The applicability limits of the lowest-order substitute model for a cantilever beam system hard-impacting a moving base.

This paper examines the circumstances under which a one-degree-of-freedom approximate system can be employed to predict the dynamics of a cantilever beam comprising an elastic element with a significant mass and a concentrated mass embedded at its end, impacting a moving rigid base. A reference model of the system was constructed using the finite element method, and an approximate lowest-order model was proposed that could be useful in engineering practice for rapidly ascertaining the dynamics of the system, particularly for predicting both periodic and chaotic motions. The number of finite elements in the reference model was determined based on the calculated values of natural frequencies, which were found to correspond to the values of natural frequencies derived from the application of analytical formulas.

Hard vs soft impacts in oscillatory systems' modeling revisited.

An application of soft and hard impact models to represent vibro-impact systems is reconsidered. The conditions that the two collision models have to satisfy to be equivalent in terms of energy dissipation are discussed and key features of the resulting soft impact models are demonstrated. Then, it is examined what effect will be exerted on the behavior of a vibro-impact system when an additional elastic-damping element and external forcing are used.