Chaos caused by fatigue crack growth

The nonlinear dynamic responses including chaotic oscillations caused by a fatigue crack growth are presented. Fatigue tests have been conducted on a novel fatigue-testing rig, where the loading is generated from inertial forces. The nonlinearity is in the form of discontinuous stiffness caused by the opening and closing of a growing crack. Nonlinear dynamic tools such as Poincaré maps and bifurcation diagrams are used to unveil the global dynamics of the system. The results obtained indicate that fatigue crack growth strongly influences the dynamic response of the system leading to chaos.     

Response of a tethered aerostat to simulated turbulence

Aerostats are lighter-than-air vehicles tethered to the ground by a cable and used for broadcasting, communications, surveillance, and drug interdiction. The dynamic response of tethered aerostats subject to extreme atmospheric turbulence often dictates survivability. This paper develops a theoretical model that predicts the planar response of a tethered aerostat subject to atmospheric turbulence and simulates the response to 1000 simulated hurricane scale turbulent time histories. The aerostat dynamic model assumes the aerostat hull to be a rigid body with non-linear fluid loading, instantaneous weathervaning for planar response, and a continuous tether. Galerkin’s method discretizes the coupled aerostat and tether partial differential equations to produce a non-linear initial value problem that is integrated numerically given initial conditions and wind inputs. The proper orthogonal decomposition theorem generates, based on Hurricane Georges wind data, turbulent time histories that possess the sequential behavior of actual turbulence, are spectrally accurate, and have non-Gaussian density functions. The generated turbulent time histories are simulated to predict the aerostat response to severe turbulence. The resulting probability distributions for the aerostat position, pitch angle, and confluence point tension predict the aerostat behavior in high gust environments. The dynamic results can be up to twice as large as a static analysis indicating the importance of dynamics in aerostat modeling. The results uncover a worst case wind input consisting of a two-pulse vertical gust.     

Dynamic solid mechanics using finite volume methods

A procedure for evaluating the dynamic structural response of elastic solid domains is presented. A prerequisite for the analysis of dynamic fluid–structure interaction is the use of a consistent set of finite volume (FV) methods on a single unstructured mesh. This paper describes a three-dimensional (3D) FV, vertex-based method for dynamic solid mechanics. A novel Newmark predictor–corrector implicit scheme was developed to provide time accurate solutions and the scheme was evaluated on a 3D cantilever problem. By employing a small amount of viscous damping, very accurate predictions of the fundamental natural frequency were obtained with respect to both the amplitude and period of oscillation. This scheme has been implemented into the multi-physics modelling software framework, Physica, for later application to full dynamic fluid structure interaction.     

动载下缝端应力强度因子计算的扩展有限元法

在扩展有限元法(extended finite element methods, XFEM)的理论框架下,重点研究了动荷载作用下稳定裂纹尖端动态应力强度因子(dynamic stress intensity factors, DSIFs)的求解方法．根据XFEM的位移模式,推导了动力XFEM的支配方程,采用Newmark隐式算法进行时间积分同时,提出一种XFEM质量矩阵的集中策略,给出了求解DSIFs的相互作用积分方法,与静态问题的相互作用积分方法相比,增加了惯性项的贡献．最后,若干典型算例的计算结果表明:XFEM可以准确评价稳定裂纹尖端的DSIFs,建议的质量矩阵集中策略是有效的,为得到正确的DSIFs,惯性项的贡献不可忽略.     

带人工雨线的拉索在风激励下的响应

通过在风洞中对一具有可调动力特性、雨线位置和风向角的带人工雨线的拉索模型进行了试验,研究了拉索的风雨激振特性.试验结果和其他研究人员的结果进行了仔细对比,得到了一些新的结论,澄清了过去的一些模糊认识.结果表明,带人工雨线的水平索在风向为零时的响应可以用Den Hartog驰振机制来解释,而风向不为零时,拉索表现为限速振动或限速和驰振的混合型振动.     

