Abstract
This work was motivated by a desire to transform an experimental dynamic substructure derived using the transmission simulator method into the Craig-Bampton substructure form which could easily be coupled with a finite element code with the Craig-Bampton option. Near the middle of that derivation, a modal Craig-Bampton form emerges. The modal Craig-Bampton (MCB) form was found to have several useful properties. The MCB matrices separate the response into convenient partitions related to (1) the fixed boundary modes of the substructure (a diagonal partition), (2) the modes of the fixture it is mounted upon, (3) the coupling terms between the two sets of modes. Advantages of the MCB are addressed. (1) The impedance of the boundary condition for component testing, which is usually unknown, is quantified with simple terms. (2) The model is useful for shaker control in both single degree of freedom and multiple degree of freedom shaker control systems. (3) MCB provides an energy based framework for component specifications to reduce over-testing but still guarantee conservatism.
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy National Nuclear Security Administration under Contract DE-AC04-94AL85000.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- CB:
-
Craig-Bampton method of substructuring
- CMIF:
-
Complex mode indicator function
- FE:
-
Finite element model
- MCB:
-
Modal Craig-Bampton model form
- TS:
-
Transmission simulator – the fixture attached to the experimental substructure of interest
- dof:
-
Degree of freedom
- sdof:
-
Single degree of freedom
- mdof:
-
Multiple degree of freedom
- p :
-
Modal dof of the experimental substructure with fixed boundary
- q :
-
Modal dof of free modes extracted from experimental substructure with TS attached
- s :
-
Free modal dof of the transmission simulator
- x :
-
Physical displacement dof
- ω :
-
Frequency in radians per second
- ζ :
-
Modal damping ratio
- K :
-
Stiffness matrix
- L fix :
-
Reduction matrix applying fixed boundary constraint to experimental equations of motion
- M :
-
Mass matrix
- T :
-
Transformation matrix to convert free modal model to modal CB model
- Φ:
-
Free mode shape matrix extracted for experimental substructure with TS attached
- Ψ:
-
Free mode shape matrix of the TS
- Γ:
-
Eigenvectors resulting from fixed boundary constraint of experimental equations of motion
- b :
-
Subscript for the fixture or boundary
- fix :
-
Subscript for the fixed boundary modes of the experimental substructure with TS as the boundary
- free :
-
Subscript for the free modes obtained in the modal test of the experimental substructure with TS
- +:
-
Superscript indicating the Moore-Penrose pseudo-inverse of a matrix
References
Allen MS, Mayes RL, Bergman EJ (2010) Experimental modal substructuring to couple and uncouple substructures with flexible fixtures and multi-point connections. J Sound Vib 329:4891–4906
Mayes RL (2015) A Craig-Bampton experimental dynamic substructure using the transmission simulator method. In: Proceedings of the 33rd international modal analysis conference, Orlando, February 2015, paper number 353
FEMA 451B Topic 4 notes. http://www.ce.memphis.edu/7119/fema_notes.htm
Technical discussion with Troy Savoie, SNLA, about the utility of the modal CB for environmental specifications, March–October 2014
Edwards TS (2009) Power delivered to mechanical systems by random vibrations. Shock Vib 16(3):261–271
Himelblau H, Hine MJ (1995) Effects of triaxial and uniaxial random excitation on the vibration response and fatigue damage of typical spacecraft hardware. In: Proceedings of the 66th shock and vibration symposium, Arlington
Acknowledgments
Notice: This manuscript has been authored by Sandia Corporation under Contract No. DE-AC04-94AL85000 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Mayes, R.L. (2015). A Modal Craig-Bampton Substructure for Experiments, Analysis, Control and Specifications. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15209-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-15209-7_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15208-0
Online ISBN: 978-3-319-15209-7
eBook Packages: EngineeringEngineering (R0)