Application of similitude to soil-machine systems

Model tests can be used to predict the performance of full-scale off-road vehicles and earth-moving and agricultural machines as an aid to their design and development. The principles of similitude as applied to soil-machine system modeling are discussed, and some past studies and examples of these applications are examined. The opportunities for future research to improve these techniques are identified.     

Structural response of stiffened plates in similitude under a turbulent boundary layer excitation

In structural dynamics, similitude laws usually deal with simple configurations as thin flat plates with point forces. Only recently, few papers have analyzed stiffened shells or stochastic pressure loads.This research activity extends the applicability of some similitude laws, developed for thin flat plates under a turbulent boundary layer load, to ribbed plates forced by the same wall pressure fluctuations.The work addresses the problem of designing a scaled experimental test-article and, successively, of re-modulating the measured data in order to get the structural response of an original (unscaled) configuration.Due to the complexity of the structural domain, the design of a scaled configuration leads to a distorted similitude. Then, a simple approach, to circumvent the distortion effects, is proposed.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW (I)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability. The Project Supported by National Natural Science Foundation of China.     

Conservation laws and symmetries of systems with unilateral constraints in phase space

By introducing the generalized quasi-symmetry of the infinitestinal transformation for transformation groupG _r , this paper studies the conservation laws and symmetries of dynamical systems with unilateral constraints in phase space. Noether's theorem and Noether's inverse theorem for mechanical systems with unilateral constraints in phase space are obtained and two kinds of equivalent forms of generalized Killing equations which are used to determine the generators of the infinitestinmal group transformation are given. The project sponsored by the National Natural Science Foundation and the Doctoral Programme Foundation of Institution of Higher Education of China.     

Measurement of interfacial distortions at a stratified entrainment interface

A laser beam scanning technique was used to measure the rms amplitude of the largest wave (interfacial distortion) that is present at the entrainment interface of a stratified fluid. Both linearly-stratified and two-layer fluid systems, subjected to entrainment by oscillating-grid induced shear-free turbulence, are considered. The measurements were found to be in general agreement with a theory due to Long (1978), which predicts /D _e Ri ^–3/4 , where D _e is the mean thickness of the mixed layer and Ri is the appropriately defined bulk Richardson number at the interface.     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

Beitrag zur Dimensionsanalyse

Übersicht Der Zusammenhang zwischen den drei in der Literatur auftretenden Grundfassungen des -Theorems wird geklärt. Diese Grundfassungen sind nicht äquivalent. — Die erste Grundfassung des -Theorems läßt sich verschärfen, wenn die zugehörige dimensionshomogene Beziehung invariant ist gegenüber einer Erweiterung des Grundgrößensystems: Einige dimensionslose Produkte in der ersten Grundfassung treten dann darin nur als Potenzprodukte kombiniert auf. Unter Ausnutzung dieser Verschärfung findet man beispielsweise bei einer speziellen natürlichen Strömung innere Ähnlichkeit zu beiden Komponenten des Lösungsvektors. Die zugehörigen Ähnlichkeitsvariablen unterscheiden sich im allgemeinen.

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Contribution to dimensional analysis

Summary The connection between the three basic versions of the -theorem, which are known in the literature, is clarified. These basic versions are not equivalent. — The first basic version can be improved if the corresponding dimensionally homogeneous relation is invariant under an enlargement of the system of basic quantities: in this case various dimensionless products in the first basic version do not occur separately but combined as power products. This finding can be used to discover internal similitude. This is demonstrated with the aid of a special flow problem where internal similitude associated with both components of the solution vector is found. The corresponding similarity variables differ from each other in general.

     

Multibody graph transformations and analysis

This two-part paper uses graph transformation methods to develop methods for partitioning, aggregating, and constraint embedding for multibody systems. This first part focuses on tree-topology systems and reviews the key notion of spatial kernel operator (SKO) models for such systems. It develops systematic and rigorous techniques for partitioning SKO models in terms of the SKO models of the component subsystems based on the path-induced property of the component subgraphs. It shows that the sparsity structure of key matrix operators and the mass matrix for the multibody system can be described using partitioning transformations. Subsequently, the notions of node contractions and subgraph aggregation and their role in coarsening graphs are discussed. It is shown that the tree property of a graph is preserved after subgraph aggregation if and only if the subgraph satisfies an aggregation condition. These graph theory ideas are used to develop SKO models for the aggregated tree multibody systems.     

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅱ)——THE LINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.     

Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is characterised by strong turbulence and air bubble entrainment. New air–water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments conducted with identical inflow Froude numbers Fr ₁ = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10⁵, some viscous scale effects were observed in terms of the rate of entrained air and air–water interfacial area.     

Simulating hydrodynamics of hot and large Group A particle systems at cold conditions to obtain data for scale-up

Scaling laws based on the concept of dimensional similitude are proposed to simulate the hydrodynamics of hot and large particle systems at conditions of cold and small particle systems. This technique uses the concept of dimensional similitude to accomplish this by maintaining certain dimensional groups constant in the large, hot and small, cold systems. However, there are certain limitations with this technique. One of them is that the particle size in the small, cold system is usually smaller than in the large, hot system. Because particle size is such a dominant parameter in fluidized systems, this can certainly affect the simulation.
An alternative method of simulating hot hydrodynamics in ambient-temperature Group A particle systems has been proposed. In this method, the same calculated drag force is maintained between the two systems. The drag force is varied by changing the gas density of the cold system so that it matches the drag force in the hot system.     