Stability of a steady flow guided by flexible walls

Flexible channels conveying fluid may loose stability by divergence or flutter, thus leading to undesirable dynamic behaviour. A lot of investigations have already been done on this subject, each involving structural models expressing a specific type of stiffness. The aim of this contribution is to investigate and compare systematically the influence of various types of structural stiffness on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is built. The fluid is bounded by a rigid and an elastical supported, flexible wall, which exhibits bending and extensional stiffness and considers effects of pre-load. The influence of the various characteristics on the stability of the steady state is discussed and a perturbation approach is used to investigate the influence of small nonlinearities. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of the elasticity of an orbital tether system on the oscillations of a satellite

An orbital tether system, including a satellite (a rigid body), an elastic ponderable tether and a terminal load, is investigated. A mathematical model is obtained using Lagrange's equation of the second kind, which enables the plane translational motion of the centres of mass of the elements of the system and the rotational motion of the satellite and the tether to be investigated. It is shown that the equations of motion for the new independent variable, that is, the true anomaly angle, obtained on the assumption that the motion of the centre of mass of the system is independent of the relative motion of its elements, are an extension of the known mathematical models. The effect of the elasticity of the tether on the angular oscillations of the tether and the satellite is investigated. The model constructed can be used both to analyse of the deployment of a tether system as well as to investigate of the combined behaviour of a satellite and a tether about the natural centres of mass.     

CFD simulation of methane dispersion and innovative methane management in underground mining faces

This study addresses methane dispersion in a mine tunnel with discrete methane sources and various methods to handle it. Air flow behavior and methane dispersion in the tunnel are simulated utilizing the computational fluid dynamics (CFD) approach. Various possible conditions which may occur in a mine tunnel are investigated. Simulation results indicate that methane dispersion inside the mine tunnel is influenced significantly by the number as well as location of the sources and quantity of methane released from each source. Furthermore, application of an innovative flow divider which comprises volumetric flow control and flow director, is investigated. It is found that by properly directing the ventilation flow to the location where methane is accumulating can reduce methane concentration below the safe level. In addition, it is noted that focusing the ventilation flow at a point is more effective as compared to dispersing it at several points. This study provides some new ideas for designing an “intelligent” underground mine ventilation system which can cost-effectively maintain methane concentration below the critical value.     

Multidimensional turbulence spectra – Statistical analysis of turbulent vortices

Strong nonlinear or very fast phenomena such as mixing, coalescence and breakup in chemical engineering processes, are not correctly described using average turbulence properties. Since these phenomena are modeled by the interaction of fluid particles with single or paired vortices, distribution of the properties of individual turbulent vortices should be studied and understood. In this paper, statistical analysis of turbulent vortices was performed using a novel vortex tracking algorithm. The vortices were identified using the normalized Q-criterion with extended volumes calculated using the Biot–Savart law in order to capture most of the coherent structure related to each vortex. This new and fast algorithm makes it possible to estimate the volume of all resolved vortices. Turbulence was modeled using large-eddy simulation with the dynamic Smagorinsky–Lilly subgrid scale model for different Reynolds numbers. Number density of turbulent vortices were quantified and compared with different models. It is concluded that the calculated number densities for vortices in the inertial subrange and also for the larger scales are in very good agreement with the models proposed by Batchelor and Martinez-Bazán. Moreover, the associated enstrophy within the same size of coherent structures is quantified and its distribution is compared to models for distribution of turbulent kinetic energy. The associated enstrophy within the same size of coherent structures has a wide distribution that is normal distributed in the logarithmic scale.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Analysis of hydrodynamic losses for various types of aortic valves

