ALBERT

Description: Passive magnetic levitation systems reported in the past were mostly confined to bulk superconducting materials. Here we present fundamental studies on magnetic levitation employing cylindrical permanent magnets floating above high-T(sub c) superconducting YBCO thin films (thickness about 0.3 mu m). Experiments included free floating rotating magnets as well as well-established flexible beam methods. By means of the latter, we investigated levitation and drag force hysteresis as well as magnetic stiffness properties of the superconductor-magnet arrangement. In the case of vertical motion of the magnet, characteristic high symmetry of repulsive (approaching) and attractive (withdrawing) branches of the pronounced force-displacement hysteresis could be detected. Achievable force levels were low as expected but sufficient for levitation of permanent magnets. With regard to magnetic stiffness, thin films proved to show stiffness-force ratios about one order of magnitude higher than bulk materials. Phenomenological models support the measurements. Regarding the magnetic hysteresis of the superconductor, the Irie-Yamafuji model was used for solving the equation of force balance in cylindrical coordinates allowing for a macroscopic description of the superconductor magnetization. This procedure provided good agreement with experimental levitation force and stiffness data during vertical motion. For the case of (lateral) drag force basic qualitative characteristics could be recovered, too. It is shown that models, based on simple asymmetric magnetization of the superconductor, describe well asymptotic transition of drag forces after the change of the magnet motion direction. Virgin curves (starting from equilibrium, i.e. symmetric magnetization) are approximated by a linear approach already reported in literature only. This paper shows that basic properties of superconducting thin films allow for their application to magnetic levitation or - without need of levitation forces, e.g. microgravity - magnetic damping devices.

Description: In September 1987, researchers at Cornell levitated a small rotor on superconducting bearings at 10,000 rpm. In April 1989, a speed of 120,000 rpm was achieved in a passive bearing with no active control. The bearing material used was YBa2Cu307. There is no evidence that the rotation speed has any significant effect on the lift force. Magnetic force measurements between a permanent rare-earth magnet and high T(sub c) superconducting material versus vertical and lateral displacements were made. A large hysteresis loop results for large displacements, while minor loops result for small displacements. These minor loops seem to give a slope proportional to the magnetic stiffness, and are probably indicative of flux pinning forces. Experiments of rotary speed versus time show a linear decay in a vacuum. Measurements of magnetic dipole over a high-T(sub c) superconducting disc of YBCO show that the lateral vibrations of levitated rotors were measured which indicates that transverse flux motion in the superconductor will create dissipation. As a result of these force measurements, an optimum shape for the superconductor bearing pads which gives good lateral and axial stability was designed. Recent force measurements on melt-quench processed superconductors indicate a substantial increase in levitation force and magnetic stiffness over free sintered materials. As a result, application of high-T(sub c) superconducting bearings are beginning to show great promise at this time.

Description: In September 1987 research at Cornell levitated a small rotor on superconducting bearing at 10,000 rpm. In April 1989 a speed of 120,000 rpm was achieved in a passive bearing with no active control. The bearing material used was YBa2Cu3O7. There is no evidence that the rotation speed has any significant effect on the lift force. Magnetic force measurements between a permanent rare-earth magnet and high T(sub c) superconducting material versus vertical and lateral displacements were made. A large hysteresis loop results for large displacements, while minor loops result for small displacements. These minor loops seem to give a slope proportional to the magnetic stiffness, and are probably indicative of flux pinning forces. Experiments of rotary speed versus time show a linear decay in a vacuum. Measurements of magnetic drag forces of a magnetic dipole over a high-T(sub c) superconducting disc of YBCO show that the drag force reaches a constant value, independent of the speed. Dampling of lateral vibrations of levitated rotors were measured which indicates that transverse flux motion in the superconductor will create dissipation. As a result of these force measurements, an optimum shape for the superconductor bearing pads which gives good lateral and axial stability was designed. Recent force measurements on melt-quench processed superconductors indicate a substantial increase in levitation force and magnetic stiffness over free sintered materials. As a result, application of high-T(sub c) superconducting bearings are beginning to show great promise at this time.

Description: An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Description: The problem of stress wave generation in a linear thermoelastic solid by a pulsed magnetic field is investigated both analytically and experimentally for a cylindrically symmetric conducting solid. A dynamic response analysis is developed to correlate magnetic, thermal, and stress fields in the solid with the time history of the electric current. In the experiment, a transient magnetic field was applied normal to a large conducting plate with a circular hole. Initially the field was confined to the interior of the circular hole. The field was generated by discharging a large capacitor bank through a solenoidal coil. The plane-stress cylindrical stress waves are 1-D in nature. The relative effects of the magnetic body force and thermoelastic stresses, both generated by the electromagnetic field, are assessed.

Description: The calculated stresses and displacements induced anisotropic plates by short duration impact forces are presented. The theoretical model attempts to model the response of fiber composite turbine fan blades to impact by foreign objects such as stones and hailstones. In this model the determination of the impact force uses the Hertz impact theory. The plate response treats the laminated blade as an equivalent anisotropic material using a form of Mindlin's theory for crystal plates. The analysis makes use of a computational tool called the fast Fourier transform. Results are presented in the form of stress contour plots in the plane of the plate for various times after impact. Examination of the maximum stresses due to impact versus ply layup angle reveals that the + or - 15 deg layup angle gives lower flexural stresses than 0 deg, + or - 30 deg and + or - 45 deg. cases.

Description: The stresses and displacements induced in anisotropic plates by short-duration impact line forces are calculated in this paper. The anisotropy is related to the lay-up angles of the fibers of a laminated fiber composite plate. A modification of Mindlin's theory of crystal plates is used. The plate responses are calculated for various fiber lay-up angles and inclination of the line load to the axes of symmetry. Use is made of the computational method of the fast Fourier transform.

Description: Anisotropic waves in composites are considered, taking into account wave speeds, wave surfaces, flexural waves in orthotropic plates, surface waves, edge waves in plates, and waves in coupled composite plates. Aspects of dispersion in composites are discussed, giving attention to pulse propagation and dispersion, dispersion in rods and plates, dispersion in a layered composite, combined material and structural dispersion, continuum theories for composites, and variational methods for periodic composites. The characteristics of attenuation and scattering processes are examined and a description is given of shock waves and impact problems in composites. A number of experiments are also reported.

Description: Stress waves induced in anisotropic fiber composite plates by transverse, short-duration impact forces

Description: Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.