Nonlinear Dynamics of Vibro-Impacting Indenter

Abstract

We investigated a vibro-impacting indenter interacting with strata in the form of metal or rock samples experimentally and via mathematical modelling. An experimental programme was undertaken on the custom-designed rig at the Centre for Applied Dynamics of the University of Aberdeen. The mathematical models captured the essential mechanics when the indenter interacted with the metal or rock samples. The mathematical functions describing the discontinuous phases were specific to the metal and rock samples. Appropriate switch functions were constructed for indenter positions, as well as for the penetration depth, wherever appropriate. To seek a correlation between the experiments and modelling, a careful direct numerical integration of the equations of motion describing each discontinuous phase of the system dynamic response enabled time histories, phase trajectories and amplitude spectra to be computed. The developed mathematical model facilitates the optimisation of vibro-impact dynamical responses.