Conclusions The creation of an automated computer-controlled hydraulic stand made it possible to measure the main hydrodynamic parameters of the flow through the investigated HVP and to determine the coefficients of Eq. (2) of fluid flow in the test chamber of the stand. The coefficients found can serve as a criterion of a comparative assessment of the hydrodynamics of HVPs. An analysis of the coefficients showed that the main contribution to pressure losses across ball and disc valves is made by viscous and convective effects. An analysis of inertial losses confirmed the presence of oscillations of the ball closing elements of the AKCh-3-06 valve around the props of the stroke limiters and made it possible to assess them quantitatively. For leaflet valves the contribution of inertial losses to the total pressure losses is more considerable than in the case of disc and ball valves both in the regime of an increase of power of the output and in the regime of a constant power. The mechanical properties of the material of leaflet valves have an effect on the hydrodynamic characteristics. The advantage of the investigated leaflet valves consists not only in that they have smaller total hydraulic losses compared with the other valves, but also in that they provide a high amplitude of pulsations of the blood stream in the case of insufficient contractility of the heart.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 506–512, May–June, 1985.     

计入气穴的水下爆炸作用下结构流固耦合三维数值模拟

水下爆炸在结构物面附近产生的气穴现象,严重影响水下爆炸作用下的流固耦合动响应,是舰船水下爆炸领域的难点,传统的边界元方法、有限元方法(FEM)难以解决水下爆炸气穴现象这类强非线性问题．针对此问题,计及流体中的气穴现象,考虑流体的可压缩型,忽略流体粘性,建立水下爆炸瞬态强非线性流固耦合三维数值模型,采用流体谱单元方法(SEM)和结构有限元方法求解该模型．计算结果表明:相对有限元法,谱单元法具有更高的计算精度,且谱单元解与解析解、试验值吻合良好．在此基础上,结合ABAQUS软件,分别探讨三维球壳、船体板架在水下爆炸作用下的瞬态流固耦合机理,给出气穴区域及其对水中结构物动响应的影响特征,旨在为舰船水下爆炸瞬态流固耦合问题的相关研究提供参考．     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

Pitfalls in the frequency response represented onto Polynomial Chaos for random SDOF mechanical systems

Uncertainties are present in the modeling of dynamical systems and they must be taken into account to improve the prediction of the models. It is very important to understand how they propagate and how random systems behave. This study aims at pointing out the somehow complex behavior of the structural response of stochastic dynamical systems and consequently the difficulty to represent this behavior using spectral approaches. The main objective is to find numerically the probability density function (PDF) of the response of a random linear mechanical systems. Since it is found that difficulties can occur even for a single-degree-of-freedom system when only the stiffness is random, this work focuses on this application to test several methods. Polynomial Chaos performance is first investigated for the propagation of uncertainties in several situations of stiffness variances for a damped single-degree-of-freedom system. For some specific conditions of damping and stiffness variances, it is found that numerical difficulties occur for the standard polynomial bases near the resonant frequency, where it is generally observed that the shape of the system response PDFs presents multimodality. Strategies to build enhanced bases are then proposed and investigated with varying degrees of success. Finally, a multi-element approach is used in order to gain robustness.     

The dynamic behaviour of elastic coaxial cylindrical shells conveying fluid

The dynamic behaviour of elastic coaxial cylindrica shells, which interact with a flow of compressible fluid in the inner shell or in the annular gap between the shells when both flows are present, is investigated by the finite element method. A number of test problems is considered in the case of cantilevered coaxial shells. The effect on the stability limit of the gap between the two shells is investigated for different values of the stiffness parameters of the outer shell and the fluid flow. An important difference is found with existing solutions in cases when the loss of stability of the coaxial shells occurs at higher oscillation modes. It is established that, for a certain value of the gap between the shells, the elasticity of the outer shell may have a stabilizing effect. It is shown that the presence of internal and annular flows simultaneously has a considerable stabilizing effect, while a loss of stability when the flow rates increase occurs at extremely high oscillation modes.     

