Design of a curved surface constant force mechanism

A new curved surface constant force mechanism which mainly consists of a roller and a curved surface has been proposed. The magnitude and the direction of normal force caused by squeezing between the roller and the curved surface satisfy a certain relationship, thus the decomposed force of the normal force keeps constant in a certain direction all the times. According to the envelope theorem, the trajectory of the roller center and the profile of the curved surface are obtained by ignoring friction. Then, the influence of the friction is discussed in detail. In addition, the simulation is performed to verify the theoretical calculation. The simulation results show that the output force is relatively constant and the friction has little effect on the output force.     

Effect of rotation on Goertler vortices in the boundary layer flow on a curved surface

This paper presents a numerical prediction of the formation of Goertler vortices on a curved surface with effect of rotation. The criterion of flow visualization marking the onset position of Goertler vortices is employed in the present paper. For facilitating the numerical study, the computation is carried out in the transformed x and ηplane. The results show that the onset position characterized by the Goertler number, depends on the rotation number Ro, the Prandtl number and the wave number. The value of critical Goertler number increases with the increase in negative rotation, while the value of Goertler number decreases with the increase in positive rotation on a concave surface. On the contrary, the value of critical Goertler number decreases with the increase in negative rotation on a convex surface. The obtained critical Goertler number and wave number are compared with the previous theoretical and experimental data. Copyright © 2002 John Wiley & Sons, Ltd.     

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF₄ premixed in the test gas. The final product C₂F₄ is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C₂F₄ is correlated to the temperature of the reflected shock wave with the initial pressureP ₁ and test time τ as parameters in the temperature range 3 300 K<T<5 600 K, pressure range 5 kPa<P ₁<12 kPa and τ≅0.4 ms. The project supported by the China Aerodynamics Project for Basic Researches (J13.5.2 ZK04)     

Residual strain evaluation of curved surface by grating-transferring technique and GPA

This paper investigates an advanced grating-transferring technique combined with geometric phase analysis (GPA) for residual strain evaluation of curved surface. A standard holographic grating is first transferred to a pre-produced epoxy resin film and then consolidated to a test region of curved surface. With a rubber mold and silicone rubber the deformed grating is replicated to a sheet metal after hole-drilling for release of residual stress. After that the grating is transferred from the sheet metal to the glass plate, which would be served as an analyzer grating (specimen grating). By GPA the local strain distributions related to the phase difference between the reference grating and analyzer grating for the released stress can be evaluated. A validation test has been conducted on the weld joint of a stainless steel tube and the obtained results demonstrate the ability of the method in measuring the residual strain of curved surface.     

基于压电曲壳单元的结构振动最优控制

曲壳结构已广泛应用于航空航天、航海等领域,结构微小的振动会极大地影响部件性能,抑制曲壳结构的振动就很必要。提出了压电曲壳结构的振动最优控制模型,利用空间曲壳单元理论及多点约束方程实现曲壳基结构壳元和压电壳元的耦合,推导了压电曲壳结构动力学有限元方程,并结合线性二次型最优控制理论,实现了压电作动器对曲壳结构的振动最优控制。数值算例表明,对曲壳结构进行动力分析和振动控制时,在达到同样精度及控制效果的情况下,与平壳相比,曲壳单元及作动器所需数目要少得多。     

空间曲线索的平衡方程及单索几何判定

空间曲线索平衡方程可在理想柔索假定的基础上进行推导,也可以由空间曲线梁平衡方程退化得到。本文给出后者的连续化分析过程并进行了初步的讨论,目的在于将空间曲线索的各种力学模型统一起来。采用理想柔索假定后单索只能是平面曲线,自然坐标系和整体直角坐标系下平面曲线索的平衡方程是等价的。同时,针对以往单索连续化分析中几何判定的不足,基于空间曲线的弧长独立参数概念,指出单根理想柔索本质上为静不定和动不定体系。     

Strain determination on curved surfaces by objective white light speckles

A close-range objective white light speckle method has been used for strain determination on simply curved surfaces. The speckle field is not the artificially printed random dots but only the radiance distribution of object surface which was slightly treated before the test to produce fine structure of optical details. The holographic film, instead of holographic plate, is attatched to the curved surface when illuminated by a flash light. Whole field fringe patterns are obtained with high sensitivities and large adjustable range. There is no longer a requirement to derive the speckle movement on the image plane from the object surface. Defocusing problem has been avoided. It can be practically applied to engineering problems with considerable convenience because of the very simple recording system and little demand for environmental stability.     

Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux

The two-dimensional (2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations (PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically. The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time. Besides, the Deborah number has a reverse effect on the pressure and surface drag force.     

应用超声散斑相关法测量水下物内层界面位移

超声散斑相关法可应用于水下物体内层界面的位移测量,在工程建设中具有广泛的应用前景。根据所建立的测量实验系统,对位于水中的有机玻璃试件内层界面的面内位移和离面位移进行了实测,测量误差一般在7%以内。进一步研究结果表明:在刚体位移情况下,一般经粗磨、粗刨和粗铣加工或砂模铸造后的粗糙外层界面对超声散斑相关法内层界面位移测量结果的影响极小;当外层界面发生应变时,其变形前后内层界面上的散斑场的相关性将随应变量的增加而减弱,但外层界面应变小于0.05ε时,内层界面上超声散斑相关系数的减小不超过4%。     

