The design of impacted structures requires the determination of the interaction force between the structures involved. This requires to take the local problem of contact into account and the global description of the structures as well: the cost of numerical calculations can be very high. Hence, a modelling with few degrees of freedom (dof) is required to minimize the durations of calculations. Usually, to determine the interaction force, structures are modelled either by a single degree-of-freedom system, or by a modal description [
]. The modal description is not adapted for non-linear simulations and is slowly convergent: hence a lot of eigenmodes are required for a good accuracy.
This interaction problem may also be studied by describing a structure with its “anti-oscillators” : they are an alternative of the traditional eigenmodes. In fact, the ideas which lead to anti-oscillators come from the component modal synthesis method, that is from Craigh and Bampton [
]. Indeed, they are based on: 1- the constraint modes of a structure; they are the eigenmodes of the structure with an extra boundary condition: the displacement at the impact location vanishes; 2- the static mode: it is the shape caused by a static load applied at the impact point in the direction of the impact, such that the displacement at the impact location is equal to one.
It is possible to show that these modes lead to a single dof system: the mass of this latter is connected to a set of single dof systems referred to as the “anti-oscillators” because their natural frequencies are some antiresonances of the structure.
This modelling is based on a modal approach, but its philosophy is very different because it uses the antioscillators which compel the structure to be motionless: the anti-oscillators have a physical meaning. Then this model allows not only a simulation of the impact with few dof, but also a better understanding of the phenomena involved. An application of cylinder to cylinder impact is given.