Scattering of a plane wave by shallow buried cylindrical lining in a poroelastic half-space

The shallow buried tunnel is frequently encountered in underground engineering. The dynamic response of a tunnel under incident wave is of great importance for guiding the safety design in tunnel engineering. In this paper, a model for predicting the dynamic response of a shallow buried tunnel in saturated soil is proposed based on nonlocal Biot theory. The analytical solution is obtained using the wave function expansion method. To consider practical engineering problem, a set of material parameters for saturated soil and tunnel lining are selected for the numerical analysis. The influence of nonlocal parameter, which is introduced in nonlocal Biot theory to consider the pore size effect and pore dynamic effect, on dynamic stress concentrate factor in the lining is investigated in detail. The dynamic responses affected by the other factors, such as incident wave angle, frequency of incident wave and buried depth of the tunnel, have also been implemented. The dynamic stress concentrate factor distributed in the lining is also shown and the position and orientation appearing maximum concentrate factor can be easily determined from the contour plot, which can provide a visual guideline for safety design of a tunnel.     

用Hadamard方法构造惯性流形

本文用Ｈａｄａｍａｒｄ方法为一类带有非线性项Ｒ：Ｄ（Ａ）→Ｈ的无限维耗散动力系统建立惯性流形．在建立惯性流形的过程中，系统的一种“不变锥性质”被充分利用着．这里，对惯性流形存在性至关紧要的谱间隙条件是．     

Dynamic analysis and passive control of viscoelastically damped nonlinear dynamic contacts

This paper presents an analytical and finite element study on nonlinear contact dynamics and controls. Nonlinear dynamic contacts between eccentrically supported masses and simply supported beams are studied. Passive control of the dynamic contacts using viscoelastic dampers is also proposed and evaluated. A nonlinear contact finite element is modeled by a set of nonlinear stiffness and damping polynomial functions; and a nonlinear viscoelastic finite element is modeled by a Standard Linear Model with frequency-dependent nonlinear stiffness and damping functions. Analyses show that the dynamic contact force increases as the initial gap increases. Application of viscoelastic dampers can effectively reduce contact loads and prevent dynamic contacts. A simple design equation is also proposed.     

Inertial Particle Motion in Recirculating Stokes Flow

Recirculation occurs in many cavity flows. In particular, alveolar flow models have been shown to exhibit recirculation patterns. However, many particles that are inhaled by the lungs do not follow this flow. Instead, they may diffuse into the surrounding flow or possess enough inertia to propel them from fluid particle paths. In this study, we construct a minimal model to observe the behavior of inertial particles caught within a recirculating Stokes flow. We find that, given favorable conditions, inertial particles can be cleared from the cavity or deposited on walls. This depends on the strength of inertia in zero gravity, but can be enhanced when gravity and the orientation of the cavity are taken into account. It is also possible for these effects to balance one another, producing a skewed limit cycle. These combined effects may play a significant part in the retention, deposition, and clearance of aerosols and particulates from alveolar cavities.     

Numerical Studies of Viscoelastic Flow Using the Software OpenFOAM

Viscoelastic fluids are a special class of non-Newtonian fluids. There are several types of viscoelastic fluid models, and all of them have a complex rheological response in comparison to Newtonian fluids. This response can be viewed as a combination of viscous and elastic effects and non-linear phenomena. This complex physics makes a numerical simulation a rather challenging task, even in simple test-cases. Studies presented in this paper are numerical studies of the viscoelastic fluid flow in several test cases. These studies have been done in OpenFOAM, an open-source CFD package. Implementation of viscoelastic models and a solver is only available in a community driven version of software (OpenFOAM-ext). One of the goals of research in this paper was to test the solver and models on some simple test cases. We considered start-up and pulsating flows of viscoelastic fluid in a channel and a circular pipe. The important thing is that an analytical solution can be found in these cases, making in possible to test all aspects of numerical simulation in OpenFOAM. Obtained results showed an excellent agreement with the analytical solution for both velocity and stress components. These results encouraged authors' motivation and a choice to use OpenFOAM for simulation of viscoelastic flows. We hope that our research will make a contribution to the OpenFOAM community. Our plan for the further research is a simulation of blood flow in arteries with the viscoelastic solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)