Lyapunov exponents in discrete modelling of a cantilever beam impacting on a moving base

•The dynamics of a cantilever beam with time-varying amplitude constraint is explored.•A new finite element reference model of the system is developed.•Substitutive models with one degree and two degrees of freedom are proposed.•The coefficient of dynamical behaviours based on the Lyapunov exponents is introduced.•The applicability limits of 1DOF and 2DOF substitutive models are examined.

The dynamic behaviour of a cantilever beam of an unnegligible large mass and with a concentrated mass fixed at its end, which impacts on a movable base according to Hertz's damp law, is studied. A new finite element reference model of the system and its lower-dimensional substitutive models with one degree or two degrees of freedom are developed. The qualitative-type as well as quantitative-type applicability limits of these substitutive models are discussed - the latter ones are described in terms of the corresponding spectra of Lyapunov exponents.