Effects of Axial Compressive Load on Chaotic Vibrations of a Clamped-Supported Beam

Yanagisawa, Dai; Nagai, Kotobu; Maruyama, Shigenao

doi:10.1299/kikaic.74.1073

Cited by 2 publications

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“…For the clamped-supported beam (4) , predominant chaotic responses were dominated by the sub-harmonic resonance response of 1/2 order and the ultra-sub-harmonic resonance response of 2/3 order of the fundamental mode of vibration, simultaneously. In this paper, to reveal the features of chaotic vibrations of the clamped-supported beam with a concentrated mass under the static axial compression, experimental and analytical results are presented precisely.…”

Section: Introductionmentioning

confidence: 99%

“…The authors have investigated precisely the chaotic vibrations dominated by dynamic snap-through both experimentally and analytically (1)(2)(3)(4) . For the both ends clamped beam, the main chaotic responses of the post-buckled beam were dominated by the sub-harmonic resonance responses of 1/2 order and 1/3 order with the fundamental mode of vibration (1)(2)(3) .…”

Section: Introductionmentioning

confidence: 99%

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Chaotic Vibrations of a Clamped-Supported Beam with a Concentrated Mass Subjected to Static Axial Compression and Periodic Lateral Acceleration

Yanagisawa

Nagai

Maruyama

2008

JSDD

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Experimental results and analytical results are presented on chaotic vibrations of a clamped-supported beam with a concentrated mass. The beam is elastically compressed by an axial spring at the simply supported end and is excited by lateral periodic acceleration. In the experiment, periodic and chaotic vibrations are detected under several conditions of the axial compression. In the analysis, the governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses of the beam are examined with the Fourier spectra, the Poincaré projections and the maximum Lyapunov exponents and the principal component analysis. Under a specific axial compression with post-buckled state of the beam, the chaotic vibrations dominated by dynamic snap-through are generated by the ultra-sub-harmonic resonance response of 2/3order of the fundamental vibration mode. The number of pre-dominant vibration modes that contribute to the chaos is found to be three. Decreasing the axial compression, the chaotic vibrations are induced by the internal resonance response between the second and the fundamental mode of vibration. The number of predominant vibration modes that contribute to the chaos is found to be two or three. Both results of the experimental and the analysis agree remarkably with each other in detail.

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Section: Introductionmentioning

confidence: 99%