A.A.F. van de Ven

Magnetoelastic buckling of a beam of elliptic cross-section

SummaryThe magnetoelastic buckling of a soft ferromagnetic elastic cantilever of elliptic crosssection due to a transverse magnetic field is discussed. The magnetic fields referring to the deflected beam are determined analytically by means of Mathieu functions. These fields are used in the derivation of the buckling value for a slender cantilever. It turns out that this value not only depends upon the thickness-to-length ratio of the beam, but also upon the shape of the cross-section. A comparison with results known from the literature is given for two limiting cases, viz. the circular cross-section and the very wide (and thin) one. In the first case complete agreement is observed; for the second case an essential improvement of the usual approach (based upon the assumption of an infinitely wide cross-section) is attained.

Magnetoelastic buckling of magnetically saturated bodies

SummaryThe buckling of magnetically saturated elastic bodies in an external magnetic field is discussed. A linearized version of the general nonlinear equations for the magnetoelastic interactions in magnetically saturated bodies is presented, from which a buckling criterion is derived. This criterion is applied in two examples, viz. a thin plate and a circular rod. Results obtained are compared with those for soft ferromagnetic bodies, as known in the literature. It turns out that, although the descriptions are essentially different, the final results for the saturation model and for the soft magnetic model are in good correspondence with one another.

Instabilities in the extrusion of polymers due to spurt

The manufacturing of plastic products from polymeric melts is one of the main processes in chemical industry. Examples are the blowing of thin films, the extrusion of fibres or the injection moulding of disc-shaped products. Sometimes peculiar, and often unpleasant, effects occur during these manufacturing processes. Generally, these effects show up when the rate of production is raised. Hence, it is of capital importance for the efficiency of the process to know when these effects appear and how they can be avoided. For this, it is necessary to discover what causes this effect and, therefore, to find a theoretical explanation for it is of great practical value in polymer processing.

Magnetoelastic stability of a superconducting ring in its own field

SummaryThe stability of the flexural vibrations of a superconducting ring in its own magnetic field is investigated. This problem is formulated as a perturbation problem: the final magnetic fields due to the deflected ring are considered as perturbations of the rigid-body fields. Both the rigid-body problem and the linearized perturbed prolem are solved analytically. These solutions are expressed in Legendre functions. A so-called ring equation for the in-plane flexural vibrations of the slender ring is constructed. From this equation a frequency-current dispersion relation is derived. It turns out that the ring is stable against in-plane vibrations and that the cigenfrequency increases with increasing current.

Analysis of resonant behavior in planar line arrays of rings by the eigencurrent approach

Resonant behavior in a finite array that appears as (modulated) impedance or current-amplitude oscillations may limit its bandwidth substantially. Therefore, simulations should predict such behavior. Recently, a new approach has been developed, called the eigencurrent approach, which can predict resonant behavior in finite arrays. Analysis of line arrays of II-plane oriented microstrip rings by the eigencurrent approach reveals that resonant behavior is caused by excitation of one of the eigencurrents. The characteristic impedance of this eigencurrent becomes small in comparison to the characteristic impedances of the other eigencurrents that can exist on the array geometry.

Thermally Induced Flow Front Instabilities in Injection Moulding

The temperature distribution of a polymer melt, injected between two, cooled, plates is calculated. For this, the two-dimensional region occupied by the melt is divided into a part (G I ) far behind the flow front and a part (G II ) near the flow front. The melt is modelled as a Newtonian fluid. The temperature is governed by a diffusion-convection equation with appropriate boundary conditions. Asymptotic expansions, based on the small value of the dimensionless thermal conductivity are used. Both in G I and G II , boundary layers exist near the cooled walls.

Spurt in the extrusion of polymeric melts : discrete models for relaxation oscillations

In the extrusion of polymer melts, several types of flow in stability can occur. One example of this is spurt. Spurt is manifested by periodic oscillations in the pressure and volumetric flow rate. These oscillations are of relaxation type. An extrusion through a cylindrical die is considered. A discrete model to describe spurt or relaxation oscillations is constructed. This model is based on observations from three-dimensional theory. When spurt occurs, the shear rates very near the wall of the die (i.e., in the spurt layer) are much higher than those in the kernel of the extruded polymeric melt. Therefore, the viscosity in the spurt layer is taken much smaller than in the kernel. In both regions a linear Newtonian fluid model is used.A no-slip boundary condition at the wall is maintained. The model developed here is compared to an analogous model, allowing for slip at the wall of the die. It is shown that corresponding results can be obtained from both models. Application of the model to a piston-driven extrusion flow shows the occurrence of spurt oscillations for a restricted range of prescribed inlet flow rates. The found oscillations are qualitatively in correspondence with experimental results.

Modelling and DEM simulations of toner behaviour in a print process

This paper describes the modelling of the toner behaviour in the development nip of the Oce Direct Imaging print process. The dynamic motion of and mechanical interactions between toner particles are explicitly modelled. The mechanical interactions are due to collisions, friction, adhesion, and electromagnetic forces. The discrete element method (DEM) is used as the simulation tool for a quantitative description of the system. The interaction rules are determined for the toner particles and the surfaces of the development rollers. The model is validated with print quality results. It is shown that it is possible to achieve quantitative agreement between DEM simulations and experimental print quality results.

Eddy currents in a gradient coil, modeled by rings and patches

The gradient coils of an MRI-scanner can be modeled by a surface current on a cylinder. A good approximation of the surface current in the z-coil is obtained from a set of rings and patches on the cylinder. In this paper, an integral equation is derived for the current distribution. To solve this integral equation, the Galerkin method is applied, using global expansion functions. We show that Legendre polynomials are an appropriate choice for the expansion functions. They provide fast convergence. So, only a restricted number of Legendre polynomials is needed. Moreover, an analytical solution is derived, which results in efficient simulations.