Impact Modes and Parameter Variations

Abstract

In this chapter, a new parameter variation and averaging tools are introduced for impact modes. It is also shown that a specific combination of two impact modes gives another impact mode. The corresponding manipulations with impact modes become possible due to the availability of closed form exact solutions obtained by means of the triangular sine temporal substitution for impulsively loaded and vibroimpact systems. In particular, the idea of Van-der-Pol and averaging tool are adapted for the case of impact oscillator. For illustrating purposes, a model of coupled harmonic and impact oscillators is considered. Further, mass-spring systems with multiple impacting particles are considered in order to illustrate impact localization phenomena on high-energy levels.