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  • 1
    Electronic Resource
    Electronic Resource
    Phase-Space Reconstructions and Stick-Slip (1997)
    Springer
    Nonlinear dynamics 13 (1997), S. 39-57 
    Details
    ISSN: 1573-269X
    Keywords: Phase-space reconstructions ; stick-slip ; method of delays ; friction oscillators ; nonsmooth systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Nonsmooth processes such as stick-slip may introduce problems with phase-space reconstructions. We examine chaotic single-degree-of-freedom stick-slip friction models and use the method of delays to reconstruct the phase space. We illustrate that this reconstruction process can cause pseudo trajectories to collapse in a way that is unlike, yet related to, the dimensional collapse in the original phase-space. As a result, the reconstructed attractor is not topologically similar to the real attractor. Standard dimensioning tools are applied in effort to recognize this situation. The use of additional observables is examined as a possible remedy for the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008245332549
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Identifying Coulomb and Viscous Friction from Free-Vibration Decrements (1998)
    Springer
    Nonlinear dynamics 16 (1998), S. 337-347 
    Details
    ISSN: 1573-269X
    Keywords: Friction oscillator ; friction estimation ; friction identification ; Coulomb friction ; free vibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This study focuses on an algorithm for the simultaneous identification of Coulomb and viscous damping effects from free-vibration decrements in a damped linear single degree-of-freedom (DOF) mass-spring system. Analysis shows that both damping effects can indeed be separated. Numerical study of a combined-damping system demonstrates a perfect match between the simulation parameters and the estimated values. Experimental study includes two types of real systems. The method is applied to an experimental industrial bearing. Experimental results are compared with numerical simulations to illustrate the reliability of this method. An analysis provides conservative bounds on error estimates. An example of the effect of quantization error on the estimations is included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008213814102
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Part 2: Proper Orthogonal Modal Modeling of a Frictionally Excited Beam (2000)
    Springer
    Nonlinear dynamics 23 (2000), S. 1-11 
    Details
    ISSN: 1573-269X
    Keywords: friction oscillator ; proper orthogonal modes ; dynamic friction ; contact compliance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Proper orthogonal modes (POMs) are used for order reduction ina beam with frictional excitation. The distributed model is based on anEuler–Bernoulli beam with frictional excitation. The friction ismodeled with Coulomb's law and contact compliance, and the contactsurface undergoes an imposed oscillation. The POMs are selected from achaotic response to build the reduced system model. These POMs areextrapolated into proper orthogonal modal functions (POMFs) by using thelinear normal modes as basis functions. The POMFs are used as the basisfor projection the partial differential equation of motion to alow-order set of ordinary differential equations. Simulated responsesbased on the POMFs and linear normal modes are compared to that of a'truth set' simulation, which is based on ten linear normal modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008303406091
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Part 1: Dynamical Characterization of a Frictionally Excited Beam (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 317-333 
    Details
    ISSN: 1573-269X
    Keywords: friction oscillator ; proper orthogonal decomposition ; proper orthogonal modes ; dynamic friction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamics of an experimental frictionally excited beam areinvestigated. The friction is characterized and shown to involve contactcompliance. Beam displacements are approximated from strain gagesignals. The system dynamics are rich, including a variety of periodic,quasi-periodic and chaotic responses. Proper orthogonal decomposition isapplied to chaotic data to obtain information about the spatialcoherence of the beam dynamics. Responses for different parameter valuesresult in a different set of proper orthogonal modes. The number ofproper orthogonal modes that account for 99.99% of the signalpower is compared to the corresponding number of linear normal modes,and it is verified that the proper orthogonal modes are more efficientin capturing the dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008344005183
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  • 5
    Electronic Resource
    Electronic Resource
    Bifurcation sequences of a Coulomb friction oscillator (1993)
    Springer
    Nonlinear dynamics 4 (1993), S. 25-37 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00047119
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    Paper (German National Licenses)
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