Upgraded reduction technique for dynamic analysis of structures with friction contact

A recent reduction technique for the nonlinear forced response analysis of structures with contact interfaces is upgraded. The evaluations of the existing method (Dual formulation), which is based on dual Craig-Bampton method, show its considerable off-line computational time saving because of no matrix manipulation, whereas the resulting reduced model is less accurate than Rubin's in approximating the full finite element model. The accuracy of this formulation is significantly improved with a low additional computational cost in the proposed upgraded formulation. That is obtained by consistent projection of all structural matrices on a reduction basis made up of two sets of vectors: free-interface normal modes and residual flexibility attachment modes. Assembly approach can be considered as dual because the interface forces are kept as generalized coordinates in opposition to primal methods, where interface displacements are retained. To reduce the computational cost, the nonlinear governing equations are also solved in frequency domain using the multiharmonic balance method and alternating frequency time method. Contact elements are introduced between adjacent interface nodes to find the nonlinear contact forces. The performance of the new formulation is demonstrated through two numerical models with friction contact.