Experimental determination of transverse vibration modes of thin I-shaped plates

The natural frequencies and the corresponding mode shapes of clamped thin I-shaped plates were experimentally determined by time-averaged holographic interferometry. The test plate was shaped as shown in Fig. 1, and eight kinds of plates were tested by taking a dimensionless length parameter ξ as a parameter. The natural-vibration modes exceeding 200 were identified using the real-time method. The corresponding natural frequencies ranged from 172 to 5606 Hz. In addition, in the case of a rectangular plate, the experimental results were shown to be good agreement with the theoretical ones.     

Energy release rates in a constrained epoxy disc with Hookean and Mooney–Rivlin materials

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually.     

Traction data analysis in reference to a unique zero condition

The lack of a unique definition for the zero condition leads to innumerable zero conditions resulting in different amounts of net traction at the same value of slip. In this paper, an attempt has been made to discuss various aspects of different zero conditions and finally result in a unique definition of the zero condition. Based on this definition, a traction prediction model using mobility number approach has been developed to evaluate the performance of tractor tyres in sandy clay loam soils.     

Log-likelihood maximization and response surface in reliability assessment

Nonlinear dynamics problems can generally be solved only in a numerical way. This prevents from a direct application of standard reliability methods. A technique which makes use of iterated response-surface analytical approximations of the system performance function was therefore proposed in view of reliability assessment. The limitation of this technique was of working in a standard normalized space, so that appropriate space transformations are preliminarly required.This paper shows how this response-surface iterative scheme can also be used in the original space of the random variables, provided a maximum log-likelihood constrained optimization problem is solved. Moreover, asymptotic theory also provides a better estimate of the probability of failure of the dynamical system against any assigned limit state.     

A numerical investigation of transient detonation in granulated material

A two-phase model based upon principles of continuum mixture theory is numerically solved to predict the evolution of detonation in a granulated reactive material. Shock to detonation transition (SDT) is considered whereby combustion is initiated due to compression of the material by a moving piston. In particular, this study demonstrates the existence of a SDT event which gives rise to a steady two-phase Chapman-Jouguet (CJ) detonation structure consisting of a single lead shock in the gas and an unshocked solid; this structure has previously been independently predicted by a steady-state theory. The unsteady model equations, which constitute a non-strictly hyperbolic system, are numerically solved using a modern high-resolution method. The numerical method is based on Godunov's method, and utilizes an approximate solution for the two-phase Riemann problem. Comparisons are made between numerical predictions and known theoretical results for 1) an inert two-phase shock tube problem, 2) an inert compaction wave structure, and 3) a reactive two-phase detonation structure; in all cases, good agreement exists. Received 4 August 1995 / Accepted 17 February 1996     

Flow of second-order fluids over an enclosed rotating disc

Summary This paper is devoted to a study of the flow of a second-order fluid (flowing with a small mass rate of symmetrical radial outflow m, taken negative for a net radial inflow) over a finite rotating disc enclosed within a coaxial cylinderical casing. The effects of the second-order terms are observed to depend upon two dimensionless parameters ₁ and ₂. Maximum values ₁ and ₂ of the dimensionless radial distances at which there is no recirculation, for the cases of net radial outflow (m>0) and net radial inflow (m<0) respectively, decrease with an increase in the second-order effects [represented by T(=₁+₂)]. The velocities at ₁ and ₂ as well as at some other fixed radii have been calculated for different T and the associated phenomena of no-recirculation/recirculation discussed. The change in flow phenomena due to a reversal of the direction of net radial flow has also been studied. The moment on the rotating disc increases with T.Nomenclature , , z coordinates in a cylindrical polar system - z ₀ distance between rotor and stator (gap length) - =/z ₀, dimensionless radial distance - =z/z ₀, dimensionless axial distance - _s = _s/z₀, dimensionless disc radius - V =(u, v, w), velocity vector - dimensionless velocity components - uniform angular velocity of the rotor - , p fluid density and pressure - P =p/(₂ z ₀₂ ² , dimensionless pressure - ₁, ₂, ₃ kinematic coefficients of Newtonian viscosity, elastico-viscosity and cross-viscosity respectively - ₁, _{2 2}/z ₀ ² , resp. ₃/z ₀ ² , dimensionless parameters representing the ratio of second-order and inertial effects - m = , mass rate of symmetrical radial outflow - l a number associated with induced circulatory flow - Rm =m/(z ₀₁), Reynolds number of radial outflow - R _l =l/(z ₀₁), Reynolds number of induced circulatory flow - Rz =z ₀ ² /₁, Reynolds number based on the gap - ₁, ₂ maximum radii at which there is no recirculation for the cases Rm>0 and Rm<0 respectively - ₁(T), ₂(T) ₁ and ₂ for different T - U _1(T) ⁽⁺⁾ = dimensionless radial velocity, Rm>0 - V _1(T) ⁽⁺⁾ = , dimensionless transverse velocity, Rm>0 - U _2(T) ^(–) = , dimensionless radial velocity, Rm=–Rn<0, m=–n - V _2(T) ^(–) = , dimensionless transverse velocity, Rm<0 - C _m moment coefficient     

The Documentation Rheology

Summary As the number of rheological and other scientific publications increases considerably year by year, documentation services should be used more extensively. The Deutsche Rheologische Gesellschaft (German Society of Rheology), 1 Berlin 45, Unter den Eichen 87, jointly with the Federal Institute for Materials Testing publishes at regular intervals an internationally useable and applicable Documentation Rheology, which contains a fairly complete collection of relevant literature subdivided into subject groups. The papers listed cover fundamentals of rheology, rheometry, rheological behaviour of polymer melts and solutions, plastics and rubber, metals, pastes, colloids and suspensions, solids, ceramics, concrete, pharmaceutical products and cosmetics, food stuffs, chemical engineering, forming processes, flow processes, mixing processes and so on.The documentation is available at a small charge. It has been published to make better use of the possibilities that lie in a systematic collection, arrangement, exploitation and application of findings achieved and published so far. Methodical and intensified research and development, as well as further rationalization and cost-saving measures in the field of practical application depend on a better utilization of existing findings. The above-mentioned documentation service covers basic research as well as technical application. With the aid of it literature search on general or more specific problems of research and practice can be done quicker and carried out much more easily. Literature search done this way guarantees that a research project will start from the current state of knowledge and that sufficient hints to solutions of practical problems are at hand. Moreover, the preparation and publication of literature reports will initiate a systematic evaluation of the numerous existing publications.

