Relationship between multibody dynamics computation and nonlinear vibration theory

This paper presents the ground-work of implementing the multibody dynamics codes to analyzing nonlinear coupled oscillators. The recent developments of the multibody dynamics have resulted in several computer codes that can handle large systems of differential and algebraic equations (DAE). However, these codes cannot be used in their current format without appropriate modifications. According to multibody dynamics theory, the differential equations of motion are linear in the acceleration, and the constraints are appended into the equations of motion through Lagrange's multipliers. This formulation should be able to predict the nonlinear phenomena established by the nonlinear vibration theory. This can be achieved only if the constraint algebraic equations are modified to include all the system kinematic nonlinearities. This modification is accomplished by considering secondary nonlinear displacements which are ignored in all current codes. The resulting set of DAE are solved by the Gear stiff integrator. The study also introduced the concept of constrained flexibility and uses an instantaneous energy checking function to improve integration accuracy in the numerical scheme. The general energy balance is a single scalar equation containing all the energy component contributions. The DAE solution is then compared with the solution predicted by the nonlinear vibration theory. It also establishes new foundation for the use of multibody dynamics codes in nonlinear vibration problems. It is found that the simulation CPU time is much longer than the simulation of the original equations of the system.     

Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium

A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates.     

两相流中密度波现象的研究及进展

密度波（又称连续波、空隙度波、运动学波）是两相流中的特殊现象，本文评述两相流密度波理论的主要研究进展，这些理论不仅研究了线性密度波和非线性密度波的特性，还研究了气液两相流的流型转变与密度波的关系，流化床中气塞的形成和床层的塌陷现象与密度波的关系等．同时介绍试验和理论研究在密度波的波速、频率、稳定性和色散性等方面取得的主要结论．最后指出密度波的理论和试验研究尚需进一步解决的问题．     

球壳结构馈通增长的瑞利-泰勒不稳定性

利用小扰动分析法 ,导出不可压缩球壳结构的馈通增长方程 ,数值模拟了高压气体驱动外表面有初始扰动的明胶球壳的瑞利 泰勒不稳定性模型。计算结果表明 :对于低波数扰动 ,外界面比较稳定 ,内表面的馈通增长较快 ,具有比较明显的三个演化阶段和波形反转现象。高波数扰动的增长恰好与低波数相反。球壳会聚结构比柱壳会聚结构的界面稳定性要好些。     

Modèles discrets de structures tissées : Analyse de stabilité et de drapéDiscrete models of woven structures: stability and draping analysis

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

Extensions to the Macroscopic Navier–Stokes Equation

A development is provided showing that for any phase, by not neglecting the macroscopic terms of the deviation from the intensive momentum and of the dispersive momentum, we obtain a macroscopic secondary momentum balance equation coupled with a macroscopic dominant momentum balance equation that is valid at a larger spatial scale. The macroscopic secondary momentum balance equation is in the form of a wave equation that propagates the deviation from the intensive momentum while concurrently, in the case of a Newtonian fluid and under certain assumptions, the macroscopic dominant momentum balance equation may be approximated by Darcys equation to address drag dominant flow. We then develop extensions to the dominant macroscopic Navier–Stokes (NS) equation for saturated porous matrices, to account for the pressure gradient at the microscopic solid-fluid interfaces. At the microscopic interfaces we introduce the exchange of inertia between the phases, accounting for the relative fluid square velocities and the rate of these velocities, interpreted as Forchheimer terms. Conditions are provided to approximate the extended dominant NS equation by Forchheimer quadratic momentum law or by Darcys linear momentum law. We also show that the dominant NS equation can conform into a nonlinear wave equation. The one-dimensional numerical solution of this nonlinear wave equation demonstrates good qualitative agreement with experiments for the case of a highly deformable elasto-plastic matrix.     

Parametric Identification of a Base-Excited Single Pendulum

A harmonic balance based identification algorithm was applied to the simulated single pendulum with horizontal base-excitation. The purpose of this simulation was to examine the applicability of the algorithm on parametrically excited, whirling chaotic systems. Modifications were adopted to adapt to the whirling systems. The system was supposed to be unknown except only the excitation frequency. Linear interpolation functions and the Fourier series functions were tested to approximate unknown nonlinear functions in the governing differential equation. After extracting unstable periodic orbits, all of the parameters were simultaneously identified. By direct comparison, Poincaré section plots and reconstructed phase portrait techniques, it was shown that the identified system had similar dynamical characteristics to the original simulated pendulum, which implies the effectiveness of the examined algorithm.     

