Seven-Parameter Linear Viscoelastic Model Applied to Acoustical Damping Materials

Abstract

In this paper, linear viscoelastic rheological properties of acoustical damping materials are predicted. A rheological model, based on a mechanical element approach, is presented. It consists of a combination of Two Springs, Two Parabolic elements and One Dashpot (2S2P1D). This model is applied to different acoustical damping materials. Its specificity comes from the fact that elements might be linked to structural and physical features. Parameters might be experimentally determined by tests. Application of the 2S2P1D linear viscoelastic model can adequately predict the behavior of acoustical damping materials with good accuracy. If the material verifies the time-temperature superposition principle the proposed model can predict the behavior on a wide frequency range, even with a small number of available data. IntroductionNowadays, acoustical foams [1-4] and acoustical composite materials [5] are widely used for sound and vibration damping in building or automotive applications. To suppress vibrations, viscoelastic materials are usually placed on the surfaces of structures. To predict the responses of the damped structure and to design it, it is important to know the properties of the foams in the frequency range relevant to their application, so in a wide frequency range for acoustic applications. Biot's theory [6] is used to describe the dynamic behavior of porous medium when the skeleton is set in motion. This theory uses the viscoelastic properties of the solid phase. Moreover, it must be underlined that the viscoelastic properties of these acoustic foams are strongly frequency and temperature dependent as emphasized by lots of experimental works on the subject [7-13]. To describe the frequency and temperature dependence efficiently, computerized numerical methods require a mathematical model on the dynamic properties. To experimentally determine those viscoelastic properties of acoustical foams different techniques are used and explained in literature. They are mainly based on mass-spring resonance [10], standing wave resonance of a longitudinally excited rod with end mass [10] or based on nonresonant techniques [11,14]. An extension of certain measurements on a wide frequency range can be performed by using the time-temperature superposition principle as done by [15]. So a theoretical modelization of the viscoelastic behavior of foams is needed to enhance the frequency range. For all those reasons, a mathematical form of frequency dependences of dynamic properties is required. Modelling the viscoelastic behavior is an old problem not only in damping polymer materials but also in the field of bituminous materials [16][17][18]. Empirical models have been used [19,20] but the disadvantages of empirical models are that they are not related to the general constitutive equation of viscoelastic materials and it is difficult to understand the physics. Moreover, to apply a mathematical model to damping material, the model parameters should be easily estimated through experiments. In many existing models, those para...

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“…The 2S2P1D model, whose name comes from the abbreviation of the combination of two Springs, two Parabolic creep element and one Dashpot [33,34], is used for the description of the rheological properties of the viscoelastic material. The complex modulus E Ã is estimated by…”

Multi Modal Dynamic Linear Viscoelastic Back Analysis for Asphalt Mixes

“…The tension-compression tests results were analyzed using the 2S2P1D LVE model developed at ENTPE [20][21][22]. It consists of a combination of two springs, two parabolic creep elements (also called fractional-derivative model [23]) and one dashpot as schematized in the 1-dimension case in Fig. 3.…”