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Fully Parameterized Reduced Order Models Using Hyper-Dual Numbers and Component Mode Synthesis

[+] Author Affiliations
Matthew S. Bonney, Daniel C. Kammer

The University of Wisconsin - Madison, Madison, WI

Matthew R. W. Brake

Sandia National Laboratories, Albuquerque, NM

Paper No. DETC2015-46029, pp. V008T13A021; 7 pages
doi:10.1115/DETC2015-46029
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 27th Conference on Mechanical Vibration and Noise
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5718-2
  • Copyright © 2015 by ASME

abstract

The uncertainty of a system is usually quantified with the use of sampling methods such as Monte-Carlo or Latin hypercube sampling. These sampling methods require many computations of the model and may include re-meshing. The re-solving and re-meshing of the model is a very large computational burden. One way to greatly reduce this computational burden is to use a parameterized reduced order model. This is a model that contains the sensitivities of the desired results with respect to changing parameters such as Young’s modulus. The typical method of computing these sensitivities is the use of finite difference technique that gives an approximation that is subject to truncation error and subtractive cancellation due to the precision of the computer. One way of eliminating this error is to use hyperdual numbers, which are able to generate exact sensitivities that are not subject to the precision of the computer. This paper uses the concept of hyper-dual numbers to parameterize a system that is composed of two substructures in the form of Craig-Bampton substructure representations, and combine them using component mode synthesis. The synthesis transformations using other techniques require the use of a nominal transformation while this approach allows for exact transformations when a perturbation is applied. This paper presents this technique for a planar motion frame and compares the use and accuracy of the approach against the true full system. This work lays the groundwork for performing component mode synthesis using hyper-dual numbers.

Copyright © 2015 by ASME

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