Single–Degree–of–Freedom Systems

Introduction

The theory of vibro–impact dynamics has been applied to classical lumped discrete systems represented by single–, two–, and multi–degree of freedom against one– or two–sided barriers. One freedom systems in the form of mass–spring–dashpot with one–sided barrier have been extensively studied in the literature. Other systems such as a ball bouncing on an oscillating table, a simple pendulum with one– or two–sided barriers, and ship roll dynamics interacting with icebergs will be considered. The study of these systems has revealed different and complex response characteristics such as periodic and quasi–periodic oscillations, grazing and period doubling motions, chattering and chaotic oscillations. A simple idealization of a vibratory plow impacting against an immovable relatively rigid obstruction was analyzed to determine possible periodic motions and the stability of these motions [921]. It should be mentioned that these systems may exhibit some peculiar periodic or chaotic response regimes (see, e.g., [811], [813], [417], [4], [418], [419], [124], [1077], [1078], [945], [12], [127], [910], [23], [199], [552]).