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An algorithm is proposed which can be applied to finite element models in or- der to efficiently perform nonlinear harmonic analyses without neglecting nonlinear effects due to joint friction and impacts. In order to decrease the size of the nonlinear differential equation to be solved, the proposed algorithm reduces the structural matrices of the system to be investigated using the Craig-Bampton method after importing them from commercially available FE codes. Depending on the geometrical setup and materials of the system joints, different discretization assumptions can be applied. The implemented contact model is based on Coulomb friction and Newton impact constraints which are being determined by a linear complementarity problem (LCP) formulation. The computation itself is performed in time domain using a modified Newmark time stepping approach for numerical stability even if the time step size chosen is fairly large. Both the mathematical approach itself as well as numer- ical results are presented for the simple system of a cylindrical beam in contact with a rigid wall in order to give an in-depth description of the proposed algorithm.

Nonlinear harmonic analysis of structures containing joints with impacts and friction