The geometrical stability of non-linear normal modes in two degree of freedom systems

The geometrical stability of the non-linear normal mode vibrations of a class of two degree of freedom dynamical systems is studied by utilizing the definitions and analysis of Synge's “Geometry of Dynamics.”It is shown that instabilities can occur for small amplitudes of vibration only if (a) one of the associated linear normal modes possesses a frequency which is nearly a multiple of the frequency of the other linear normal mode, or (b) the frequency of one linear normal mode is nearly zero.     

Evaluation of thermophysical characteristics on shape-stabilized paraffin as a solid-liquid phase change material

This report deals with thermophysical properties and measuring methods of shape-stabilized paraffin as a new type of latent heat storage material, which keeps the same shape in a solid state when the paraffin melts. Therefore, this type paraffin can be used in a latent heat storage system without encapsulation. A transient hot wire method, a differential scanning calorimeter (DSC), a water calorimeter and a volume expansion meter, which were developed in the present study, were used to measure effective thermal conductivity, latent heat, specific heat and density of the shape-stabilized paraffin, respectively. From the obtained data, useful correlation equations of the above-mentioned thermophysical properties of the shape-stabilized paraffin were expressed as functions of physical property and mass fraction of each constituent of the shape-stabilized paraffin.     

Free convection from horizontal screened plates

Experimental investigations of laminar free convection from horizontal isothermal surfaces screened by cylindrical vertical walls are presented. Screen diameters (D) were equal to the diameter of a heating plate while their heights (H) were varied. Results obtained for several heating fluxes and two different liquids indicate that depending on the (H/D) ratio of cylindrical screens, the heat flux transferred from the heating plate to the liquid varies. Three subranges of screening effect have been distinguished: primary inhibition, intensification and secondary inhibition. For primary inhibition, a theoretical model has been proposed and critical ratio of (H/D) has been predicted. The results of flow visualization are also discussed.

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Freie Konvektion von horizontalen, seitlich abgeschirmten Platten

Zusammenfassung Es werden experimentelle Untersuchungen der laminaren freien Konvektion an horizontalen, isothermen Flächen mit vertikalen zylindrischen Abschirmflächen beschrieben. Die Schirmdurchmesser (D) waren gleich dem einer Heizplatte, während die Schirmhöhen (H) variiert wurden. Die Resultate, welche für mehrere Wärmeflüsse und mit zwei verschiedenen Flüssigkeiten gewonnen wurden, zeigen, daß — abhängig von VerhältnisH/D der zylindrischen Schirme — der von der Heizplatte an das Fluid übergehende Wärmestrom stark variiert. Drei Bereiche konnten bezüglich des Abschirmeffektes unterschieden werden: erste Hemmung, Verstärkung und zweite Hemmung. Für den Fall der ersten Hemmung wird ein theoretisches Modell vorgeschlagen und das kritischeH/D-Verhältnis vorausberechnet. Abschließend erfolgt die Diskussion von Ergebnissen, welche aus der sichtbaren Darstellung des Strömungsfeldes gewonnen wurde.

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Nomenclature a thermal diffusivity [m²/s] - D external diameter of the plate, internal diameter of screens [m] - g gravitational acceleration [m/s²] - H height of screen [m] - Nu= D/ Nusselt number - Nu _(H/D)=0 Nusselt number for plate without screens - Nu _H/D Nusselt number for plate with screen of heightH - Ra=g (T _w1–T _F)D ³/( a) Rayleigh number - Ra _H=g (T _w–T _w1)H ³/( a) Rayleigh number inside screen - q heat flux density [W/m²] - T _w surface temperature of the heating plate [°C] - T _w1 boundary temperature of the motionless liquid [°C] - T _F bulk temperature of the liquid [°C] - heat transfer coefficient [W/(m²·K)] - coefficient of volumetric expansion [1/K] - kinematic viscosity - thermal conductivity [W/(m·K)]     

The evolution of initially uniform shear flow through a nearly two-dimensional 90° curved duct

An experimental study has been made in a nearly two-dimensional 90° curved duct to investigate the effects of interaction between streamline curvature and mean strain on the evolution of turbulence. The initial uniform shear at the entrance to the curved duct was varied by an upstream shear generator to produce five different shear conditions; a uniform flow (UF), a positive weak shear (PW), a positive strong shear (PS), a negative weak shear (NW) and a negative strong shear (NS). The variations of surface pressure and the mean velocity profiles along the downstream direction under different initial shears are carefully measured. The responses of turbulent Reynolds stresses and triple velocity products to the curvature and the mean strain are also investigated. The evolution of turbulence under the curvature with the different shear conditions is described in terms of the turbulent kinetic energy and the various length scales vs the angular distance θ or a curvature parameters S _c which is defined by S _c = (U/R)/(dU/dy- U/R). The results show that the turbulent kinetic energy and the integral length scale are augmented when S _c < 0.054 whereas they are suppressed when S _c > 0.054. It is also observed that the micro-length scales of Taylor and Kolmogoroff are relatively insensitive to the curvature.     

