Nonlinear flexural waves in fluid–filled elastic channels

Nonlinear waves on liquid sheets between thin infinite elastic plates are studied analytically and numerically. Linear and nonlinear models are used for the elastic plates coupled to the Euler equations for the fluid. One-dimensional time-dependent equations are derived based on a long-wavelength approximation. Inertia of the elastic plates is neglected, so linear perturbations are stable. Symmetric and mixed-mode travelling waves are found with the linear plate model and symmetric travelling waves are found for the nonlinear case. Numerical simulations are employed to study the evolution in time of initial disturbances and to compare the different models used. Nonlinear effects are found to decrease the travelling wave speed compared with linear models. At sufficiently large amplitude of initial disturbances, higher order temporal oscillations induced by nonlinearity can lead to thickness of the liquid sheet approaching zero.     

根部柔性梁的不确定性建模与确认

首先导出了包含根部挠性参数的悬臂梁动力学方程近似解,将平动和转动柔性参数作为不确定性源,根据若干预紧力矩下的模态实验结果完成了柔性参数识别,并假定其服从正态随机分布,识别了均值与标准差,进而通过回归分析建立了不确定参数随预紧力矩变化的数学模型.最后通过新的模态实验结果对所建模型进行了确认,通过确认结果,明确了该模型的使用范围.     

Experiment and modelling of birefringent flows using commercial CFD code

It is well-known that certain fluids are birefringent and when flows are viewed in polarised light interference fringes are observed. The fringes are caused by a phase shift in the light passing through the fluid and are proportional to the integral of the maximum shear strains in the fluid. In order to understand what is happening within the three dimensional flow and overcome the difficulties due to this integration, additional computational or experimental information is needed.

In this work, a commercially available computer code (Fluent) is used for the first time to model the flows. The flow data are then exported to a spreadsheet where the shear rates are integrated across the field and then banded for graphical output. The results from this are then compared to results generated from birefringent flow experiments and the agreement is found to be good since the modelled fringes show the same patterns as those in the experiment. This novel use of computational and experimental techniques together will allow quantitative analysis of three-dimensional flows in the future.

Currently, there are still a lot of empirical variables involved in fitting the computational fringes to the experiment, but the results of this preliminary study show that this is a promising approach to this type of problem.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

Supersonic Inviscid Corner Flows with Regular and Irregular Shock Interaction

The results of a numerical and analytical investigation of steady-state supersonic inviscid flows in corners formed by intersecting compression wedges are presented. The flows considered are symmetric about the corner bisector. The distinctive features of flow pattern formation related with the reflection of wedge-generated shocks from the bisector plane are studied. The wedge angles at which transition from regular to irregular shock reflection occurs are determined both numerically and analytically using the criteria available for plane flows; the data thus obtained are found to be in agreement. Flow patterns with irregular shock reflection, namely, single, transitional, and double Mach, as well as von Neumann reflection, are identified; they are similar to the known types of reflection for plane quasi-steady-state flows. Varieties of these types not observed in the plane flows are found to exist. The effects of the angle of inclination of the plane surfaces of the corner to the freestream direction, the sweep angle of the leading edges, and the dihedral angle are investigated. Some previously unknown parameters of corner configurations for which transition may occur in accordance with the von Neumann criterion are determined.     

Improvements on the arc-length-type method

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods. The project supported by the Special Research Fund for Doctor Program of Universities (9424702)     

高锰钢帽型样品在高速冲击下的剪切行为

绝热剪切带是材料在高速变形时一种典型的破坏形式,为了更好地理解高速冲击过程中绝热剪切带的形成和扩展,基于Johnson-Cook本构模型,利用ANSYS/LS-DYNA软件对高锰钢帽型样品高速冲击过程的剪切行为进行了二维数值模拟。结果表明:横穿剪切带方向,应力应变分布都是剪切带中心最高,然后向两边逐渐降低,类似于高斯分布; 平行于剪切带方向,应力应变分布则是呈两端高中间低的特点。然后利用模拟的应力应变场分布确定了剪切带和裂纹形成及扩展方向,即从剪切区两端形成并向中间扩展;最后通过编辑软件的k文件直接得到了剪切带内部及周围形变影响区和基体的温度分布,其和应力应变场分布规律一致,结果与实验结果基本吻合。     

错位云纹干涉法同步测量三维位移导数场

本文提出一种变载波双曝光错位云纹干涉法,将变形信息的记录过程与错位分析分开进行。通过对一级衍射波引入适当载波后,用双曝光法将变形信息记录在一张底板上,尔后通过滤波分离变形信息及错位处理,实现了三维位移导数场的同步测量。文中给出了较为严密的理论推导,并给出了平面模型静态下的面内和离面位移场测量结果。     

Approximate symmetries of creeping flow equations of a second grade fluid

Creeping flow equations of a second grade fluid are considered. Two current approximate symmetry methods and a modified new one are applied to the equations of motion. Approximate symmetries obtained by different methods and the exact symmetries are contrasted. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.     

Balancing aspects of numerical dissipation,dispersion, and aliasing in time-accurate simulations

The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.     