Laboratory Investigation of Variable-Density Flow and Solute Transport in Unsaturated–Saturated Porous Media

In many groundwater systems, fluid density and viscosity may vary in space and time as a function of changes in concentration and temperature of the fluid. When dense groundwater plumes interact with less dense ambient groundwater, these density variations can significantly affect flow and transport processes. Under certain conditions, gravitational instabilities in the form of lobe-shaped fingers can occur. This process is significant because it can lead to more rapid and spatially extensive solute transport. This paper presents new experiments carried out in a sand filled glass flow container under both fully saturated and variably-saturated conditions and focuses upon the processes that occur at the capillary fringe and below the water table, as affected by a dense contaminant plumes migration through the unsaturated zone. Source fluids stained with Rhodamine-WT were introduced at the upper boundary of the tank at a range of low and high densities. In addition to the fluid density gradients and porous medium permeability that determine the onset conditions for instabilities in fully saturated experiments, volumetric water content appears critical in the variably-saturated laboratory runs. Plume behaviour at the water table appears dependent upon the density of the fluid that accumulates there. For neutral and low density fluids, plumes accumulate at the water table and then spread laterally above it and the water table forms a barrier to further vertical flow as pore water velocities reduce with increasing water content. For medium and high density fluids, vertical movement continues as instabilities form at the capillary fringe and fingers begin to grow at the water table boundary and move downwards into the saturated zone. In these cases, lateral spreading of the plume is small. Despite these more qualitative observations, the exact nature of the relevant stability criteria for the onset and growth of instabilities in variably-saturated porous media presently remain unclear. All experimental results suggest, however, that the unsaturated zone and position of the water table must be considered in contaminant studies in order to predict the migration pathways, rates and ultimate fate of dense contaminant plumes. It is possible that the results of experiments presented in this paper could form a useful basis for the testing of variable-density (and variably-saturated) groundwater flow and solute transport numerical codes because they offer controlled physical laboratory analogs for comparison. They also provide a strong basis for the development of more rigorous mathematical formulations that are likely to be either developed or tested using numerical flow and solute transport simulators.     

Investigation of a combustion driven oscillation in a refinery flare: Part B: Visualisation of a periodic flow instability in a bifurcating duct following a contraction

A flow visualisation study was performed to investigate a periodic flow instability in a bifurcating duct within the tip of the flares at the Shell refinery in Clyde, NSW, to verify the trigger of a combustion-driven oscillation proposed in Part A of this study, and to identify its features. The model study assessed only the flow instability, uncoupled from the acoustic resonance and the combustion that are also present in the actual flare. Three strong, coupled flow oscillations were found to be present in three regions of the fuel line in the flare tip model. A periodic flow separation was found to occur within the contraction at the inlet to the tip, a coupled, periodic flow oscillation was found in the two transverse “cross-over ducts” from the central pipe to the outer annulus and an oscillating flow recirculation was present in the “end-cap” region of the central pipe. The dimensionless frequency of these oscillations in the model was found to match that measured in the full-scale plant for high fuel flow rates. This, and the strength of these flow oscillations, gives confidence that they are integral to the full-scale combustion-driven oscillation and most likely the primary trigger. The evidence indicates that the periodic flow instability is initiated by the separation and roll-up of the annular boundary layer at the start of the contraction in the fuel section of the flare tip. The separation generates an annular vortex which interacts with the blind-ended pipe downstream, leading to a pressure wave which propagates back upstream, initiating the next separation event and repeating the cycle. The study also investigated flow control devices with a view to finding a practical approach to mitigate the oscillations. The shape of these devices was constrained to allow installation without removing the tip of the flare. This aspect of the study highlighted the strength and nature of the coupled oscillation, since it proved to be very difficult to mitigate the oscillation in this way. An effective configuration is presented, comprising of three individual components, all three of which were found to be necessary to eliminate the oscillation completely.     

Euler杆大挠度屈曲的解析逼近

研究Euler杆大挠度屈曲问题，将控制方程的线性化与谐波平衡法组合起来，分别建立以杆端转角形式表示的屈曲荷载及最大挠度的解析逼近公式，这些公式既适用于小变形又适用于大变形。