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  • bifurcations  (2)
  • Numerical and geometrical techniques  (1)
  • numerical simulation  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Numerical and geometrical analysis of bifurcation and chaos for an asymmetric elastic nonlinear oscillator (1995)
    Springer
    Nonlinear dynamics 7 (1995), S. 249-272 
    Details
    ISSN: 1573-269X
    Keywords: Numerical and geometrical techniques ; local and global bifurcations ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An asymmetric nonlinear oscillator representative of the finite forced dynamics of a structural system with initial curvature is used as a model system to show how the combined use of numerical and geometrical analysis allows deep insight into bifurcation phenomena and chaotic behaviour in the light of the system global dynamics. Numerical techniques are used to calculate fixed points of the response and bifurcation diagrams, to identify chaotic attractors, and to obtain basins of attraction of coexisting solutions. Geometrical analysis in control-phase portraits of the invariant manifolds of the direct and inverse saddles corresponding to unstable periodic motions is performed systematically in order to understand the global attractor structure and the attractor and basin bifurcations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00053711
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part I: Local Analysis (1997)
    Springer
    Nonlinear dynamics 14 (1997), S. 89-117 
    Details
    ISSN: 1573-269X
    Keywords: Experimental analysis ; cables ; nonlinear vibrations ; modal interaction ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An experimental model of an elastic cable carrying eight concentrated masses and hanging at in-phase or out-of-phase vertically moving supports is considered. The system parameters are adjusted to approximately realize multiple 1:1 and 2:1 internal resonance conditions involving planar and nonplanar, symmetric and antisymmetric modes. Response measurements are made in various frequency ranges including meaningful external resonance conditions. A ‘local’ analysis of the system response is made on the basis of numerous amplitude-frequency and amplitude-forcing plots obtained in different ranges of the control parameter space. Attention is mainly devoted to the detection of the main features of the regular motions exhibited by the system, and to the analysis of the relevant phenomena of nonlinear modal interaction, competition, and local bifurcation between planar and nonplanar regular responses. The resulting picture appears very rich and varied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008246504104
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical simulations of chaotic dynamics in a model of an elastic cable (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 23-38 
    Details
    ISSN: 1573-269X
    Keywords: numerical simulation ; chaos ; cable ; resonances ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The finite motions of a suspended elastic cable subjected to a planar harmonic excitation can be studied accurately enough through a single ordinary-differential equation with quadratic and cubic nonlinearities. The possible onset of chaotic motion for the cable in the region between the one-half subharmonic resonance condition and the primary one is analysed via numerical simulations. Chaotic charts in the parameter space of the excitation are obtained and the transition from periodic to chaotic regimes is analysed in detail by using phase-plane portraits, Poincaré maps, frequency-power spectra, Lyapunov exponents and fractal dimensions as chaotic measures. Period-doubling, sudden changes and intermittency bifurcations are observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01857583
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