On using non-Gaussian distributions to perform statistical linearization

In statistical linearization non-linear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure. The recipes require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response. Because the exact non-linear response distribution is unknown it has become traditional to use a Gaussian distribution as an approximation to the exact distribution. With the modern computing tools now available it is easy to use non-Gaussian distributions which can provide better approximations in cases where Gaussian distributions are not appropriate. Examples are displayed for power-law oscillators with stiffening and softening springs, and for the Duffing oscillator, and for a double-well oscillator. Two families of probability distributions with varying shape are studied.     

Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians

We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables.     

Cloud dispersion models

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows. An initial distribution of material is discretised into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by Kinematic Simulation or by a stochastic model for the motion of each cloud centroid. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by Kinematic Simulation. The ensemble of discrete clouds is periodically rediscretised, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow and in a coastal flow, and the results are compared with analytic, steady state solutions where available.     

Liquid-structure-foundation interaction of slender water towers

Summary The dynamic behaviour of a slender water tower based on a (deep) foundation is studied by a lumped model in which the parameters have been derived analytically from continuous models. The effects of the liquid and foundation on the structural dynamics can be studied analytically using this model, sensitivity analyses are easily performed. Ring baffles in the liquid tank and the local yielding of the pile-soil interaction along the shaft of the foundation piles may reduce the dynamic response.

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Wechselwirkung von Flüssigkeitsfüllung, Bauwerk und Fundament von schlanken Wassertürmen

Übersicht Das dynamische Verhalten eines auf ein tiefes Fundament gegründeten schlanken Wasserturms wird anhand eines diskreten Modells analysiert, in dem die Parameter analytisch aus kontinuierlichen Modellen hergeleitet wurden. Mit Hilfe des Modells kann der Einfluß des Wassers und des Fundamentes auf das dynamische Konstruktionsverhalten analytisch studiert werden. Empfindlichkeitsanalysen lassen sich somit leicht durchführen.Zwischenringe im Flüssigkeitsbehälter und lokales Fließen in den Kontaktflächen zwischen Gründungspfählen und Boden können die Strukturschwingungen mindern.

     

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E, the skin-friction at the plate decreases with increase in the permeability parameter K₁. However for the same value or Pr and E, the heat transfer rate at the plate increases with increasing K₁. The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K₁ with Pr = 0.73. It is also shown that for fixed values of K₁, and KPr, the skin-friction increases with increase in the dissipation parameter E.     

Strain-gage-stability measurements for years at 75°C in air

The authors have evaluated the performance of three types of metal-foil strain gages for two and a half years at a constant temperature of 75°C in air. The studies included polyimide-backed and phenolic-glass-backed gages with copper-nickel foil (constantan) and glass-fiber-rein-forced epoxy-phenolic-resin-backed gages with nickel-chromium foil (modified Karma). All gages were tested in a three-wire-lead, single-active-gage Wheatstone bridge system at nominal mechanical-strain levels of 0, +1000 and ?1000 μm/m. The polyimide-backed constantan gages used in Installation No. 1 typically zero-shifted more than +200 μm/m after 30 days' testing at 75°C. The phenolic-glass-backed constantan gages used in Installation No. 2 zero-shifted ?40 to +20 μm/m after 30 days and +270 to +350 μm/m after 900 days. The glass-fiber-reinforced, epoxyphenolic-resin-backed Karma gages used in Installation No. 3 zero-shifted about +5 μm/m after 30 days, and +20 to +45 μm/m after 900 days. The Karma gages used in Installation No. 3 performed better than the other two types of gages. The measured results for the Karma gages appeared to be independent of the adhesives, test-part material, and mechanical-strain levels that we tested. The high stability and low zero drifts of this gage at 75°C allowed us to reliably correct the measured static-strain data on actual test parts.