On the use of neural networks for identification of linear and nonlinear systems

A procedure based on neural networks for the classification of linear and nonlinear systems is presented, using excitation and response data under swept sine excitation. Special attention is paid to the classification and identification of linear and bilinear systems, the latter being considered since they exhibit typical characteristics of cracked systems. The computer simulations show that: (1) using the procedure presented in this paper the trained classification network can reliably classify a linear system and different nonlinear systems; (2) the output of the trained identification neural network for a linear system and a bilinear system can be used as a quantitative indicator of characteristics of bilinear systems having different stiffness ratios (k _(x>0)/k _(x<0)) with respect to the bilinear system used in the training stage; (3) for two-degree-of-freedom systems, the trained network can not only determine the existence of a bilinear stiffness and the magnitude of its stiffness ratio, but also specify which stiffness is bilinear, i.e. indicate its position. These results provide a possibility of using the trained neural networks to detect and locate structural cracks which have the characteristics of bilinear systems.Visiting scholar, from People's Republic of China.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （II）

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406)     

A New Methodology for the Analysis of Periodic Systems

A new numerical-analytical method for the combined global-localanalysis of nonlinear periodic systems referred to as an ExpandedPoint Mapping (EPM) is presented. This methodology combines thecell to cell mapping and point mapping methods toinvestigate the basins of attraction and stability characteristics ofequilibrium points and periodic solutions of nonlinear periodicsystems. The proposed method is applicable to multi-degrees-of-freedomsystems, multi-parameter systems, and allows analytical studies oflocal stability characteristics of steady state solutions. Inaddition, the EPM approach allows the study of stabilitycharacteristics as function of system parameters to obtain analyticalconditions for bifurcation. In the paper, the theoretical basis forthe EPM method is formulated and a procedure for the analysis ofnonlinear dynamical systems is presented. Analysis of a pendulum witha periodically excited support in the plane is used to illustrate themethod. The results demonstrate the efficiency and accuracy of theproposed approach in analyzing nonlinear periodic systems.     

The relative variance criterion for stability of delay systems

A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.     

Asymptotic Behavior of Global Classical Solutions to the Mixed Initial-Boundary Value Problem for Quasilinear Hyperbolic Systems with Small BV Data

In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial-boundary value problem with small BV data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space {(t,x)|t≥0,x≥0}. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the solution approaches a combination of C ¹ traveling wave solutions, provided that the C ¹ norm of the initial and boundary data is bounded and the BV norm of the initial and boundary data is sufficiently small. Applications to quasilinear hyperbolic systems arising in physics and mechanics, particularly to the system describing the motion of the relativistic string in the Minkowski space-time R ¹⁺ⁿ , are also given.     

A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam

This paper delineates a class of time-periodically perturbed evolution equations in a Banach space whose associated Poincaré map contains a Smale horseshoe. This implies that such systems possess periodic orbits with arbitrarily high period. The method uses techniques originally due to Melnikov and applies to systems of the form x=f _o(X)+f ₁(X,t), where f _o(X) is Hamiltonian and has a homoclinic orbit. We give an example from structural mechanics: sinusoidally forced vibrations of a buckled beam.     

Quasiconformal mappings as a tool to study certain two-dimensional G-closure problems

A recent theorem due to Astala establishes the best exponent for the area distortion of planar K-quasiconformal mappings. We use a refinement of Astala's theorem due to Eremenko and Hamilton to prove new bounds on the effective conductivity of two-dimensional composites. The bounds are valid for composites made of an arbitrary finite number n of possibly anisotropic phases in prescribed volume fractions. For n= 2 we prove the optimality of the bounds under certain additional assumptions on the G-closure parameters.     

Determination method of scaling laws based on least square method and applied to rectangular thin plates and rotor-bearing systems

Abstract

In this study, we investigate the dynamic scaling laws of geometrically similitude models and systems for predicting their vibration characteristics accurately. A determination method of scaling laws based on least square method for calculating weighted powers of scaling factors is proposed for the first time. Taking geometric parameters as input (design) parameters and vibration characteristics parameters as output parameters, the weighted powers of scaling factors are calculated by least squares similitude method (LSSM) with several design models, and then scaling factors of the output parameters are obtained by combining weighted powers and corresponding scaling factors. Applicability of the LSSM is verified in the following two cases with rectangular plate and rotor-bearing system that the stiffness of supports is taken into account. The vibration characteristics are calculated by using finite element method in MATLAB and compared with simulation analysis software ANSYS. As a result, stable weighted powers and good predictions are obtained for two cases.     

Pansystems clustering analysis of complex systems

In this paper, by use of equivalence operators δ_i and semi-equivalence operators ε_i we study the clustering problems of complex systems, present δ_i(1,3) disconnection principle,dual transformation principle and large-scale systems decomposition principle for analizing and operating complex systems, discuss interconnectivity and disconnectivity of complex systems in detail and present some related theorems. Finally, we discuss the levels of systems according to pansystems, clustering approach proposed in this paper.