bluuebunny/crossref_metadata_2025_split huggingface dataset:
Instability and Steady-State Coupled Motions in Vibration Isolating Suspensions
Authors: Henry R. F. , Tobias S. A. 
Published: February 2007

When using non-linear spring systems for vibration isolating suspensions, motion initiated in one of the degrees of freedom may cause another degree of freedom to become unstable and commence to vibrate. Subsequently, the two motions become coupled. The paper deals with instability and coupling phenomena observed with a six degree of freedom model suspension. This is done by reducing the system to equivalent two-degree of freedom non-linear systems, and subsequently discussing the various types of solution of these. The equations of motion discussed are of the form It is shown that when the value of the coefficients n and r is n = r = 3·0 then the equations describe the instability and coupling phenomena relating to the vertical motion and the pitching motion of the mass. When n = r = 1·0 then the equations describe the conditions arising between the vertical motion and the yawing motion. The various solutions of these equations are discussed. It is shown that instability in a mode can arise only when the ratio of the linear natural frequencies of the mode initially at rest and the mode initially disturbed lies within certain limits. For n = r = 3·0 the mode with the lower natural frequency may, upon motion having been initiated in the higher mode, become unstable and commence to vibrate. On the other hand, the mode with the lower natural frequency can vibrate on its own since the higher mode remains stable at rest. For n = r = 1·0 the conditions are reversed. Thus, in both systems the coupling is non-symmetrical, but it can be reversed by changing the ratio of the natural frequencies in the appropriate way. The steady-state coupled solutions of the two types of systems are also different. For n = r = 3·0 the steady coupled solution involves a motion in which the degrees of freedom vibrate with equal or opposite phase. For n = r = 1·0 the coupled modes vibrate with a phase difference of ±90°. In both cases the amplitudes of the two degrees of freedom are related, their frequencies are equal and are determined by the amplitudes.
Approximate Theory for the Thermal and Irradiation Creep Buckling of a Uranium Fuel Rod and Its Magnesium Can
Authors: Alexander J. M. 
Published: February 2007

A simplified theory is developed for calculating the creep buckling of a fuel element, including both thermal and irradiation creep of the uranium, and thermal creep of the magnesium alloy can. This is made possible by introducing creep rate moduli for both uranium and can, analogous to Young's Moduli for simple elastic buckling. The relationship between these rate moduli and the fundamental creep equations is discussed in detail and justification given for the proposal that the rate modulus should be defined as the slope of the stress strain-rate curve at the mean stress. The theoretical inter-relation between the results of sagging bar tests and the fundamental creep equation is also discussed. A typical calculation for a highly rated channel is included, and it is shown that the contribution of the can to resisting buckling is quite significant, more than doubling the buckling time for half the elements, and adding about half the buckling time for the remainder. Suggestions for further work are put forward.
Notch Effects and the Critical Alternating Stress Required to Propagate a Crack in an Aluminium Alloy Subject to Fatigue Loading
Authors: Frost N. E. 
Published: February 2007

Fatigue tests at zero mean load have been carried out on aluminium alloy (BS.L65) specimens containing edge cracks of various lengths. It was found that the relationship between the crack length l (inches) and the critical alternating propagation stress σ (ton/in2) was given by σ3 l = 0·2. A similar type of relationship (i.e., σ3 l = 5·5) was obtained previously for mild steel (2). Fatigue tests have also been carried out on notched specimens and the occurrence of non-propagating cracks discussed in terms of the above relationship.
The Creep Buckling of Composite Members
Authors: Alexander J. M. , Webster G. A. 
Published: February 2007

The simplified theory put forward in an earlier paper (***)‡ is extended and generalized to cover the case of the thermal creep buckling of prismatic two-member components such as reactor fuel elements, all phases of creep and elastic strains being considered. The tangent modulus approach is used and small deflections are assumed; it is shown that even with these assumptions a solution in closed form can be obtained only in the case of a single rod. Approximate methods of solution are then discussed, in which primary and secondary creep phases only are considered, but with certain simplifying assumptions. Throughout most of the analysis a modified form of Andrade's creep equation is used, namely ε = α t1/3+β t+γ t3, where α, β, and γ are functions of stress and temperature, ε and t are creep strain and time. Typical curves are presented, based on data for an aluminium alloy, illustrating the contribution to buckling deflection likely to be expected from primary creep, for the single rod.
Plastic Stress–Strain Relations and Yield Surfaces for Aluminium Alloys
Authors: Ivey H. J. 
Published: February 2007

