Fractional derivatives model to predict high frequency moduli of acoustic foams

Abstract eng:
This paper presents a time domain method to determine viscoelastic properties of open-cell foams on a wide frequency range. This method is based on the adjustment of the stress-time relationship, obtained from relaxation tests on polymeric foams samples under static compression, with the four fractional derivatives Zener model. The experimental relaxation function, well described by the Mittag-Leffler function, allows to predict straightforward the frequency-dependence of complex modulus of polyurethane foams. A curve was reconstructed on the reduced frequency range (0.1Hz – 1 MHz) using the time-temperature superposition principle. Very good agreement was obtained between experimental complex moduli values and the fractional Zener model predictions. The proposed time domain method may constitute an improved alternative to resonant and non-resonant techniques often used for dynamic characterization of polymers for the determination of viscoelastic moduli on a broad frequency range.

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