The effect of discretization on the numerical simulation of the vibrations of the impacting cantilever beam

We study the dynamics of a cantilever beam with an unnegligible large mass and with a concentrated mass fixed at the end, which impacts on the base during motion. Generally to model such a system, the finite element method with appropriate number of degrees of freedom has to be employed. However, to analyse some selected aspects of its dynamic behaviour, particularly to predict if the motion with impacts will be periodic, lower-dimensional substitutive models with one degree or two degrees of freedom can be employed. The way to determine the parameters of such models and their applicability limits are discussed.