Mechanical characterisation of acoustic foams: fractional derivatives approach

Generalized constitutive relationships of viscoelastic foams are investigated in which the time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification of such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the three-parameter fractional Kelvin Voigt model is compared to the four-parameter fractional Zener model in frequency domain and applied to the prediction of the relaxation function in time domain. These three-parameter and four-parameter models are theoretically analyzed in time domain. The fitted storage and loss moduli over wide range of frequency, up to 10 kHz, can be used in the Biot poroelasticity theory to predict the sound absorption coefficient of the foam.