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  • 1
    Electronic Resource
    Electronic Resource
    Experimental Investigation of Single-Mode Responses in a Fixed-Fixed Buckled Beam (1998)
    Springer
    Nonlinear dynamics 15 (1998), S. 155-177 
    Details
    ISSN: 1573-269X
    Keywords: Buckled beam ; clamp design ; asymmetric responses ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonlinear, single-mode responses of a fixed-fixed, buckled beam are investigated under the case of a uniform, transverse, harmonic excitation. In order to avoid axial slipping and to obtain meaningful data, a clamping apparatus was designed to maximize the clamping force applied to the beam. To fully characterize the single-mode responses, data were obtained at various levels of buckling up to 3.3 times the thickness of the beam. The data demonstrate that at a low level of buckling, supercritical period doubling occurs during an amplitude sweep in which the first mode is directly excited. However, as the buckling level increases, the period-doubling bifurcation becomes subcritical during such amplitude sweeps. In addition, a period-five motion, broadband responses, and responses with an unexplained sideband structure were observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008231012968
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  • 2
    Electronic Resource
    Electronic Resource
    Experimental Validation of Reduction Methods for Nonlinear Vibrations of Distributed-Parameter Systems: Analysis of a Buckled Beam (1998)
    Springer
    Nonlinear dynamics 17 (1998), S. 95-117 
    Details
    ISSN: 1573-269X
    Keywords: Buckled beam ; experiment ; Galerkin method ; direct approach ; method of multiple scales
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An experimental validation of the suitability of reduction methods for studying nonlinear vibrations of distributed-parameter systems is attempted. Nonlinear planar vibrations of a clamped-clamped buckled beam about its first post-buckling configuration are analyzed. The case of primary resonance of the nth mode of the beam, when no internal resonances involving this mode are active, is investigated. Approximate solutions are obtained by applying the method of multiple scales to a single-mode model discretized via the Galerkin procedure and by directly attacking the governing integro-partial-differential equation and boundary conditions with the method of multiple scales. Frequency-response curves for the case of primary resonance of the first mode are generated using both approaches for several buckling levels and are contrasted with experimentally obtained frequency-response curves for two test beams. For high buckling levels above the first crossover point of the beam, the computed frequency-response curves are qualitatively as well as quantitatively different. The experimentally obtained frequency-response curves for the directly excited first mode are in agreement with those obtained with the direct approach and in disagreement with those obtained with the single-mode discretization approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008389810246
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    Paper (German National Licenses)
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