Cognate Space Identification for Forced Response Structural Redesign

[+] Author and Article Information
Vincent Y. Blouin

Mechanical Engineering,  Clemson University, 240 Fluor Daniel EIB, Box 340921 Clemson, 29634-0921vblouin@clemson.edu

Michael M. Bernitsas

Naval-Architecture and Marine Engineering,  The University of Michigan, 2600 Draper Road, Ann Arbor, Michigan 48109-2145michaelb@umich.edu

J. Offshore Mech. Arct. Eng 127(3), 227-233 (Jan 26, 2003) (7 pages) doi:10.1115/1.1979512 History: Received February 19, 2002; Revised January 26, 2003

Large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the incremental method (IM) and the direct method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate spaces, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Tubular cantilever beam finite element model

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Figure 2

Comparison of solutions at first and last increments with incremental method

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Figure 3

Comparison of contributions at first and last increments with incremental method

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Figure 4

Comparison of contributions using the incremental and the direct methods

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Figure 5

Contributions for the first 40 modes of cantilever beam with direct method

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Figure 6

Mode shapes 8 and 9 of the symmetrical beam

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Figure 7

Mode shapes 8 and 9 of the asymmetrical beam

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Figure 8

Offshore tower finite element model

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Figure 9

Stiffness and mass contributions of the first 20 modes

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Figure 10

Total contributions of the first 20 modes (stiffness and mass)

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Figure 11

Computational time vs percentage of error cases 1, 2, 4, and 5 of Table 3



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