含有启动压力梯度的渗流问题及其无网格解法

针对两种典型的涉及启动压力梯度的渗流问题,给出了无量纲化的渗流控制方程、初始条件和边界条件,并使用无网格方法进行数值模拟。计算结果使用Gringarten—Bourdet图版进行井底压力分析,给出了一种计算动边界位置的方法,并详细讨论了动边界变化情况。     

Governing equations, experiments, and the experimentalist

It is argued that the most important test of the understanding of any experiment is whether or not the results are consistent with the equations and boundary conditions believed to govern the flow. If they are not, then either the measurements are incorrect, the equations or boundary conditions are wrong, or the experiment performed was not the one believed to have been done. It is suggested that many apparently contradictory experimental results are, in fact, the result of the latter and have not been recognized as such because of a failure to apply the governing equations to the data. The arguments are supported by examples from turbulent shear flow experiments.     

几类非线性系统平稳随机响应的概率密度

本文考虑非保守力依赖于系统能量的非线性系统,构造了四类这种系统对白噪声外激与/或参激的平稳响应的精确概率密度,讨论了存在平稳响应的条件。同时指出,迄今为止已有的非线性系统平稳随机响应的精确解皆属本文给出一般结果的特殊情形。最后还给出几个例子说明一般结果。     

Behaviour of macroscopic rigid spheres in lid-driven cavity flow

Experiments are conducted to investigate the behaviour of macroscopic rigid particles suspended in a fully three-dimensional viscous flow. The flow considered takes place in a closed cubic cavity, steadily driven along its upper face by a translating lid. Navier–Stokes computations are first performed to characterize the fluid flow, and the resulting kinematic template is checked using laser-illuminated micro-particles. Nearly neutrally buoyant rigid spheres are then inserted in the cavity, and their three-dimensional motions are tracked using stereoscopic imaging. The measured macro-particle motions are compared with those of simulated passive tracers, and their responses to changes in experimental conditions are examined. Although steric effects are observed to hinder passage through narrow throats of the flow field, macro-particle trajectories are otherwise found to align closely with passive tracer paths. The macro-particle orbits, however, are not evenly distributed within the cavity, and cluster closer to the periphery as the Reynolds and Stokes numbers increase. With support from observations of particle rotations relative to the fluid, we interpret this behaviour as resulting from weak forces pulling the macroscopic spheres towards preferential paths, similar to the Segré–Silberberg effect in Poiseuille flow.     

Elastic metamaterials with local resonances: an overview

Metamaterials are artificial composite materials engineered to have properties that may not be found in nature. By exploring locally resonant effect of the building units, elastic metamaterials are able to possess negative values of effective mass, effective bulk or shear modulus. Mass-spring and continuum material versions of these elastic metamaterials are reported and the physical mechanisms of negative effective parameters are demonstrated. Applications of metamaterials to acoustic cloaking and superlensing are also discussed.     

大地构造分析中的一些力学问题

综述了应用固体力学连续介质理论分析大地构造运动的问题,讨论了它们和通常力学问题的差别。主要的不同在于这里是反演问题:从地表的大地构造表现模拟出内部过程,从当前的资料追索它们的历史。依靠地球科学家所收集到的资料来引导这些反演。在数值模拟中建立适当的本构关系和破坏准则是头等重要的环节。最后提出固体力学中有关的研究课题。      

多边形有限单元形函数的比较研究

多边形有限单元形函数有wachspress插值、Laplace插值和平均值插值三种类型.本文对三种多边形有限单元形函数的性质作了比较研究,给出了三种形函数各自的优点和局限性.Waclaspress和Laplace形函数是有理函数形式,而平均值形函数是无理函数形式.三种形函数均满足单位分解性、线性完备性,且在单元边界上呈线性.在三角形单元上,它们都等价于三角形面积坐标插值.在矩形单元上,Wachspress和Laplace形函数等价于双线性多项式插值形函数.Wachspress和平均值形函数适用于任意凸多边形单元,Laplace形函数更适用于圆内接多边形单元.Wachspress形函数不能推广到含有边节点的单元,平均值形函数可以直接推广到含有边节点的单元.数值试验,验证了本文理论分析的结论.     

均布载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用格林函数方法，波纹膜片的非线性边值问题化为了非线性积分方程的求解。为了求解积分方程并防止发散，一个插值参数被引入到迭代格式中。计算表明，当载荷很小时，任何插值参数值均能保证迭代的收敛性，取插值参数值接近或等于1获得较快的收敛速度，而当载荷较大时，插值参数值不能取得过大。绘出了波纹膜片的特征曲线，得到的特征曲线可供设计参考。可以断言，当载荷不大时，特征曲线是近似线性的，随着载荷的增大，特征曲线开始向上弯曲，明显偏离线性。本文中提出的解决方法适应于任意轴向截面的波纹壳体。     

Implications for Fisheries Policy of Complex Ecologic–Economic Dynamics

Fishery dynamics are considered within the context of an integrated ecologic–economic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary principle to mitigate the threat of catastrophic discontinuities and the scale-matching principle to ensure that management and property rights system are properly implemented.     

Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated.