On stability and self-excited vibrations in fluid-structure-interaction

In flexible channels conveying fluid the steady state may loose stability by divergence or flutter. The aim of this contribution is to investigate the basic excitation mechanisms of flow-induced vibrations and to evaluate the influence of various parameters on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is proposed. The fluid is assumed to be inviscid and irrotational and both incompressible and compressible flow is considered. It is guided by a planar, rectangular channel with a rigid wall and a thin, flexible wall. The latter is modelled as a one-parametric continuum on an elastic foundation, which exhibits bending and extensional stiffness. By examining the energy balance over one oscillation circle it is possible to reveal the mechanisms of energy transfer between the coupled components of the system. Based on this analysis a physical explanation of the arising instabilities is possible. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.     

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing.     

Synchronization effects in rotors partially filled with fluid-influence on propulsion

In fluid-filled Rotors occur self-excited vibrations induced by surface waves of the fluid. A characteristic property is the instability over an interval of angular velocity above the natural frequency of the system. One explanation is the occurrence of synchronization effects between fluid waves and the critical rotor speed. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable for observer-based real-time control. This paper analyses a model based on a laval rotor and shows synchronization effects between fluid waves and rotor model and its influence on the rotor propulsion. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

边界条件对梁类结构系统刚度的影响

车身骨架是由大量梁类结构单元构成的.除了这些梁的截面形状和尺寸外,边界条件也对系统刚度影响很大.讨论了各种边界条件和载荷模式下的梁系统的合成刚度.基于两端固支的均匀截面梁的弯曲和扭转刚度,研究了各联结刚度的大小对系统刚度的贡献,并绘制了相应的影响曲线.最后,通过上述解析公式和有限元法计算了某汽车仪表板横梁系统的实际弯曲和扭转刚度.文中获得的静态刚度公式对其它梁类结构也适用。     

Numerical study of forebody wake effect on axisymmetric parachute opening shock and drag reduction

ABSTRACT

Parachute–forebody distance is a parameter which is amongst the most critical factors to be considered in forebody wake effect. In this study, a new axisymmetric parachute–forebody coupling model is developed. Axisymmetric wrinkling membrane element is built to assess the dynamic response of the parachute canopy membrane under fluid pressure. Besides, fluid model and its further implementation on the fluid structure analysis are discussed. With the proposed method, the wake effect on both the opening shock during inflation state and the drag reduction during steady state can be obtained efficiently. Finally, numerical model is validated with published experimental result and further employed to investigate the influence of distance parameters on fluid–parachute coupling behaviour. On the basis of numerical results, failure distance during the inflation process and critical forebody–parachute distance are determined. The results show that forebody–parachute distance has a strong influence on flow behaviour around the parachute in both inflation state and steady descent state.     

On Burgers fluids

We investigate several qualitative aspects concerning the solutions to the flow of a Burgers fluid, a model that has been used to describe a variety of materials: polymeric liquids, asphalt and asphalt mixtures, and the earth's mantle. Continuous dependence of the solutions with respect to initial data and supply terms, uniqueness of solutions and the impossibility of localization of the solutions are proved. Exponential stability and structural stability are analysed. We also consider uniaxial shear flows. We prove instability of solutions whenever the constitutive parameters do not satisfy certain relations. Also we study the spatial behaviour of the solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Vibration of submerged floating tunnels due to moving loads

The concept of submerged floating tunnel (SFT) has become an increasingly attractive idea to cross the straits. The structural solution in this scheme includes buoyancy force on tunnel body plus tension in mooring tethers. This paper investigates the effect of submergence on the dynamic response of SFT due to moving load. The inertial effect of the fluid is accounted for by evaluating the added mass of tunnel using two and three dimensional models. It is found that fluid–structure interaction increases dynamic amplification of the tunnel deflection (in some cases very significantly). The results show that although the 3D model predicts lesser inertial contribution for surrounding fluid, it is not always possible to associate the larger response with the 2D or 3D models. The discrepancy between the results of the two models decreases as the tether stiffness increases. This indicates that the adoption of Morison’s equation for evaluating the fluid loading on the tunnel is a reasonable assumption when the tether stiffness is high. It is also found that by increasing the tether stiffness, it is possible to introduce a major reduction in the dynamic amplification of the response and by this way control the dynamic response of the SFT.     

Plane stress finite element analysis of filler reinforced polymers

The characteristics of polymers such as force-deformation behaviour, strength, fatigue and wear resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the material behaviour significantly depends on the size and geometric form of the filler aggregates, which vary under mechanical loading. The concept of super element is used to model filler particles. This is now coupled with the polymer matrix to generate a finite element model of filler reinforced polymers. In this work, we investigate the effect of filler geometry and volume fraction of fillers on the overall stiffness of the filler reinforced polymer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-steady interaction of fluids with free surfaces and rigid bodies

Interaction between fluids and rigid bodies is a phenomenon, which occurs for example in floating bearings or turbines. Mostly the focus is on domains with rigid boundaries on every side or defined influx or effusion of fluid over the boundaries. The interaction between fluids with free surfaces and a rigid body were mostly studied under the aspect of stability for steady-state conditions, e. g. for fluid-filled centrifuges. A characteristic property is the instability over non-empty intervalls of angular velocities, so the analysis of non-steady behaviour is essential to investigate the stability of the drive through these instable domains. A first approach to this topic is the qualitative investigation of a fluid domain with the shallow water theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hopf-Takens-Bogdanov interaction for a fluid-conveying tube

We investigate the dynamics after loss of stability of the downhanging configuration of a fluid conveying tube with a small end mass and an elastic support. By varying the fluid flow rate and the stiffness and location of the elastic support, different degenerate bifurcation scenarios can be observed. In this article we investigate the bifurcating solution branches of the codimension 3 interaction between a Hopf bifurcation and a Bogdanov-Takens bifurcation. A complete discussion of the primary and secondary solution branches was already given by W. F. Langford and K. Zhan. After reducing the system to the three-dimensional Normal Form equations we apply a numerical continuation procedure to locate the expected higher order bifurcation branches and detect more complicated dynamics, like Shilnikov orbits. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect

For a single-walled carbon nanotube (CNT) conveying fluid, the internal flow is considered to be pulsating and viscous, and the resulting instability and parametric resonance of the CNT are investigated by the method of averaging. The partial differential equation of motion based on the nonlocal elasticity theory is discretized by the Galerkin method and the averaging equations for the first two modes are derived. The stability regions in frequency–amplitude plane are obtained and the influences of nonlocal effect, viscosity and some system parameters on the stability of CNT are discussed in detail. The results show that decrease of nonlocal parameter and increase of viscous parameter both increase the fundamental frequency and critical flow velocity; the dynamic stability of CNT can be enhanced due to nonlocal effect; the contributions of the fluid viscosity on the stability of CNT depend on flow velocity; the axial tensile force can only influence natural frequencies of the system however the viscoelastic characteristic of materials can enhance the dynamic stability of CNT. The conclusions drawn in this paper are thought to be helpful for the vibration analysis and structural design of nanofluidic devices.     

机床结构刚度非线性条件下动态切削过程的定性分析

本文用定性分析的方法,研究了切削过程中在机床结构刚度非线性条件下速度型颤振的动态稳定性以及自激周期振动等问题。文中指出,对于速度型颤振,其动态稳定性主要取决于切削力而与结构刚度非线性特性元关,当动态切削过程为不稳定时,机床振动将出现稳定的自激极限环型周期振动。     

Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural stability for a Brinkman fluid

In this paper the authors investigate the structural stability of the Brinkman equations which describe the flow of a fluid containing a solute. A model proposed by Straughan and Hutter (Proc. Roy. Soc. London A 1999; 455 :767–777) is employed. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of the rail pad on a vehicle travelling on a straight track

In the following text, the influence of the stiffness of rail fastening systems of high‐speed railway lines on the dynamic stability of a vehicle travelling along a straight track is investigated. The dynamic behaviour of the rail head in lateral direction is incorporated in the model by means of mechanical models derivedfrom a preceding frequency analysis of the track. For the wheel‐rail interface, linear contact mechanics and kinematic relations are applied. The investigation leads to the conclusion that on high‐speed lines the critical velocity of vehicles is reduced as a result of the increased elasticity of the rail pads. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analysis for a nonlinear model of a hydraulic servomechanism in a servoelastic framework

The effects of mounting structure stiffness on mechano-hydraulic servomechanisms actuating aircraft primary flight controls are modeled by a six-dimensional nonlinear system of ordinary differential equations. Stability analysis of equilibria reveals the presence of a critical case that is handled through the use of the Lyapunov–Malkin theorem. Stability charts are drawn using the Routh–Hurwitz criterion for the stability of a fifth-degree polynomial. Comparison with previous results shows how the stability of equilibria can be ensured exploiting the positive influence of structural feedback.     

Stability and bifurcation behaviour of a Laval-Rotor considering fluid forces in compliant liquid seals

This contribution discusses the influence of fluid forces, stemming from compliant, contact-free annular rotor seals, on the steady state stability and bifurcation behaviour of a rotor. The model used in this work consists of a Laval-Rotor where the disc runs in a turbulently streamed seal. The compliance of the seal is reduced to a visco-elastically supported outer seal ring. In order to account for the fluid seal forces the Childs-Hirs-model is used. An investigation of the eigenvalues shows that the compliance of the seal support may lead to a significant increase in the stable operating range. A stability-loss via Hopf-, Hopf-Hopf or secondary Hopf-Bifurcations can occur depending on the system parameters. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)