STRONGLY NON-LINEAR OSCILLATIONS OF WINDING MACHINES, PART I: MODE-LOCKING MOTION AND ROUTES TO CHAOS

✍ Scribed by Y. Kang; Y.-P. Chang; S.-C. Jen

• Book ID: 102607777
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 458 KB
• Volume: 209
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1250

✦ Synopsis

This study investigates the dynamics of a single-degree-of-freedom (SDOF) wire in a winding machine. This system has piecewise-linear stiffness and is subjected to a forcing excitation due to imbalance and a parametric excitation due to tension. The frequencies of both parametric and forcing excitations are not equal or do not have a ratio of two simple integers. Using the fourth order Runge-Kutta method and introducing a J-integral, this strongly non-linear system can be estimated for various parameters. Then, the mode-locking motions, main resonant intervals, and subharmonic modes can be found. Also, all possible combined subharmonics and superharmonic motions and routes to chaos are observed by J-bifurcation illustrations with the assistance of Poincare´maps, phase portraits, response waveforms, frequency spectra and Lyapunov exponents. Thus, the physical illustrations of such a system can provide stabilization by appropriate design parameters.