Zu J.

Discontinuous systems exist in many mechanical systems such as those under dry friction. In automotive timing belt drive systems, for instance, the tensioner arm motion is subjected to strong dry friction. Discontinuous vibration systems exhibit complex dynamic behavior especially under multiple excitations. Among the large volume of studies on dry friction damped vibrations, nevertheless, only a handful of works have considered the case of multiple excitations. It is therefore the objective of this study to investigate the impact of multi-excitations on the dynamics of a two-degree-of-freedom system with dry friction. The system consists of two spring-coupled blocks connected to a fixed body via another spring and supported by a moving belt. Two harmonic excitations with different frequencies are applied to the blocks and Coulomb friction can occur between the blocks and the moving belt. To handle the discontinuity due to the dry friction, we develop a new two-dimensional (2-D) map, which reduces the system without losing its essential dynamic features and greatly simplifies the investigation. Based on the 2-D map, bifurcation analysis and the computation of Poincar¨¦ sections and Lyapunov exponents can be carried out straightforwardly. Numerical simulations prove the proposed 2-D map to be very effective in providing a powerful tool to understand the dynamical behavior of the system. Numerical results show that the system possesses rich dynamics characterized by periodic, quasi-periodic and chaotic attractors. Furthermore, it is found that the two-frequency excitations, specifically the amplitudes and the frequency ratio, have significant influence on the dynamical behavior of the system.