Recursive Feedback Structural Properties Appeared in General Solution for Impact Oscillator Systems

Abstract

In this paper, it was analytically made clear that general solutions for the impact oscillator systems have accurate recursive feedback structural properties. First, general solutions previously obtained in terms of self-reference form was replaced by those which do not have explicit terms of impact velocity. As a result of this procedure, general solutions in the form of "reference value decomposition" was achieved in which explicit expression of the equation was obtained by taking the impact time as only parameter. Secondly, this formulation was furthermore developed by proposing the analytical procedure for getting "general solutions of recurrence form" which can lead the solutions expressed by the impact recurrence. From this formulation, it was exactly clarified that these solutions have recursive feedback structural property with respect to the impact. Finally, through the formulation proposed in this examination, a kind of "binary-tree structure" can be recognized in the linear system transform from the velocity domain into the time domain when we get the pseudo-feedback response solutions.