Fractional derivative viscoelastic model for frequency-dependent complex moduli of automotive elastomers
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Fractional derivative viscoelastic model for frequency-dependent complex moduli of automotive elastomers Y. Charles Lu
Received: 4 March 2007 / Accepted: 19 July 2007 / Published online: 1 August 2007 Springer Science+Business Media B.V. 2007
Abstract Finite element modeling has been used extensively nowadays for predicting structural vibration and noise radiation of automobile engines and subsystems. However, many elastomeric components on the engines or subsystems are often omitted in the FE models due to primarily the lack of material properties at higher frequencies. The present paper describes a form of fractional derivative viscoelastic model for characterizing frequency-dependent complex moduli of elastomers. The model is used to predict the high frequency complex moduli of some fluoroelastomers with varying durometers. Excellent correlations between testing and prediction are obtained. Keywords Viscoelasticity Elastomer Fractional derivative model Complex modulus Dynamic mechanical analysis
1 Introduction Finite element (FE) modeling has been used extensively in designing automobile engines and subsystems for predicting structural vibration and
Y. C. Lu (&) Department of Mechanical Engineering, University of Kentucky, 4810 Alben Barkley Drive, Paducah, KY 42002, USA e-mail: [email protected]
noise radiation. However, one of the key components is often omitted in the FE models: the elastomer seals and gaskets at the interfaces (Michel et al. 2001; Lu and D’Souza 2004; Zubeck and Marlow 2003). These elastomer components are used primarily to seal the interfaces of engine components to prevent the fluid from leaking, thus much of the design consideration has been given to the sealibility aspect. Due to their excellent damping characteristics, the elastomer components also have the abilities to reduce vibration and noise radiation. Thus, there have been increased demands lately that these components be included in the FE models so that the noise and vibration performance of the engines and subsystems can be predicted accurately (Hong et al. 2001; Lu and D’Souza 2004; Zouani 2006; Zubeck and Marlow 2003). One of the reasons for omitting elastomer components in FE models is the lack of dynamic properties of these components at higher frequencies. For the design of automobile engines and subsystems, the frequency of interest is typically in the range of several thousand hertz. The frequency-dependent dynamic properties of elastomers can be measured through conventional dynamic mechanical analyzer (DMA). The DMA tests elastomer samples in simple deformation modes such as tension, compression or shear with a sinusoidal excitation, from which the complex modulus and damping are measured. However, limited by the resonant responses of the testing jigs, the DMA only yields properties in the frequency range of a couple of hundred hertz (Lake 2004).
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Elastomeric materials exhibit frequency dependent viscoelastic property which is generally characterized by the complex modulus E*x Ex ¼ E0x þ i
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