The theoretical study of the behaviour of materials in the ‘plastic’ state has progressed rapidly on the basis of a few assumptions, some of which are insufficiently well supported, and even occasionally contradicted, by available experimental evidence. In the present work three types of experiment are carried out. In the first several different materials are ‘overstrained’ into the plastic region, either by tensile or by shear stresses, and then subjected to additional stresses, shear or tensile respectively, the modulus of resistance to the additional stresses being measured. Similar experiments have been carried out previously but the results are not wholly concordant. The present work indicates that for initially stress-free material the ‘incremental’ type of theory is well founded. An explanation for the behaviour of material in other conditions is suggested which does not involve the existence of ‘corners’ on the ‘yield surface‘overstrained’ into the plastic region, either by tensile or by shear stresses, and then subjected to additional stresses, shear or tensile respectively, the modulus of resistance to the additional stresses being measured. Similar experiments have been carried out previously but the results are not wholly concordant. The present work indicates that for initially stress-free material the ‘incremental’ type of theory is well founded. An explanation for the behaviour of material in other conditions is suggested which does not involve the existence of ‘corners’ on the ‘yield surface’. In the second type of experiment one material is subjected to a complicated ‘stress history’, and the corresponding strains are measured. Certain improvements are made in relation to previous experimental techniques. The results indicate that the Reuss equations, used in conjunction with the Maxwell (or Mises-Hencky) flow function, give a very satisfactory prediction of the behaviour of this material. In the third type of experiment, one material is subjected to varying ‘overstrains’ of a particular type and its subsequent ‘yield stress’ (or, more strictly, limit of proportionality) under different combinations of complex stress determined. The results indicate that in the case of this material the ‘subsequent yield surface’ to a first approximation translates in the direction of the overstrain, but is considerably modified in shape by strain-hardening and by the Bauschinger effect. It remains concave towards the inner (elastic) region but this region does not necessarily contain the stress-free origin.
Stress Distribution on the Boundary of a Circular Hole in a Large Plate during Passage of a Stress Pulse of Short Duration
Authors: Riley W. F. , Durelli A. J. 
Published: February 2007

A solution to the problem of the stress distribution on the boundary of a circular hole in a large plate during passage of a stress pulse of short duration is presented. The solution was experimentally obtained by using a low-modulus urethane rubber model in a combined photoelasticity, moiré, and grid analysis. The stress pulse of short duration was generated by detonating a small charge of lead azide on an edge of the plate. The hole was placed at a location in the plate where both dilatational and distortional waves would be felt. It was also located in such a way that a symmetric point was available in the free field for making free-field stress determinations. The short-duration pulse at the free-field symmetric point had a length of approximately 25 hole diameters; the portion associated with the pulse front (rise from zero to peak) was approximately 5 hole diameters. The results of the study indicate that the stress of greatest magnitude is a compressive stress which develops on the hole boundary as the front of the stress pulse passes the hole. The maximum tensile stress which develops much later is only about half as large. As the end of the stress pulse passes the hole, the tensile and compressive stresses on the hole boundary are essentially equal in magnitude. The isochromatic fringe pattern during this period indicates that the hole is located in a stress field of pure shear. The orientation of the pattern indicates that the stress pulse is primarily a distortional wave at this time. The maximum dynamic compressive stresses on the boundary of the hole can be computed to a first approximation by applying the Kirsch solution for a hole in an infinite plate, considering the biaxial stress field and assuming an average value of stress over the hole diameter. The free-field biaxial stresses as computed from photoelasticity and moiré data were used in making this check. The maximum dynamic tensile stresses on the hole boundary were always smaller than the values computed using the same procedure.
Effect of Oil on the Pitting of Rollers
Authors: Martin J. B. , Cameron A. 
Published: February 2007

The apparatus used in this investigation was an opposed double roller machine with rollers 70 mm diameter loaded against a 30 mm 3 per cent nickel steel shaft rotated at 3000 rev/min. The viscosities of the test oils which were of two types, naphthenic and paraffinic, were between 3 and 530 centistokes. Above about 20 cS the pitting endurance limit increased with the fourth root of the viscosity alone, and was not influenced by the type of oil. The effect of viscosity is thought to be due to the damping of the pressure wave in the crack. This index (1/4) and the critical viscosity (20 cS) are probably dependent on the speed of rolling. The slope of the fatigue line, before the endurance limit, varies with the oil. This has an important bearing on the ‘time to pitting’ method of test. The pitting cracks were shown to be of two sorts, shallow and deep. This is due to there being a band of work-hardened steel at approximately the Hertzian depth. Most cracks did not penetrate this band and gave rise to shallow pits 0·002-0·004 in. deep. Those which did get through it went down at an angle of about 40° to the surface and were 0·020-0·030 in. long, giving pits of greater depth. In Appendix I the equation for the viscous pressure loss in a crack, due to the compressibility of the oil, is derived.
Modes at Rest and Their Stability in Coupled Non-Linear Systems
Authors: Henry R. F. , Tobias S. A. 
Published: February 2007

