Figure 4: Displacement-time graph of mass 425 and relative displacement between mass 425 and mass 424 Figure 5: Displacement field of the entire structure at end t Figure 4 and Figure 5 indicate that the results of methods (II) and (III) are almost equivalent and thus, the assumption that Eq.(23) is valid for this example is verified. Moreover, (II) and (III) are coinciding with the reference solution. The minor deviation in the right figure of Figure 4 results form both, considering only the first three fixed-interface normal modes and retaining only 12 local Ritz-vectors. It has to be pointed out that the left and right figures of Figure 4 are scaled differently. Figure 5 shows, that the additionally nonlinear springs between mass 400 up to mass 450 act almost like a rigid connection. This is caused by the 10-times higher spring stiffness of the additionally nonlinear springs with respect to the linear springs of the system. In this example, the required computational time for solving Eq.(25) is approximately 25 % lower than for solving Eq.(21). Contact problems of two elastic bodies could be computed analogously to this example. Therefore each elastic body has to be represented by both global vibration modes and mass-orthogonal local Ritz-vectors, and for such problems the contact force depends of course on the generalized coordinates of both elastic bodies. 6 Conclusion This contribution is devoted to a more efficient handling of a system, which is reduced by global vibration modes together with Ritz-vectors needed for local effects. By a mass decoupling procedure together with the reasonable assumption of weak stiffness coupling, the differential equations of the local Ritz-vector DOF are replaced by nonlinear algebraic constraints. The presented generic example demonstrates the successful reduction of the system of differential equations, while the numerical results show acceptable accurate. 45
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