A Consistent Approach of Damping Treatment in Coupled Dynamic Analysis and Test

Paper number

IAC-11,C2,1,2,x10418

Author

Dr. Jochen Albus, Astrium GmbH, Germany

Coauthor

Mr. Werner Beuchel, Astrium GmbH, Germany

Coauthor

Dr. Stefan Dieker, Ingenieurbuero Stefan Dieker, Germany

Year

2011

Abstract

The coupled dynamic load analysis of space transportation systems like Ariane 5 makes use of the coupling of mathematical models of the substructures to build the mathematical model of the complete system that is object of the coupled load analysis. 

The mathematical models of the substructures are condensed and than assembled to build-up the mathematical model of the complete system. During this process, special attention has to be paid on the damping matrix.

The damping is normally introduced on subsystem level as modal viscous damping. Experience shows, that coupled dynamic response analysis often reveals strange behaviour. This problem can be overcome, if the damping is introduced as an Equivalent Structural Damping (ESD) on substructure level. 

The substructure damping is derived from subsystem tests under test boundary conditions and complies with the corresponding component modes of the test configuration. The test boundary conditions are often different from the boundary conditions of the subsystem, when integrated into the complete space transportation system. For use in coupled dynamic analysis, the subsystem mathematical models are condensed with boundary conditions in compliance with those of the integrated substructure. The corresponding component modes differ from those of the test configuration. That is the reason why the damping derived under test boundary conditions has to be re-computed in order to comply with the component modes used for the condensation of the mass and stiffness matrix. In order to re-compute the modal damping values, the modal damping matrix of the test configuration has to be transformed into a physical structural damping matrix. This is done by the Inflated Damping Matrix (IDM) process. Once the physical damping matrix is computed, it can be condensed using the same transformation as applied on the mass and stiffness matrix.

Dynamic test set-ups generally consist not only of the substructure of interest, but also of test adapters and dummy structures. The question is how to separate the damping of substructure of interest from the damping matrix of the complete test assembly. A procedure has been developed, which allows the Separation of this Component Damping (SCD).

The Equivalent Structural Damping (ESD), the Inflated Damping Matrix (IDM) process as well as the Separation of the Component Damping (SCD) allows the consistent damping treatment in coupled dynamic analysis and test. The established procedures will be explained within this paper and illustrated with examples.

Abstract document

IAC-11,C2,1,2,x10418.brief.pdf

Manuscript document

IAC-11,C2,1,2,x10418.pdf (🔒 authorized access only).

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