488 S.E. Obando and P. Avitabile a Reduce components/systems b Add couplings for all configurations Reduced Unconnected Systems Original State Configuration 1 Configuration 2 Configuration 3 [ T ] 2 [ T ] 1 System 2 System 1 NDOF Components Fig. 44.4 (a) Assembly of reduced order model from uncoupled full space subcomponents and (b) computation of relevant system configurations due to nonlinear interactions of the gap-springs (in green) Fig. 44.5 Calculation of nonlinear response of three beam system from the linear combination of all configurations of the structure (indicated from the contact interactions of the greengap-spring as seen on the time response) and obtained using Newmark direct integration of the equations ofmotion the response of the nonlinear reduced order model is obtained as the piecewise combination of all linear states (configurations 0–3) and calculated from the direct integration of the equations of motion of the system. The response is obtained for the selected ADOF present in the reduced model (blue and red dots in Figs. 44.4, 44.5, and 44.6). Expansion is performed using the same projection mode shape vectors obtained from the reduction process of the unassembled unreduced subcomponents as seen in Fig. 44.6a.
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