Publication

Abstract : The transition of synchronization behavior in a coupled friction-induced oscillators during its route to chaos is investigated in this paper. The coupled system consists of two cantilever beams attached with tip-masses and subjected to base excitations. Each tip-mass is in nonlinear frictional contact with a rotating rigid disc. A linear spring connecting the tip-masses provides the coupling for the system. Modal analysis is employed to reduce the partial differential equation governing the motion of the system to a set of ordinary differential equations. A bifurcation study is conducted for the coupled system wherein the base excitation frequency is considered as the bifurcation parameter. A transition from periodic to chaotic behavior through a quasiperiodic route with multiperiodic windows is observed for the coupled system. In this work, we report the numerical observations of synchronous behavior between two friction-induced oscillators exhibiting such a transition. The synchronization behavior is characterized using the linear time correlation coefficient between the time displacement responses of the two systems. During the quasiperiodic route to chaos, the coupled system undergoes for a transition from synchronized periodicity to a state of desynchronized chaos. Poincaré maps are plotted to identify the periodic, quasiperiodic and chaotic behaviour of the coupled system. The qualitative nature of the oscillations is further confirmed by plotting the time responses and the phase plane diagrams for each tip-mass. Fast Fourier Transform of the time displacement response is obtained to determine the fundamental frequencies and the harmonics of the tip-mass motions.