This paper deals with the stability of modes at rest in free, undamped non-linear two-degree-of-freedom systems governed by equations of motion of the form The conditions necessary for the existence of motion in a single mode are discussed and a criterion for stability of the mode at rest established. The theory is compared with results of tests made on an experimental model. The effect of viscous damping on stability is also examined. The results obtained are applicable to current practical problems in the field of vibration isolation and suppression.
Energy Dissipation at Spherical Surfaces in Contact Transmitting Oscillating Forces
Authors: Johnson K. L. 
Published: February 2007

In a previous experimental investigation the author has shown that two spherical surfaces pressed together and subject to an oscillating tangential force, however small, exhibit microscopic interfacial slip which leads to energy dissipation and surface damage in the manner predicted theoretically by Mindlin. The analysis has been extended by Mindlin and Deresiewicz to include the effect of an oscillating force whose line of action lies at an oblique angle to the surface of contact. They show that the angle of obliquity of the oscillating force has a predominant effect on the energy dissipated at the contact and that no slip or dissipation would be expected if the line of action of the force lies within the cone of friction for the two surfaces. These conclusions have been the subject of the experimental investigation reported in this paper. The theoretical predictions are supported by the observations on almost all counts. Such discrepancies as occur are shown to be due to the inadequacy of the theoretical assumption of a constant coefficient of friction to describe accurately the actual behaviour of metallic surfaces in contact which are undergoing oscillating interfacial slip and fretting whose amplitude varies throughout the contact area.
Synchronous Whirl of a Vertical Shaft Having Clearance in One Bearing
Authors: Johnson D. C. 
Published: February 2007

If a vertical undamped shaft has one clearance bearing, the other bearings having zero clearance and all being in line, then there are two possible regimes of synchronous whirl which can hold, namely: that in which the shaft does not touch the clearance bearing, that in which the shaft touches the clearance bearing continuously, the point of contact running round the bearing at the shaft speed. It is shown that in some speed ranges regime (1) holds and in others (2). There are also speed ranges in which either regime is possible. When damping is allowed for, these results are not greatly modified. The whirling behaviour of the shaft differs however from that of a shaft with zero bearing clearance in several ways. In particular the critical speeds are lower, and also there is a more abrupt drop in the whirl amplitude curve above the critical speeds. The behaviour of the shaft when it is accelerated through a critical can differ from that when it is decelerated.
Measurement of the Drag on Spheres Moving through Gaseous Fluidized Beds
Authors: Daniels T. C. 
Published: February 2007

Certain substances float on the surfaces of gaseous fluidized beds and others sink. This phenomenon has industrial applications in separation by creaming and sedimentation. To help the development of these applications the author measured the drag on metallic spheres falling through various fluidized beds of glass beads and certain granular powders. The meta***llic spheres were attached to a nylon thread which passed over a pulley system. Different balance weights were attached to the other end of the thread to produce different uniform velocities of fall. The friction of the system and the buoyancy of the immersed metallic spheres were predetermined. The drag on the sphere was then the only unknown. It was found that the drag is a function of three dimensionless groups, namely Reynolds number, Froude number and the ratio of the diameter of the metallic spheres to the mean diameter of the glass beads or powders forming the fluidized beds. For spheres above a certain diameter deviation occurred in the measurement of the drag owing to wall effect.
Matrix Techniques for Determination of Fundamental Mode Shape and Frequency Parameter of Torsional Oscillations in Engines
Authors: Gupta K. N. 
Published: February 2007

Matrix techniques for the solution of natural frequencies of a torsional system are proposed for their simplicity and easy manipulation. The tedious calculations in obtaining a dynamic matrix are alleviated by evolving a general expression for dynamic matrix for fundamental mode of a multi-degrees of freedom straight torsional system. Further, the dynamic matrices for engine systems having four to eight cylinders with equal moments of inertia per cylinder line and equal shaft stiffnesses between the cylinder centres are deduced from a general expression. They are iterated upon five times to obtain expressions for the fundamental frequency parameter, which are further used to obtain the relative amplitudes and the frequency parameter of different engine systems. The results obtained by five times iteration are in close agreement with the exact values.
Tensile Instability in Thin-Walled Tubes
Authors: Mellor P. B. 
Published: February 2007

An analytical solution giving conditions at instability of a thin-walled tube subjected to internal pressure and independent axial load is presented. An attempt is made to explain the physical reasons for the occurrence of an instability. The analysis shows that a given material has greatest ductility when the ratio of the hoop stress to axial stress has the value one half. The material has least ductility when it is in the form of a closed-ended tube subjected to internal pressure. The terms ‘tensile strength’ and ‘percentage elongation’ are discussed within the framework of the present investigation.
Calculation of Rolling Load and Torque in the Hot Planetary Rolling Mill
Authors: Sparling L. G. M. 
Published: February 2007

