Impact oscillations and wear of loosely supported rod subject to harmonic load

The non-linear dynamic behaviour of a damped rod oscillator with elastic two-sided amplitude constraints is analyzed using finite element method. Symmetric and asymmetric elastic double-impact motions, both harmonic and sub-harmonic, are studied by way of a Poincaré mapping that relates the states at subsequent impacts. It is found that by increasing the forcing frequency (ω) for the beam at a certain frequency a stable period one motion turns into a stable period two motion without bifurcation and subsequently moves to an infinite number of solutions characteristic of chaotic behaviour through a cyclic fold bifurcation. By further increasing ω a series of windows in the bifurcation diagram (impact velocity vs. ω) comprising periodic solutions within the chaotic domain appear. The kinds of bifurcations involved are discussed. Furthermore, impact work-rate of the beam, i.e., the rate of energy dissipation to the impacting surfaces, is calculated. Computations show that the work-rate for asymmetric orbits is substantially higher than for symmetric orbits at or near the same frequency. For the vibro-impacting beam, under conditions that exhibit a stable attractor, calculation of work-rate allows prediction of the “lifetime” of the contacting beam due to fretting-wear damage by extending the stable branch and using the local gap between contacting surfaces as a control parameter.