Bifurcations in Hysteresis Systems Due to Vibrations and Impacts

Abstract

Operators of industrial machinery, in their daily work, are affected by vibrations produced by equipment. These vibrations are transmitted to the body, with a considerable health risk amount for the long-time period, and leading to a heavy environmental workplace. Vibrations can also cause damage to the machinery, misadjusting pieces and rising up maintenance costs. In order to correctly modeling these nonlinear systems we use the well-known Bouc-Wen model, which shows a good agreement between numerical simulations and experiments. Other models like Masing, Biot, and Spencer, which is a generalization of Bouc-Wen, can also be considered in order to display the same hysteretic phenomena. The Bouc-Wen model, due to its simplicity and versatility has been extensively studied in the scientific community, and successfully applied to several hysteresis problems. In the work we will show in our paper, we study the bifurcation diagrams of an application of the Bouc-Wen model to industrial machinery.We found transitions from periodicity to quasiperiodic and chaotic motion. Moreover, recently described big-bang codimension-two bifurcation has also been found. Close to the codimension-two point, an infinite number of periodic orbits exists.