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Research Papers

Component-Centric Reduced Order Modeling of the Dynamic Response of Linear Multibay Structures

[+] Author and Article Information
Yuting Wang

Faculties of Mechanical and
Aerospace Engineering,
SEMTE,
Arizona State University,
501 E. Tyler Mall,
Tempe, AZ 85287-6106
e-mail: ywang394@asu.edu

Marc P. Mignolet

Professor
Fellow ASME
Faculties of Mechanical and Aerospace Engineering,
SEMTE,
Arizona State University,
501 E. Tyler Mall,
Tempe, AZ 85287-6106
e-mail: marc.mignolet@asu.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 10, 2016; final manuscript received March 12, 2017; published online May 30, 2017. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 139(4), 041007 (May 30, 2017) (13 pages) Paper No: VIB-16-1396; doi: 10.1115/1.4036277 History: Received August 10, 2016; Revised March 12, 2017

Component-centric reduced order models (ROMs) are introduced here as small-size ROMs providing an accurate prediction of the linear response of part of a structure (the β component) without focusing on the rest of it (the α component). Craig–Bampton (CB) substructuring methods are first considered. In one method, the β component response is modeled with its fixed interface modes while the other adopts singular value eigenvectors of the β component deflections of the linear modes of the entire structure. The deflections in the α component induced by harmonic motions of these β component modes are processed by a proper orthogonal decomposition (POD) to model the α component response. A third approach starts from the linear modes of the entire structure which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component, i.e., these nondominant modal contributions are “lumped” onto dominant ones. This lumping permits to increase the accuracy in the β component at a fixed number of modes. The three approaches are assessed on a structural finite element model of a nine-bay panel with the modal lumping-based method yielding the most “compact” ROMs. Finally, good robustness of the ROM to changes in the β component properties (e.g., for design optimization) is demonstrated and a similar sensitivity analysis is carried out with respect to the loading under which the ROM is constructed.

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References

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Figures

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Fig. 1

Finite element model of the nine-bay fuselage sidewall panel: (a) isometric view and (b) top view from Ref. [8]

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Fig. 2

Magnitude of the frequency response at the middle point of bay 4, transverse displacement

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Fig. 3

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, six β-fixed and 30 α-POD modes and baseline model

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Fig. 4

Comparison of the representation errors in α and β components, six β-fixed and 30 α-POD modes

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Fig. 5

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, six β-fixed and 20 α-POD modes and baseline model

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Fig. 6

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, 30 α-POD and ten β-POD modes and baseline model

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Fig. 7

Comparison of the representation errors in α and β components, 30 α-POD and ten β-POD modes

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Fig. 8

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, 30 α-POD and five β-POD modes and baseline model

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Fig. 9

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, 20 α-POD and ten β-POD modes and baseline model

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Fig. 10

Comparison of the magnitudes of the frequency responses at the middle point of bay 4, baseline model and 21 selected modes from (a) the recursive algorithm (Table 2) and (b) Eq. (16) (Table 3)

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Fig. 11

Contour plots of the norm of displacements for linear modes 8–12 (in order (a)–(e)) in the band [127,136] Hz. Dark blue/red zones correspond to the lowest/highest values.

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Fig. 12

Contour plots of the norm of displacements for the linear modes of Fig. 11 but each mode is normalized in each bay

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Fig. 13

Mode shapes before, Ui and Uj—left column, and after rotation, Ũi and Ũj—right column. (row 1, 2) Entire structure and (row 3, 4) β-component (bay 4) only.

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Fig. 14

Comparison of magnitudes of the frequency responses of the middle point of bay 4 obtained with 17 selected linear modes and the 17 modes model resulting from a direct and optimized lumping of modes 8, 9, 10, and 12 on mode 11

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Fig. 15

Comparison of magnitudes of the frequency responses of the middle point of bay 1 obtained with 20 selected linear modes and the 20 modes model resulting from direct lumping and optimized lumping. Frequency band: (a) [127,136] Hz, (b) [140,145] Hz, (c) [191,196] Hz, and (d) [280,300] Hz.

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Fig. 16

Illustration of the optimization process using the AR modeling

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Fig. 17

Simulation data for the identification based lumping of the linear modes 8–12; bay 4

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Fig. 18

Zoom of the response shown on Fig. 17 near the peak of the response at 0.0668 s

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Fig. 19

Comparisons of frequency responses at the middle of bay 4 obtained with the component-centric ROM and with the appropriate baseline model for (a) nominal thickness/uniform pressure, (b) 80% of the nominal thickness/uniform pressure, (c) 120% of the nominal thickness and uniform pressure, (d) nominal thickness and triangular pressure distribution, and (e) same as (d) but ROM includes mode 3

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