Transient responses of repeated impact of a beam against a stop

The transient behavior of a cantilever beam, driven by periodic force and repeated impacting against a rod-like stop, is the subject of this investigation. As impact and separation phase take place alternately, the transient waves induced either by impacts or by separations will travel in more complicated ways. Thus the transient responses of both the beam and the rod during repeated impact become an important issue. In both impact phase and separation phase, the transient wave propagations are solved by the expansion of transient wave functions in a series of Eigenfunctions (wave modes). From the solutions, the answer of impact force is derived directly, so that the divergence problem, encountered in solving impact force numerically by a strongly non-linear equation coupled the unknown impact force with motions, has been avoided. Numerical results show the convergence of the time-step size and truncation number of wave modes in the calculations of impact force by the present method. As the transient wave effect is considered, the numerical results can show several transient phenomena involving the propagation of transient impact-induced waves, sub-impact phases, long-term impact motion, chatter, sticking motion, synchronous impact, non-synchronous impact (including asynchronous impact) and impact loss.