A tight coupling scheme for smooth/non-smooth multibody co-simulation of a particle damper

To simulate coupled problems, composed of smooth and non-smooth particle subsystems, a tight, i.e. iterative coupling scheme is implemented. In the proposed setup, the non-smooth solver iterations are enclosed in each iteration of the smooth solver at every time step. The stability properties of the coupling scheme are tested using Dahlquist's test equations for co-simulation methods, highlighting the higher degree of stability of the tight coupling scheme, compared to the loose, non-iterative one. Results also denote that the properties of the solvers used to analyse the subsystems play an important role in the stability of co-simulation. The performance of the proposed scheme is further assessed by two illustrative examples: a particle damper subjected to prescribed motion, and a cantilever beam, modelled using finite elements, with a particle damper mounted at the free end. The proposed numerical solutions agree well with results from reduced order models and experiments, which demonstrates that the proposed scheme can effectively handle coupled problems of multibody systems and particle dampers.