Impact Element as a Dynamical Absorber for a Duffing Oscillator
This paper analyzes the application of a vibro-impact element as a dynamic absorber for a Duffing oscillator. The Duffing oscillator is a nonlinear oscillator, modeled here as a single-degree-of-freedom system with a nonlinear spring. The complete system consists of a body performing translational oscillatory motion, a drive mechanism, a slider, a spring that connects the oscillator to the slider, and a vibro-impact element, in the form of the ball, that performs translational motion with impacts. For comparison, the response of the Duffing oscillator without the absorber is also analyzed. The differential equations of motion of both systems are derived using Lagrange’s equations of the second kind, and solved numerically. The results are presented in the form of amplitude–frequency diagrams and time–displacement diagrams. It is shown that the amplitude of the main body is reduced when it is coupled with an impact element. The way in which this is affected by the stiffness of the spring, that connects the ball and Duffing oscillator, is presented. For selected excitation frequencies the basins of attraction of the ball are obtained. In this way, the set of possible initial conditions for which the system behaves like vibro-impact or purely oscillatory one, is determined.