Assessment tools for numerical resolution of a contact dynamic problem with modal basis reduction.

This paper is devoted to the study of the modal basis reduction method in the framework of the dynamical behavior of a mechanical system with multiple joint clearances. The final objective is to estimate contact forces in a confined tube bundle during a dynamic loading for nuclear components sizing. The modal basis reduction combined with an explicit integration scheme is envisioned to deal with the large number of tubes and potential contact zones. In this paper, method is first applied to the example of a clamped-free beam impacting on a spring on its free edge. A semi-analytical resolution allows assessing the validity of the modal basis reduction method depending of some parameters, like frequency truncation and ratio between the bending stiffness and the spring stiffness. This study leads to criteria on numerical parameters which have to be respected to ensure stability and accuracy of results.