. The optimal cfl number for some numerical schemes namely Lax–Wendroff, Beam–Warming, Crowley and Upwind Leap‐Frog when discretized by the 1‐D linear advection equation is computed. The optimal cfl number obtained is in agreement with the shift condition. Some numerical experiments in 1‐D have been performed which consist of discontinuities and shocks. The dissipation and dispersion errors at some different cfl numbers for these experiments are quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

The study of equivalent material parameters in a hyperelastic model

We study a hyperelastic model of some biological soft tissues with emphasis on the problem of its matching with the material parameters acquired by experimental mechanical tests. First, we study the polyconvexity property of the hyperelastic model. Then, we explore the notion of equivalent sets of material parameters. We perform a numerical study of the regions of equivalent material parameters characterizing the curves predicted by the hyperelastic model that are close, within a prefixed tolerance, to those given by the experimental data. In the numerical study we use the quadratic variation and the Hausdorff distance. The study suggests that a qualitative knowledge of shape and volume of the regions of equivalent material parameters can provide both a criterion for the optimal match between the model with the experimental data and an indication on the reducibility of the number of parameters used in the model.     

The Rayleigh quotient method for computing eigenvalue bounds of vibrational systems with interval parameters

In this paper, an effective method, the Rayleigh quotient iteration, for computing the bounds of structures with interval parameters is presented. When the uncertainty of the structural parameters is described by using the interval, i.e. an unknown-but-bounded version, the structural vibration eigenvalues will become the interval. It is desirable to give these interval eigenvalues. An application of this method is illustrated by a numerical example. The results show that the Rayleigh quotient iteration method is very effective for constructing the upper and lower bounds on the eigenvalues of structures with interval parameters.The Project Supported by National Natural Science Foundation of China     

Some applications of the concept of minimized integrated exponential error for low dispersion and low dissipation

Several techniques to optimize parameters that regulate dispersion and dissipation effects in finite difference schemes have been devised in our previous works. They all use the notion that dissipation neutralizes dispersion. These techniques are the minimized integrated square difference error (MISDE) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD). It is shown in this work based on several numerical schemes tested that the technique of MIEELDLD is more accurate than MISDE to optimize the parameters that regulate dispersion and dissipation effects with the aim of improving the shock‐capturing properties of numerical methods. First, we consider the family of third‐order schemes proposed by Takacs. We use the techniques MISDE and MIEELDLD to optimize two parameters, namely, the cfl number and another variable which also controls dispersion and dissipation. Second, these two techniques are used to optimize a numerical scheme proposed by Gadd. Moreover, we compute the optimal cfl for some multi‐level schemes in 1D. Numerical tests for some of these numerical schemes mentioned above are performed at different cfl numbers and it is shown that the results obtained are dependent on the cfl number chosen. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Finally, we make use of a composite scheme made of corrected Lax–Friedrichs and the two‐step Lax–Friedrichs schemes like the CFLF4 scheme at its optimal cfl number, to solve some problems in 2D, namely: solid body rotation test, acoustics and the circular Riemann problem. Copyright © 2011 John Wiley & Sons, Ltd.     

冲击波超压测试系统二次仪表频域特性

从二次仪表对冲击波的峰值、持续时间和比冲量3个主要参数的影响出发,首先构建了冲击波信号用以分析冲击波信号特性;搭建了适配器等效电路,对适配器的低频特性进行了实验研究;在MATLAB平台上构建了5种常用滤波器模型,模拟了不同类型滤波器和不同截止频率下测试系统的输出。模拟和实验结果表明:适配器的低频特性影响冲击波信号的持续时间和比冲量;在5种滤波器中贝塞尔滤波器最适合冲击波测试系统;滤波器截止频率对冲击波超压峰值影响明显;小型试验对测试系统的带宽要求高。     

A method for the identification of dynamic constraint parameters in multi-supported flexible structures

In this paper, a new method for identifying the dynamical parameters of local constraining supports such as mass, stiffness, and damping was developed through combining the measured frequency transfer functions and structural modification techniques. Since measurement noise often leads to erroneous identifications, regularization techniques have been implemented to reduce noise amplification in the inverse problem. The developed technique has been validated by numerical tests on a multi-supported flexible structure, which can be seen as an idealized electricity generator rotor shaft. The results are satisfactory for noise-free data as well as under realistic noise levels. The sensitivity of the identified support features to noise levels is asserted through a parametric study