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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta mechanica 107 (1994), S. 153-169 
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Two examples of the effect of nonlinearities on the scattering of nondispersive waves are presented. It is shown that nonlinear boundary conditions can lead to broadband, chaotic scattered waves when the scatterer is excited by a single wavelength plane wave. One of the examples treats a spherical scatterer in a linear elastic medium. A number of modern techniques in nonlinear analysis is used to diagnose the chaotic dynamics including Poincaré maps, fractal dimensions and Lyapunov exponents.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9605
    Keywords: High-T c superconductor ; levitation ; magnetic stiffness ; flux pinning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Experimental results are reported on the differential levitation forces (magnetic stiffness) between permanent rare-earth magnets and high-temperature superconductors. Using a clamped beam cantilever, the amplitude-dependent magnetic stiffness for five configurations of the test magnets has been investigated for the melt-quenched YBa2Cu3O7-δ(Y123) superconductors in a range of 1 μm−1 mm. The configuration where the moment of the magnet and the direction of motion are perpendicular to the upper surface of the superconductor has the highest stiffness value among the five configurations. Compared with the data from a sintered Y123 superconductor, the magnetic stiffness for the melt-quenched materials has a much higher value and a much weaker dependence on the oscillation amplitudes. The results are compared with the current experimental and theoretical results.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 4 (1993), S. 25-37 
    ISSN: 1573-269X
    Keywords: Bifurcations ; chaos ; Coulomb friction ; universality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In some parameter ranges, the dynamics of a forced oscillator with Coulomb friction dependent on both displacement and velocity is reducible to the dynamics of a one-dimensional map. In numerical simulations, period-doubling bifurcations are observed for the oscillator. In this bifurcation procedure, the map arising from the Coulomb model may not have ‘standard’ form. The bifurcation sequence of the Coulomb model is compared to that of the standard one-dimensional maps to see if it exhibits ‘universal’ behavior. All observed components of the bifurcation sequence fit the universal sequence, although some universal events are not witnessed.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 1 (1990), S. 209-219 
    ISSN: 1573-269X
    Keywords: Homoclinic and heteroclinic orbits ; bifurcation and chaos ; fractal basin boundaries
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The final state for nonlinear systems with multiple attractors may become unpredictable as a result of homoclinic or heteroclinic bifurcations. The fractal basin boundaries due to such bifurcations for a four-well, two-degree-of-freedom, nonlinear oscillator under sinusoidal forcing have been studied, based on a theory of homoclinic bifurcation inn-dimensional vector space developed by Palmer. Numerical simulation is used as a means of demonstrating the consequences of the system dynamics when the bifurcations occur, and it is shown that the basin boundaries in the configuration space (x, y) become fractal near the critical value of the heteroclinic bifurcations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 3 (1992), S. 347-364 
    ISSN: 1573-269X
    Keywords: Nonlinear vibrations ; normal modes ; perturbation methods ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work we investigate the existence, stability and bifurcation of periodic motions in an unforced conservative two degree of freedom system. The system models the nonlinear vibrations of an elastic rod which can undergo both torsional and bending modes. Using a variety of perturbation techniques in conjunction with the computer algebra system MACSYMA, we obtain approximate expressions for a diversity of periodic motions, including nonlinear normal modes, elliptic orbits and non-local modes. The latter motions, which involve both bending and torsional motions in a 2:1 ratio, correspond to behavior previously observed in experiments by Cusumano.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 52 (1988), S. 1534-1536 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Magnetization forces between small permanent magnets and bulk high Tc superconducting ceramic materials have been measured and show marked hysteretic behavior as a function of the distance between the magnet and superconductor. Magnetic forces of up to 2500 dyn, both normal and tangential to the superconductor surface, have been made. Near-reversible forces are obtained for small motions of the magnet, however, which are believed to be related to flux pinning.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 56 (1990), S. 397-399 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Levitation and rotation of cylindrical rare-earth magnets on yttrium-barium-copper-oxide superconducting bearings has been sustained at speeds of up to 120 000 rpm with a surface speed of 40 m/s. The decay of the free rotation rate has been measured at both atmospheric pressure and a partial vacuum to 2.6 μm Hg. The decay measurements in vacuum indicate that the flux drag torques are constant and independent of speed. The magnetic shear stress on the rotor magnet is estimated to be 150 dyn/cm2. It is believed that drag torques on rotating magnets are related to asymmetry in the flux density pattern of the magnet.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 4358-4360 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Levitation forces between a small permanent magnet and a disk of bulk high-temperature superconductor at 77 K were measured as a function of vertical separation for disks of composition Y-Ba-Cu-O, Ag/Y-Ba-Cu-O, (Pb,Bi)-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-O. The forces were highly hysteretic; however, for all samples, on the initial descent of the magnet toward the disk, the force was unique, independent of magnet speed, and varied approximately as the negative exponential of the separation distance. Magnetic stiffness, associated with minor hysteresis loops, was found to be approximately proportional to the levitation force, and nearly independent of magnet configuration and superconductor composition.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 3 (1993), S. 93-99 
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The existence of spatially chaotic deformations in an elastica and the analogous motions of a free spinning rigid body, an extension of the problem originally examined by Kirchhoff are investigated. It is shown that a spatially periodic variation in cross sectional area of the elastica results in spatially complex deformation patterns. The governing equations for the elastica were numerically integrated and Poincaré maps were created for a number of different initial conditions. In addition, three dimensional computer images of the twisted elastica were generated to illustrate periodic, quasiperiodic, and stochastic deformation patterns in space. These pictures clearly show the existence of spatially chaotic deformations with stunning complexity. This finding is relevant to a wide variety of fields in which coiled structures are important, from the modeling of DNA chains to video and audio tape dynamics to the design of deployable space structures.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 61 (1991), S. 438-448 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht In dieser Arbeit wird ein Modell für deterministische, aber stochastisch erscheinendes Rauschen von Maschinen vorgestellt, bei denen gleitende Bauteile, die als Starrkörper modelliert werden, auf lineare, kontinuierliche Strukturen aufschlagen. Derartige Probleme treten bei Getrieben auf. Vorgeschlagen wird ein mathematisches Modell, um diese zufällig erscheinenden Geräusche zu erklären, die durch das Auftreffen der Masse von der Struktur sowohl direkt als auch indirekt erzeugt werden. Die als starr angenommenen Stoßmassen werden jedoch von keinem stochastischen, sondern von einem deterministischen, periodischen Signal angeregt. Eine das Modell unterstützende, experimentelle Untersuchung wird vorgestellt: Eine dünne, kreisförmige Scheibe wird von einer sich chaotisch bewegenden Masse angestoßen, die selbst von einer sinusförmig schwingenden Basis erregt wird. Die Ergebnisse legen nahe, die von der chaotisch schwingenden Masse ausgelöste Bewegung der Scheibe mit Hilfe einer gleichwertigen stochastischen Anregung vorherzusagen. Die Bauteile, die die Scheibe anstoßen, zeigen klassische Periodenverdopplung vor dem übergang in eine chaotische Bewegung.
    Notes: Summary In this paper a model is posited for deterministic, random-like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random-like structure-borne and air-borne noise from such systems when the input is a periodic deterministic excitation of the quasi-rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena.
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