Non-isothermal flow of polymer melts in a curved tube

The results of a numerical study (using finite differences) of heat transfer in polymer melt flow is presented. The rheological behaviour of the melt is described by a temperature-dependent power-law model. The curved tube wall is assumed to be at constant temperature. Convective and viscous dissipation terms are included in the energy equation. Velocity, temperature and viscosity profiles, Nusselt numbers, bulk temperatures, etc. are presented for a variety of flow conditions. Br — Brinkman number - c specific heat, J/kg K - De — Dean number - E dimensionless apparent viscosity, eq. (14d) - G dimensionless shear rate, eq. (19) - k parameter of the power-law model, °C^–1, eq. (7) - mass flow rate, kg/s - m ₀ parameter of the power-law model, Pa · s ⁿ , eq. (7) - n parameter of the power-law model, eq. (7) - Nu 2r _p/ — Nusselt number, eqs. (28,31) - p pressure, Pa - Pe — Péclet number - P —(p/)/r _c — pressure gradient, Pa/m - dissipated energy, W, eq. (29) - total energy, W, eq. (30) - r radial coordinate, m - r _c radius of tube-curvature, m, fig. 1 - r _p radius of tube, m, fig. 1 - r _t variable, m, eq. (6) - R dimensionless radial coordinate, eq. (14a) - R _c dimensionlessr _c, eq. (14a) - R _t dimensionlessr _t, eq. (14a) - t temperature, °C - bulk temperature, °C, eq. (27) - t ₀ inlet temperature of the melt, °C - t _w tube wall temperature, °C - T dimensionless temperature, eq. (14c) - T _w dimensionless tube wall temperature - T dimensionless bulk temperature - u ₁ variable, s^–1, eq. (4) - u ₂ variable, s^–1, eq. (5) - U ₁ dimensionlessu ₁, eq. (18) - U ₂ dimensionlessu ₂, eq. (18) - v velocity in-direction, m/s - average velocity of the melt, m/s - V dimensionlessv, eq. (14b) - dimensionless , eq. (15) - z r _c — centre length of the tube, m - Z dimensionlessz, eq. (14e) - heat transfer coefficient, W/m² K - shear rate, s^–1, eq. (8) - — shear rate, s^–1 - apparent viscosity, Pa · s, eq. (7) - ₀ — apparent viscosity, Pa · s - angular coordinate, rad, fig. 1 - thermal conductivity, W/m K - melt density, kg/m³ - axial coordinate, rad, fig. 1 - rate of strain tensor, s^–1, eq. (8) - (—p) pressure drop, Pa     

Free-surface flow over curved surfaces: Part I: Perturbation analysis

The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.     

Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.     

On the application of slip boundary condition on curved boundaries

Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not assure good approximation of the continuum slip condition in the discrete problem, and non‐physical recirculating flow fields may be observed. As a remedy, we consider the Navier slip condition, and more successfully, the so‐called BC‐free boundary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

Modeling low Reynolds number incompressible flows with curved boundaries using SPH

In this paper, a method that can be used to model low Reynolds number incompressible flows with curved boundaries using SPH was presented. In contrast to that usually used for the flows with flat and straight boundaries, the hydrostatic pressure gradient is treated as a variable body force in this method, and thus, it can be applied to simulate the flows with curved boundaries. Three numerical examples of low Reynolds number incompressible flows, including Poiseuille flow, flow in a section of blood vessel with a local expansion, and flow between inclined plates were calculated to test the method. The results obtained with the proposed method were in good agreement with the analytical solutions. It implies that the method presented in this paper can be successfully used to simulate low Reynolds number incompressible flows not only with flat and straight boundaries but also with curved boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

On the stability of elastic curved bars

A general discussion about the stability of arbitrary elastic curved bars in space under combined actions of bending and twisting is given in this paper. A system of Eqs. (28)–(36) for perturbation functions near some equilibrium state is presented. With appropriate boundary conditions, the nontrivial solution corresponds to the critical state. Five examples are analysed in this paper. Some of them are new results and others are old problems treated using the new method.     

Approximate vibration analysis of laminated curved panel using higher-order shear deformation theory

An approximate analysis for free vibration of a laminated curved panel (shell) with four edges simply supported (SS2), is presented in this paper. The transverse shear deformation is considered by using a higher-order shear deformation theory. For solving the highly coupled partial differential governing equations and associated boundary conditions, a set of solution functions in the form of double trigonometric Fourier series, which are required to satisfy the geometry part of the considered boundary conditions, is assumed in advance. By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions, an approximate solution, capable of providing a reliable prediction for the global response of the panel, is obtained. Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.     

Test method for measuring strength of a curved sandwich beam

A fixture for testing curved sandwich beams in flexure was designed and evaluated. The test specimen is a continuous sandwich beam consisting of a central circular 90° region connected by two straight legs. The fixture was designed according to the four-point flexure principle to produce a pure bending moment in the curved region. The validity of the test fixture in producing the desired loading was examined by fitting a curved aluminum bar of similar bending stiffness as the sandwich beams considered. Strain gage readings were successfully compared to predictions from curved homogeneous beam theory. In addition, the deflection of the beam at the loading points was analyzed using straight and curved beam theory for the various sections of the beam, and predictions were compared to measured load-displacement response. Good agreement was achieved between experimental and analytical results lending confidence to the test principle. Curved sandwich beams consisting of glass/polyester face sheets over a PVC foam core were tested to failure and the loading response of the beams and their failure behavior are discussed. It was found that the beams failed at the upper face/core interface due to radial tension stress.     

Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.     

Stress distribution in a composite materialwith a row of antiphase periodically curved fibers

The stress distribution in an infinite matrix containing a row of antiphase periodically curved fibers is studied using the piecewise-homogeneous body model and the exact three-dimensional equations of elasticity theory for anisotropic bodies. It is assumed that the midlines of the fibers are located in the same plane and the materials of the fibers are the same. Numerical results are presented for the case where the materials of the fibers and matrix are isotropic and homogeneous Published in Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 136–144, April 2006.     

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education