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.