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Research Papers

Optimization Based Identification of the Dynamic Properties of Linearly Viscoelastic Materials Using Vibrating Beam Technique

[+] Author and Article Information
Zhiyong Ren

Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, CanadaZhiyong.Ren@USherbrooke.ca

Noureddine Atalla

Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, CanadaNoureddine.Atalla@USherbrooke.ca

Sebastian Ghinet

Aeroacoustics and Structural Dynamics, Institute for Aerospace Research, National Research Council, 1200 Montreal Road, Building U-66A, Ottawa, ON, K1A 0R6, Canadasebastian.ghinet@nrc-cnrc.gc.ca

J. Vib. Acoust 133(4), 041012 (Apr 11, 2011) (12 pages) doi:10.1115/1.4003594 History: Received February 16, 2010; Revised November 08, 2010; Published April 11, 2011; Online April 11, 2011

Sandwich structures with viscoelastic core and metal face sheets are increasingly used in automotive industry to significantly reduce the amplitude of vibration and noise radiation. Several experimental methods such as dynamic mechanical analysis (DMA) and vibrating beam technique (VBT) are used to characterize the dynamic properties of viscoelastic materials as a function of frequency and temperature. This paper investigates the use of a free-free beam setup, as an alternative solution to the classical clamped-free VBT, for a better control of the effect of boundary conditions on the laminated steel specimen. The new setup is developed in combination with a frequency response function based optimization method, to automatically derive the dynamic properties of viscoelastic core materials and generate their master curves. A solver based on the normal mode superposition method, considering the added mass effect of the impedance head, is used in the cost function of the optimization approach. The sandwich model is based on the Ross–Kerwin–Ungar equation, and the four-parameter fractional derivative model is used in conjunction with the Williams–Landel–Ferry equation to describe the frequency and temperature dependent behavior of the viscoelastic material. The master curves are a direct result of the optimization process. Several applications are described to assess the performance of the present method. In particular, a systematic comparison with both the classical VBT and DMA (when available) is presented.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Diagram of the proposed experimental setup: (a) for bare beam, (b) for sandwich beam, and (c) for added mass

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Figure 2

Frequency dependent complex added mass: (a) amplitude and (b) phase

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Figure 3

Measured and corrected input mobilities at 30°C: (a) bare beam and (b) sandwich beam

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Figure 4

Free-free boundary for beam with added mass and concentrated force at the middle point of the beam

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Figure 5

Comparison of the standard and proposed methodologies

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Figure 6

Comparison of master curves of reference, optimization and standard results: (a) core shear modulus and (b) core loss factor (reference: ○, optimization: ◻, and standard:  ∗)

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Figure 7

Comparison of input mobilities of experimental, optimization, and standard results: (a) 0°C and (b) 20°C (reference: solid line; optimization: – – –, and standard: ……)

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Figure 8

Master curves of core material in C: (a) core shear modulus and (b) core loss factors (○ and ◻ represent the core properties from optimization and standard, respectively)

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Figure 9

Simulated and experimental input mobilities: (a) 8°C and (b) 24°C (experimental: solid line, optimization: ……, and standard: – – – )

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Figure 10

Master curves of core material in C: (a) core shear modulus and (b) core loss factors (○ and  ∗ represent the core properties from optimization and standard, respectively)

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Figure 11

Simulated and experimental input mobilities: (a) 16°C and (b) 32°C (experimental: solid line, optimization: ……, and standard: – – –)

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Figure 12

Master curves of material D: (a) core shear modulus and (b) core loss factors (optimization:  ∗, standard: ○, and DMA: ◻)

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Figure 13

Experimental and simulated input mobilities at typical temperatures: (a) 0°C and (b) 40°C (experimental: solid line, optimization: …, standard: – – –, and DMA: – . –. –)

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