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Research Papers

Optimal Designs for Vibrating Structures Using a Moving Isosurface Threshold Method With Experimental Study

[+] Author and Article Information
Quantian Luo

School of Aerospace,
Mechanical and Mechatronic Engineering,
The University of Sydney,
Sydney, NSW 2006, Australia

Liyong Tong

School of Aerospace, Mechanical
and Mechatronic Engineering,
The University of Sydney,
Sydney, NSW 2006, Australia
e-mail: liyong.tong@sydney.edu.au

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 29, 2014; final manuscript received May 26, 2015; published online July 14, 2015. Assoc. Editor: Corina Sandu.

J. Vib. Acoust 137(6), 061005 (Dec 01, 2015) (13 pages) Paper No: VIB-14-1273; doi: 10.1115/1.4030771 History: Received July 29, 2014; Revised May 26, 2015; Online July 14, 2015

This paper studies optimal designs for vibrating structures using a moving isosurface threshold method (MIST). In the present study, a combination of strain and kinetic energy densities is selected as a response function of natural frequency and then formulations to maximize a specific frequency, frequency separation, and average-mean are derived. An efficient algorithm is developed to find a moving isosurface threshold level for evolving the design boundary and updating the weighting factor. The present algorithm coupled with commercial finite element analysis (FEA) software is used to study optimal designs for vibrating structures. The obtained optimal designs are fabricated and the experimental tests are conducted to validate the optimal topologies.

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References

Figures

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Fig. 1

Beamlike structure: (a) model A—fixed at two ends and (b) model B—simply supported

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Fig. 2

Frequency versus iteration and optimal designs to maximize frequencies ω1 and ω2 of model A: (a) frequency versus iteration, (b) optimal design to maximize ω1, (c) frequency versus iteration, and (d) optimal design to maximize ω2

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Fig. 3

Frequency versus iteration and optimal designs to maximize ω1 and ω2 of model B (a = 1 and b = 8): (a) frequency versus iteration, (b) optimal design to maximize ω1, (c) frequency versus iteration, and (d) optimal design to maximize ω2

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Fig. 4

Frequency variations for maximizing (a) ω2 and (b) ω2-ω1 of model B (a = 1 and b = 10)

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Fig. 5

Optimal designs for maximizing (a) ω2 and (b) ω2-ω1 of model B (a = 1 and b = 10)

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Fig. 8

The Φ function surfaces for model A at (a) iteration 48, (b) iteration 49, (c) iteration 50, and (d) iteration 51

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Fig. 7

Optimization to maximize Λ in Eq. (19a) (i = 2, j = 3, and w3=0.1) for model B (a = 1 and b = 10): (a) frequency versus iteration and (b) optimal design to maximize Λ

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Fig. 6

Topology optimization to maximize Λ in Eq. (19a) for model A: (a) frequency versus iteration, (b) optimal design to maximize Λ (i = 1, j = 2, and w2=0.1), (c) frequency versus iteration, and (d) optimal design to maximize Λ (i = 2, j = 3, and w3=0.1)

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Fig. 19

Contours of eigenvector and translation for mode 1 of specimens 1–4: (a) eigenvector contour and translation of mode 1 for specimen 1 (F1 = 1296 Hz), (b) eigenvector contour and translation of mode 1 for specimen 2 (F1 = 1426 Hz), (c) specimen 3 (F1 = 89.21 Hz), and (d) specimen 4 (F1 = 72.19 Hz)

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Fig. 13

Optimal designs for the aluminum beamlike structure: (a) Vf = 0.5; αK1 = 0; F1 = 1204 Hz and (b) Vf = 0.5; αK1 = 0.8; F1 = 1347 Hz

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Fig. 12

Optimal topologies by using the Φ function with αK1= 0 and αK1= 0.3 for Vf=0.3 and Vf=0.4 : (a) Vf = 0.3; αK1 = 0; F1 = 49.2 Hz, (b) Vf = 0.3; αK1 = 0.3; F1 = 49.9 Hz, (c) Vf = 0.4; αK1 = 0; F1 = 51.5 Hz, and (d) Vf = 0.4; αK1 = 0.3; F1 = 55.6 Hz

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Fig. 17

The FFT input data-signals measured by using laser vibrometer: (a) and (b) sampling frequency: 8000 Hz and (c) and (d) sampling frequency: 400 Hz

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Fig. 18

Frequency spectrums computed by FFT: (a) fundamental frequency = 1168 Hz; (b) fundamental frequency = 1279 Hz; (c) fundamental frequency = 88.75 Hz; and (d) fundamental frequency = 70.22 Hz

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Fig. 14

Frequency variations and optimal design to maximize ω1 of an aluminum plate: (a) frequency versus iteration and (b) optimal design of a plate F1 = 125.5 Hz

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Fig. 15

Photos of specimens 1 and 2 where an arrow indicates a hitting position and light is emitted by the laser vibrometer: (a) specimen 1 for the optimal design of a beamlike structure (αK1 = 0) and (b) specimen 2 for the optimal design of a beamlike structure (αK1 = 0.8)

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Fig. 16

Experimental setup and specimens 3 and 4: (1) antivibration table (KS2210); (2) DC power supply (BK PECISION 1761); (3) data logger (NI cDAQ 9172/9221); (4) polytec CLV-1000 compact laser vibrometer; (5) specimen 3; and (6) specimen 4

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Fig. 11

The first-order frequency versus coefficient αK1 for Vf= 0.3, 0.4, and 0.5

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Fig. 10

Optimal topologies for different values of αK1: (a) αK1 = 0.1, (b) αK1 = 0.2, (c) αK1 = 0.3, (d) αK1 = 0.4, (e) αK1 = 0.5, and (f) αK1 = 0.54

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Fig. 9

Frequencies ω1–ω5 versus iteration for different values of αK1: (a) αK1 = 0.1; ω1 = 60.6 Hz, (b) αK1 = 0.2; ω1 = 62.5 Hz, (c) αK1 = 0.3; ω1 = 65.7 Hz, (d) αK1 = 0.4; ω1 = 67.8 Hz, (e) αK1 = 0.5; ω1 = 72.1 Hz, and (f) αK1 = 0.54; ω1 = 76.9 Hz

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