Estimation of dynamic responses at internal points of a nested sub-structure with two-level Craig-Bampton reduction

Dynamic analyses of large and complex structural assemblies usually employ sub-structure coupling or Component Mode Synthesis (CMS) methods. The most widely used CMS method for dynamic analyses is the Craig-Bampton (CB) method. The displacement transformation of the CB method employs fixed-interface normal modes and interface constraint modes as the component modes. Dynamic analyses utilizing Craig-Bampton-reduced sub-structure matrices will provide information about dynamic responses at interface degrees-of-freedom (DOFs) and at generalized DOFs corresponding to fixed interface normal modes. However, physical responses at internal DOFs cannot be obtained directly from these analyses. In order to extract dynamic responses at selected internal DOFs, Output Transformation Matrices, which define a relation between responses at component modes and at internal DOFs, are used. In this paper, an approach to estimate and validate the internal point dynamic responses in a nested sub-structure with two-level CB-reduction is presented. This approach was used for validating the analytical estimates of dynamic responses at internal DOFs of the Crew Seat Assembly (CSA), which is a pallet structure housed inside the Crew Module (CM) for test missions of ISRO’s Gaganyaan program. Dynamic responses at internal DOFs of CSA due to excitations expected during the ascent phase of Gaganyaan test missions are usually estimated through a Coupled Loads Analysis (CLA) using the structural dynamic model of launch vehicle coupled with CM. In this coupled model, two-levels of CB-reduction are involved - the CSA is represented as a CB-reduced model within the structural dynamic model of CM which is further CB-reduced and coupled with the launch-vehicle model. To validate the dynamic responses estimated from such a model, a typical transient force excitation is considered and dynamic responses at internal points are estimated first from a full model (which has physical finite element idealization for all required elements of the Crew Module, including the CSA) and compared with corresponding results obtained from the model with two-level CB-reduction. A comparison is drawn between the results and validity of the approach is established.