Dynamics of dry friction damped systems subjected to multi-frequency excitations

This thesis is devoted to the nonlinear vibration analysis of mechanical systems subjected to both dry friction and multi-frequency excitations, with emphasis laid on analyzing the effects of the dry friction and the multi-frequency excitations on the system's dynamic characteristics.Various types of steady-state motions the systems may experience are analyzed in the thesis, including periodic, quasi-periodic and chaotic motions. The systems investigated contain those of single-degree-of-freedom (single DOF) as well as the multi-degree-of-freedom (multi-DOF) systems. First, single-degree-of-freedom systems are studied. The nonstick and stick-slip periodic responses are derived analytically for a single DOF dry friction oscillator with two-frequency excitations. Furthermore, the dynamics of a single-degree-of-freedom dry friction damped block-on-belt system under two-frequency excitations is studied with bifurcation analysis as well as analysis of Poincare sections and Lyapunov exponents. Two types of system models are investigated: one is excited by two external forces whereas the other is excited both externally and parametrically. Both systems possess rich dynamic behavior characterized by periodic, quasi-periodic and chaotic attractors.As for the multi-degree-of-freedom systems, the rotational vibration of a belt drive system with a Coulomb-damped tensioner and subjected to multi-frequency excitations is studied, with an analytical method presented for the first time. Two kinds of periodic responses of the system characterized by the nonstick and stick-slip motions of the tensioner arm are obtained analytically. The impacts of the tensioner dry friction and the excitation frequencies on the dynamic behavior of the system are illustrated via evaluating the frequency responses of a prototypical belt drive. Besides, the dynamics of a multi-DOF system with simultaneous Coulomb friction and multi-frequency excitations is studied. An original two-dimensional map is proposed, which reduces the system without losing its essential dynamic features and greatly simplifies the investigation.