This paper presents a completely new approach to the mechanics of the Sendzimir hot planetary rolling mill. Previous work on this subject, by R. Tovini, included determinations for the distribution of the advance of the strip, the draft, the rolling load, the torque and the horizontal backthrust for the whole range of positions which the planetary rolls made, whilst contacting the hot metal. The new approach differs vastly from that of Tovini, the main four differences being as follows. First, whereas the method of Tovini is based upon the forward displacement of surface metal, as a ripple, along the surface of a rigid core which extends in the central portion of the metal for the full length of the working arc, the new approach assumes that the plastic zones between the planetary rolls extend from each roll to the centre of the material. The effect of this assumption is that the local deformation due to a pair of planetary rolls can be considered as an extension which is effectively uniform throughout the thickness of the strip which is instantaneously between the planetary rolls. Secondly, the method used by Tovini is one of successive approximations to obtain values for the advance of the strip, whereas the new method finds a close approximation for the advance of the strip by direct analysis. Thirdly, Tovini neglects the friction hill in roll load and torque calculations and uses the mean strain rate for the equivalent simple roll in order to calculate the mean yield stress, whereas the new method defines and uses both local and overall mean strain rates, these being necessary to obtain a realistic value for the resistance to deformation. Fourthly, in Part 1 of Tovini's paper, intermittent advance of the strip was assumed, whereas in the present method uniform entry speed is assumed and it is then shown how the results for any distribution of entry speed can be obtained by superposition. (In Part 2 of Tovini's paper continuous advance of the slab is briefly considered but, the process is not analysed in detail.) Appendix I shows a method of tabular calculation, which gives results for the distribution of roll separating force, torque and backthrust for the whole range of angular positions during which a pair of planetary rolls contact the strip or slab. From these results the back-up roll separating force, the horizontal backthrust and the horsepower for the process can be derived.
Experimental Study of the Flexibility of a Full-Scale Two-Dimensional Steam Pipeline
Authors: Smith R. T. , Ford Hugh 
Published: February 2007

This paper describes tests made to check the reliability of the calculation methods used to predict the flexibility, forces, and stresses in a typical pipework system. A test rig set up in the laboratory has been used to carry out tests on a full-scale pipeline of 6 1/2-in. nominal bore pipe for 450 lb/in2 working pressure and 750°F steam temperature with two right-angle bends. Tests at room temperature have been made with controlled anchor movements corresponding to those which would occur on cold pull-up, thermal expansion, or pure bending, all without internal pressure. In addition tests have been made with internal pressure only, and with internal pressure combined with controlled anchor movements. Further tests were carried out by heating the pipeline and measuring the increase of the forces at the restrained anchors, but no strain measurements were made at high temperatures. The results show that the calculation methods are sufficiently reliable for predicting the forces and stresses in such a pipeline, having regard to the allowable tolerances on pipe dimensions.
Investigation of the Behaviour of a Four-Stand Tandem Mill, Using an Electronic Analogue
Authors: Sekulic M. R. , Alexander J. M. 
Published: February 2007

A study is made of systems based on screw-setting and tension control, and the behaviour of a four-stand tandem mill when subjected to small disturbances from the steady state is investigated by using an electronic simulator. Screw-setting control and control of tension through control of roll speed are the practical variables which can be used in the automation of a tandem mill and a possible closed loop system of control is discussed.
Vortex Excited Vibration of a Heat Exchanger Tube Row
Authors: Livesey J. L. , Dye R. C. F. 
Published: February 2007

The results are presented of an experimental investigation into the possible modes of gas-excited vibration of a single row of tubes in a heat exchanger at typical practical spacings. The vibrations discussed are vortex excited and, for damping which permits large amplitudes, occur at values of the Strouhal number 0·26 < ND/V < 0·89. The critical range of ND/V is affected by both Reynolds number and spacing. Four distinct modes of vibration are found, all consisting of motion principally transverse to the flow direction. Preliminary studies of pairs of tubes, at varying spacing, indicate similarly large ranges of the parameter ND/V in which vibration will occur at typical practical spacings. The types of vibration described are distinct from, and should not be confused with, either the acoustically coupled type or the equally important modes, in which the motion is principally streamwise, occurring at much lower values of ND/V.
Stiffness of Broad-Faced Gasketted Flanged Joints
Authors: Kenny B. , Moore G. G. , Duncan J. P. 
Published: February 2007

The mechanism by which broad-faced flanged joints retaining a circular plate exert restraint against the flexure of the plate due to pressure differentials is discussed and studied experimentally. The theory proposed by Yi-Yuan Yu for determining the stiffness of an ungasketted joint is reconsidered and modified to suit the observed behaviour of metal-to-metal joints and of joints where one or more gaskets are included between mating surfaces of the joint assembly. Hence, a more exact method for calculating stiffness factors for such joint assemblies is formulated. Experiments were conducted on a particular design of header to tube-plate assembly and the results used to check the validity of the modified theory.