Nonlinear response of a parametrically excited buckled beam
| Autor: | M. A. Nayfeh, A. H. Nayfeh, A. M. Abou-Rayan, Dean T. Mook |
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| Rok vydání: | 1993 |
| Předmět: |
Floquet theory
Phase portrait Applied Mathematics Mechanical Engineering Mathematical analysis Aerospace Engineering Ocean Engineering Nonlinear Sciences::Chaotic Dynamics Nonlinear system Amplitude Control and Systems Engineering Control theory Attractor Electrical and Electronic Engineering Parametric oscillator Bifurcation Mathematics Multiple-scale analysis |
| Zdroj: | Nonlinear Dynamics. 4:499-525 |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/bf00053693 |
| Popis: | A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented. |
| Databáze: | OpenAIRE |
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