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Zusammenfassung Die Zahl der Veröffentlichungen pro Jahr nimmt auf dem Gebiet der Rheologie ebenso wie auf anderen Gebieten stetig zu. Es erscheint daher an der Zeit, auf eine stärkere Nutzung vorhandener Dokumentationsdienste hinzuwirken. Die Deutsche Rheologische Gesellschaft, 1 Berlin 45, Unter den Eichen 87, gibt gemeinsam mit der Bundesanstalt für Materialprüfung in regelmäßiger Folge einen international verwendbaren Dokumentationsdienst Rheologie heraus, der einen weitgehend vollständigen und nach Sachgebieten geordneten Nachweis der einschlägigen Weltliteratur enthält. Die erfaßten Arbeiten betreffen die allgemeinen Grundlagen der Rheologie, die Rheometrie, das rheologische Verhalten von Polymerschmelzen und -lösungen, Kunststoffe und Kautschuk, Metalle, Pasten, Kolloide und Suspensionen, Böden, Keramik, Beton, pharmazeutische Präparate und Kosmetika, Lebensmittel, Verfahrenstechnik, Formungsvorgänge, Strömungs- und Fließvorgänge, Mischvorgänge usw.Der Dokumentationsdienst steht allen Interessenten gegen einen Unkostenbeitrag zur Verfügung. Seine Herausgabe wurde dadurch veranlaßt, daß die in der systematischen Erfassung, Ordnung, Auswertung und Anwendung der bereits erzielten und veröffentlichten Forschungs- und Untersuchungsergebnisse noch liegenden Möglichkeiten längst nicht ausreichend genutzt werden. Sowohl eine gezieltere und intensivierte Forschung und Entwicklung einerseits als auch eine weitere Rationalisierung und Kostensenkung im Bereich der Praxis andererseits setzen eine bessere Anwendung bisher erzielter Ergebnisse voraus. Die Dokumentation Rheologie bezieht sich daher sowohl auf die Grundlagenforschung als auch auf die Belange der betrieblichen Praxis. Mit Hilfe dieser Dokumentation werden Recherchen zu allgemeinen und speziellen Fragestellungen aus Forschung und Praxis der Rheologie wesentlich erleichtert. Solche Recherchen bieten die Gewähr, daß zu beginnende Forschungsvorhaben vom Stand des Wissens ausgehen und Hinweise für die Lösung praktischer Probleme gefunden werden. Darüber hinaus wird eine planmäßige und systematische Auswertung der vorhandenen umfangreichen Literatur durch Erstellung und Veröffentlichung von Literaturberichten angeregt.

     

On the temperature rise at the tip of a fast running crack2

The high energy concentration at the tip of a running crack leads to irreversible deformations, and a great amount of the deformation energy is set free as heat. Assuming that this moving heat source is of circular shape, the temperature distribution around the crack tip has been calculated. The temperatures are dependent on the radius of the heat source and the crack velocity. Some examples for the material glass are given. The very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.     

Some peculiarities of two-phase flow in nozzles

Calculations are conducted for unidimensional two-phase flow in nozzles for a wide range of particle concentrations and dimensions. It is established that there exists a maximum in loss of specific momentum due to a lag in particle velocity and temperature relative to the gas. The results obtained are compared with calculations using linearized theory as well as with experimental data. The agreement between calculation and experiment is noted. Equilibrium flow of a two-phase mixture with solidification of liquid particles is considered. The presence of an anomalous flow region is established, where in the model of an ideal unidimensional equilibrium flow in a nozzle with discharge into a vacuum the presence of two successively located minimum sections is necessary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–57, May–June, 1973.     

Multi-Stage Upscaling: Selection of Suitable Methods

Reservoirs are often composed of an assortment of rock types giving rise to permeability heterogeneities at a variety of length-scales. To predict fluid flow at the full-field scale, it is necessary to be aware of these different types of heterogeneity, to recognise which are likely to have important effects on fluid flow, and to capture them by upscaling. In fact, we may require a series of stages of upscaling to go from small-scales (mm or cm) to a full-field model. When there are two (or more) phases present, we also need to know how these heterogeneities interact with fluid forces (capillary, viscous and gravity). We discuss how these effects may be taken into account by upscaling. This study focusses on the effects of steady-state upscaling for viscous-dominated floods and tests carried out on a range of 2D models are described. Upscaling errors are shown to be reduced slightly by the increase in numerical dispersion at the coarse scale. We select a combination of three different upscaling methods, and apply this approach to a model of a North Sea oil reservoir in a deep marine environment. Six different genetic units (rock types) were identified, including channel sandstone and inter-bedded sandstone and mudstone. These units were modelled using different approaches, depending on the nature of the heterogeneities. Our results show that the importance of small-scale heterogeneity depends on the large-scale distribution of the rock types. Upscaling may not be worthwhile in sparsely distributed genetic units. However, it is important in the dominant rock type, especially if there is good connectivity through the unit between the injector wells (or aquifer) and the producer wells.This revised version was published online in May 2005. In the previous version one of the authors name was missing.