Asymptotic approximations for vibrational modes of helices

The free vibrations in the plane normal to the helical axis are studied under the assumption that the helical pitch is small. Asymptotic approximations for eigenvalues and eigenfunctions are derived for both small and large numbers of helical turns. The analytic approximations reveal interesting features of helix vibrations and the connection between the vibrational modes of a helix and the flexural modes of a curved beam. Comparison with numerical calculations shows that the approximations derived cover with sufficient accuracy a wide range of number of helical turns

Web lateral dynamics with buckling in sheet metal rolling

The stability of web lateral motion is of importance in many engineering applications where the deviation of the web from the processing direction is highly undesirable and can cause various defects. This is especially true for sheet metal rolling, where sudden lateral deviations of the web from the rolling direction, known as strip track-off, is a serious operational problem that can lead to catastrophic consequences, such as mill crashes and damaged rolls.The early studies of strip track-off in metal rolling showed that neither the magnitude of lateral deviations nor the catastrophic track-off observed in practice can be explained by the model of strip deformation in the span based on beam theory, common in the web handling literature. It has been suggested that strip buckling may play an important role in strip track-off phenomenon. In addition, it has also been observed in web handling literature (1,2] that the model predictions based on conventional beam bending analysis do not agree with observed web lateral motion in the situations when buckling of the web is present.This paper presents a discussion of the recent studies of the effect of strip buckling on strip lateral dynamics in metal rolling. The analysis is based on the model of strip plastic deformation in the mill and a simplified physically based strip buckling model suggested by Benson [l]. Introduction of budding changes the nature of the strip lateral motion, which becomes unstable once a critical level of asymmetry in rolling conditions is exceeded.In metal rolling, the longitudinal residual stresses in the strip are usually present due to non-uniform plastic reduction. In this paper, an extension of the Benson's buckling model to include the effect of residual stress is proposed. The numerical analysis of the extended model suggests that the web with the tensile residual stress at the edges and compressive stress in the middle is less susceptible to instability compared to the web with compressive residual stresses at the edges and the case without residual stress

Numerical analysis of lateral movement of a metal strip during cold rolling

A model and numerical algorithm for the analysis of lateral movement of a metal strip during cold rolling are presented. The model includes a simplified description of the physical processes responsible for strip lateral movement, such as plastic deformation of the strip, elastic deformation of rolls, deformation and dynamics of the strip outside the plastic reduction region. The study is motivated by the operational problem experienced in the metal rolling industry. Numerical simulations reveal possible mechanisms of strip track-off and identify issues inviting further study

On adoption of new technology under uncertainty

7 page(s

Efficient algorithms of pathwise dynamic programming for decision optimization in mining operations

© 2018 Springer Science+Business Media, LLC, part of Springer Nature Complexity and uncertainty associated with commodity resource valuation and extraction requires stochastic control methods suitable for high dimensional states. Recent progress in duality and trajectory-wise techniques has introduced a variety of fresh ideas to this field with surprising results. This paper presents a concept which implements this promising development and illustrates it on a selection of traditional commodity extraction problems. We describe efficient algorithms for obtaining approximate solutions along with a diagnostic technique, which provides a quantitative measure for solution performance in terms of the distance between the approximate and the optimal control policy. All quantitative tools are efficiently implemented and are publicly available within a user friendly package in the statistical language R, which can help practitioners in a broad range of decision optimization problems

Wave Propagation on Helices and Hyperhelices: A Fractal Regression

A hyperhelix of order N is defined to be a self-similar object consisting of a thin elastic rod wound into a helix, which is itself wound into a larger helix, until this process has been repeated N times. Wave propagation on such a structure can be discussed in a hierarchical manner, ultimately in terms of the wavenumber κ defining propagation on the elementary rod. It is found that the dispersion curve expressing the wave frequency ω as a function of the elementary wavenumber κ on the rod making up the initial helix is also a fractal object, with all the macroscopically observable wave phenomena for a hyperhelix of arbitrarily large order being compressed into a small wavenumber range of width about 2R2-1α centred on the value κ = R1-1, where R1 is the radius, α is the helical pitch angle of the smallest helix in the progression, and R2 is the radius of the next-larger helix

A comparison of adaptive management and real options approaches for environmental decisions under uncertainty

Two approaches to sequential decisions under uncertainty in the environmental management adaptive management and real options analysis -have evolved independently over the last decades

A comparison of adaptive management and real options approaches for environmental decisions under uncertainty

Two approaches to sequential decisions under uncertainty in the environmental management - adaptive management and real options analysis – have evolved independently over the last decades. Adaptive management, or learning by doing, originated from adaptive control. Adaptive management is acknowledged as one of the best-practice methods to manage biological systems under structural uncertainty. Adaptive management has been used for the management of renewable natural resources (such as fisheries and waterfowl) and the conservation of species (such as assisted colonization, restoration and threatened species management). In this context, stochastic dynamic models and historical data would be valuable for describing and predicting responses of management decisions, but these are either non-existent or severely limited in their scope. Real options analysis originated from mathematical finance and is based on financial options pricing theory. The real options analysis can be viewed as both sequential decision-making and project valuation in a highly uncertain environment with non-stationary dynamics. Real options analysis has most often been used for industrial applications (such as mining, asset management, infrastructure, energy, defence, and agriculture). In this context, reasonably good stochastic dynamic models and historical data exist for describing and forecasting the behaviour of risk factors. In mathematical terms, both adaptive management and real options approaches are based on stochastic optimal control and Markov decision processes. In environmental decision-making both enable practitioners and managers to make optimal decisions under uncertainty. However, the numerical methods of solving adaptive management versus real options problems are different, as their development has been motivated by the different needs of respective application areas. An important feature of adaptive management is the presence of and need to account for a small number of hidden variables. In contrast, real options focus on the development of techniques capable of dealing with high-dimensional problems with multiple stochastic risk factors. Limited for a long time by the inefficiency of the solution methods, recent advances in both adaptive management and real options now allow us to solve more realistic environmental decision problems under uncertainty, widening the scope of their applications. Growing availability of data in the environmental management arena and an emerging need to conduct industrial operations in the proximity of conservation areas will require new decision-making approaches that can combine recent advances in adaptive management and real options. This paper reviews recent advances in both adaptive management and real options methodologies, and compares methods for solving decisions under uncertainty problems based on the type of uncertainty they are addressing, the type of decision-making approach, important assumptions, and the size of the problems they are capable of dealing with. This paper proposes new areas of development that could inspire future research and better-informed environmental decisions under uncertainty

Asymptotic Analysis of The Free In-Plane Vibrations of Beams With Arbitrarily Varying Curvature And Cross-Section

An asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross!section[ The effect of splitting the asymptotic limit for eigenvalues into two families is revealed and its connection with boundary conditions is discussed[ The analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams[ The asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are dif_cult to analyse by other means[ The asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature[ An experimental veri_cation of the asymptotic behaviour of mode frequencies is presente