Numerical stability analysis and control of umbilical–ROV systems in one-degree-of-freedom taut–slack condition

In this paper, the stability of an umbilical–ROV system under nonlinear oscillations in heave motion is analyzed using numerical methods for the uncontrolled and controlled cases comparatively. Mainly the appearance of the so-called taut–slack phenomenon on the umbilical cable produced by interactions of monochromatic waves and an operated ROV is specially focused. Nonlinear elements were considered as nonlinear drag damping, bilinear restoring force and saturation of the actuators. Free-of-taut/slack stability regions are investigated in a space of physical bifurcation parameters involving a set of both operation and design parameters. They indicate a wide diversity in qualitative behaviors, both in the periodicity and possible routes to chaos from the stability regions to outside. For detection of periodicity of the nonlinear oscillations inside and outside the stability regions, a method based on Cauchy series is developed. The first part of the results is dedicated to the stability of the uncontrolled dynamics. These results suggest the design of a control system that is able to counteract hefty hauls of the cable during the sinking/lifting operation under perturbation. A combination of a force and cinematic controller based on nonlinear model–reference control is proposed. Through a comparative study of the stability regions for uncontrolled and controlled dynamics, it is shown that the control system can extend considerably these regions without appearance of the taut–slack phenomenon despite the presence of wave perturbations. The limits between the taut and taut–slack zones are defined by the wave steepness and the available energy of the actuators.     

Micromechanics modeling of strength for nanocrystalline copper

We present a model in this paper for predicting the inverse Hall–Petch phenomenon in nanocrystalline (NC) materials which are assumed to consist of two phases: grain phase of spherical or spheroidal shapes and grain boundary phase. The deformation of the grain phase has an elasto-viscoplastic behavior, which includes dislocation glide mechanism, Coble creep and Nabarro–Herring creep. However the deformation of grain boundary phase is assumed to be the mechanism of grain boundary diffusion. A Hill self-consistent method is used to describe the behavior of nanocrystalline pure copper subjected to uniaxial tension. Finally, the effects of grain size and its distribution, grain shape and strain rate on the yield strength and stress–strain curve of the pure copper are investigated. The obtained results are compared with relevant experimental data in the literature.     

“Simple” solutions of the equations of dynamics for a polytropic gas

The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999.     

Polymeric liquids in extension: fluid mechanics or rheometry?

We use a transient 3D free surface finite element method to simulate flow of entangled polymer fluids in the dual cylinder wind-up extensional rheometer. The constitutive equations are K-BKZ integral representations of the Doi–Edwards models with and without the independent alignment approximation (IA). It is demonstrated that the actual kinematics in this rheometer is a mixture of planar and uniaxial extension. Moreover, the ratio of planar to uniaxial deformation is highly dependent upon whether IA is invoked. Without IA, the flow has a tendency toward planar extension, while it tends to be more uniaxial with IA invoked. As a second illustration of the techniques, we simulate the phenomenon of delayed rupture after rapid extension of entangled polymer systems. It is demonstrated that this phenomenon can be explained on the basis of the Doi–Edwards model in terms of a Considere-type instability after chain stretch relaxation.     

Rebounding of a shaped-charge jet

The phenomenon of rebounding of a shaped-charge jet from the armour surface with small angles between the jet axis and the target surface is considered. Rebounding angles as a function of jet velocity are obtained in experiments for a copper shaped-charge jet. An engineering calculation technique is developed. The results calculated with the use of this technique are in reasonable agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 17–20, September–October, 2007.     

Vortex Rings in Fast Rotating Bose–Einstein Condensates

When Bose–Einstein condensates are rotated sufficiently fast, a giant vortex phase appears, that is, the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper (Correggi et al. in Commun Math Phys 303:451–308, 2011) we have studied this phenomenon by minimizing the two-dimensional Gross–Pitaevskii (GP) energy on the unit disc. In particular, we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold, there are vortices in the condensate. We prove that they gather along a particular circle on which they are uniformly distributed. This is done by providing new upper and lower bounds to the GP energy.     

Numerical studies of transportation of granular material by a pin-point blast using models of the mechanics of continuous and granular media

Mathematical models for numerical studies of transportation of a mass of loose granular material during occurrence of a series of deep gas-dynamic ejections are developed using methods of the mechanics of continuous and granular media. Features of the kinematics and dynamics of development of this phenomenon are analyzed. Results of a numerical experiment and recommendations on use of the models in studies of specific transportation regimes are given. Mozhaisk Military Space-Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 3–14, January–February, 1998.     

Effect of deformation and external load on the characteristics of martensite transformations and shape-memory effects in alloys based on titanium nickelide

The effect of plastic deformation and external load on the characteristics of shape-memory effects is studied for alloys based on titanium nickelide of nearly equiatomic composition. A nonmonotonic dependence of the characteristic temperatures of martensite transformations on the strain degree of deformation is obtained. This phenomenon is explained in relation to the stages of development of plastic deformation. Optimal loading and deformation conditions for obtaining maximum values of reversible deformation are determined. Russian Medical-Engineering Center, Tomsk 634034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 175–181, March–April, 1998.     

