My problem involves two equal masses; one sliding on other and impacting at the boundaries of first mass. I need the nonlinear Eigen frequencies and Nonlinear Normal Modes (NNMs), to characterize my system. I don't need the analytical solution for its motion; just the NNMs.

Although I found several literature but they are mostly based on continuous, single nonlinearity, for instance cubic nonlinearity in spring stiffness. But this model involves two piecewise discontinuities; dry friction and clearance.

I have attached a rough sketch for your consideration.

Seeking your guidance and help in finding suitable method to solve its NNMs.

Thanks.