Abstract
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 aJ-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 superhamonic motions and routes to chaos are observed byJ-bifurcation illustrations with the assistance of Poincaré 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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