Measurement of He II evaporation induced by impingement of a thermal pulse on a He II–vapor interface

The transient evaporation phenomenon in a pure superfluid helium (He II)–vapor system was experimentally studied. Evaporation is caused by the impingement of a second sound thermal pulse onto a He II–vapor interface. The resulting gas dynamic phenomena are visualized with the aid of a laser holographic interferometer, and are also measured with a pressure transducer and a superconductive temperature sensor. It is clearly seen in the interferograms that a clear shock wave is formed at the front of an evaporation wave. We obtained the condensation coefficient of He II as being 0.70 ± 0.05 in the temperature range between 2.04 K and 1.74 K by the comparison of the experimental data with the kinetic theory results. Received: 24 June 1999/Accepted: 28 March 2000     

Atmospheric pressure waves in the field of volcanology

Atmospheric pressure waves are a notable phenomenon associated with explosive volcanic eruptions. They can provide us with information about eruption processes that are useful both scientifically and practically. In this paper, we give a brief review of studies that have been carried out on this phenomenon in the field of volcanology. Then, we introduce a prototype tool called ‘MOVE’ (Mobile Observatory for Volcanic Explosions). It is a remote-controlled vehicle carrying various instruments to observe pressure waves and the eruption processes. PACS 91.40.Dr · 91.40.Ft · 93.65.+e · 93.85.+qThis paper was based on work presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan on March 1–3, 2005.     

Buckling of elastic composite rings under internal impulsive loading

The experimentally detected phenomenon of compression fracture of a composite ring made of unidirectional fiberglass plastic under initial internal impulsive (explosive) loading is analyzed. Fracture results from bending in the compression phase because of loss of stability of the radial axisymmetric mode of motion. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 185–194, September–October, 1999.     

Nonlinear Normal Modes and Their Bifurcations for an Inertially Coupled Nonlinear Conservative System

This work concerns the nonlinear normal modes (NNMs) of a 2 degree-of-freedom autonomous conservative spring–mass–pendulum system, a system that exhibits inertial coupling between the two generalized coordinates and quadratic (even) nonlinearities. Several general methods introduced in the literature to calculate the NNMs of conservative systems are reviewed, and then applied to the spring–mass–pendulum system. These include the invariant manifold method, the multiple scales method, the asymptotic perturbation method and the method of harmonic balance. Then, an efficient numerical methodology is developed to calculate the exact NNMs, and this method is further used to analyze and follow the bifurcations of the NNMs as a function of linear frequency ratio p and total energy h. The bifurcations in NNMs, when near 1:2 and 1:1 resonances arise in the two linear modes, is investigated by perturbation techniques and the results are compared with those predicted by the exact numerical solutions. By using the method of multiple time scales (MTS), not only the bifurcation diagrams but also the low energy global dynamics of the system is obtained. The numerical method gives reliable results for the high-energy case. These bifurcation analyses provide a significant glimpse into the complex dynamics of the system. It is shown that when the total energy is sufficiently high, varying p, the ratio of the spring and the pendulum linear frequencies, results in the system undergoing an order–chaos–order sequence. This phenomenon is also presented and discussed.     

Theory of the shimmy phenomenon

The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1–6]. This problem is most serious for the aircraft fore wheels.     

On plane self-excited vibrations of a cantilever suspended wheel

Torsional vibrations of a wheel about its leg axis arising in the carriage rectilinear motion were dubbed the shimmy phenomenon. Because of insufficient understanding of dry friction laws in the case of point contact, the causes of the shimmy phenomenon were explained by specific features of tyre deformation [1–3].     

Stability of a vertical high-concentration fine suspension flow

The neutral stability conditions are found with allowance for the effects associated with the disappearance of the particle free volume on transition to the close-packed state and the characteristics of the disturbances with the maximum growth rate are investigated on the interval of intermediate and high particle concentrations. Results relating to the effect of quasi-viscous stresses and Brownian motion on flow stabilization on this concentration interval are obtained. The stability of a bounded uniform vertical flow of not too small particles is investigated and the well-known scale effect, associated with the phenomenon of increasing instability on transition from laboratory to geometrically similar industrial apparatus, is examined. Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 87–96, July–August, 1994.     

Unsteady nonlinear problem of the horizontal motion of a contour under the interface between two liquids

A method of solving the initial boundary-value problem of the horizontal motion of a circular cylinder under the interface between two liquids is developed within the framework of nonlinear theory and implemented numerically. Profiles of generated waves and hydrodynamic loads are calculated for the problem of the acceleration of a circular cylinder under the free surface of a heavy liquid. The phenomenon of wave breaking is considered in detail. Omsk Department, Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 37–43, May–June, 1999.     

Jets of incipient liquids

Jets of incipient water escaping into the atmosphere through a short channel are photographed. In some experiments. complete disintegration of the jet is observed. The relationship of this phenomenon with intense volume incipience is considered. The role of the Coanda effect upon complete opening of the jet is revealed. Measurement results of the recoil force R of the jets of incipient liquids are presented. Cases of negative thrust caused by the Coanda effect are noted. Generalization of experimental data is proposed. Institute of Thermal Physics, Ural Division, Russian Academy of Sciences, Ekaterinburg 620219. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41. No. 3, pp. 125–132, May–June, 2000     

The rheological characterisation of bread dough using capillary rheometry

An Australian hard wheat flour–water dough has been characterised using parallel plate and capillary rheometers over an extensive range of apparent shear rates (10^− 3–10³ s^− 1) relevant to process conditions. Torsional measurements showed that the shear viscosity of the dough increased with strain to a maximum value and then decreased, suggesting a breakdown of the dough structure. Both torsional and capillary experiments revealed the shear-thinning behaviour of the dough. The wall slip phenomenon in capillary rheometry was investigated and found to be diameter dependent and occurred at a critical shear stress of approximately 5–10 kPa. A two-regime power law behaviour was observed, with the power law index approximately 0.3 in the low shear rate range increasing to 0.67 in the high shear rate range. Pressure fluctuation was observed in the capillary data and increased with shear rate, in particular, at shear rates approaching 10⁴ s^− 1. The results demonstrate that capillary rheometry is a viable means of rheologically testing dough at high shear rates provided pressure fluctuation is carefully monitored and capillary rheometry corrections, including wall slip, are accounted for.