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Research Papers

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

[+] Author and Article Information
Masih Mahmoodi

Department of Mechanical and
Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: masih.mahmoodi@utoronto.ca

Kamran Behdinan

Department of Mechanical and
Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada
e-mail: behdinan@mie.utoronto.ca

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 2, 2015; final manuscript received March 29, 2016; published online May 25, 2016. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 138(4), 041015 (May 25, 2016) (8 pages) Paper No: VIB-15-1242; doi: 10.1115/1.4033340 History: Received July 02, 2015; Revised March 29, 2016

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

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Figures

Grahic Jump Location
Fig. 1

Flowchart of the proposed SOIRKA algorithm

Grahic Jump Location
Fig. 2

Engine compressor: (a) full casing and (b) the 18 deg portion casing

Grahic Jump Location
Fig. 3

FE meshed casing portion with loading and boundary conditions

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Fig. 4

(a) Input nodes and (b) output nodes for the casing

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Fig. 5

FRF of the reduced systems

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Fig. 6

Relative error of the reduced systems

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