A New Empirical Model for Predicting the Sound Absorption of Polyfelt Article

A New Empirical Model for Predicting the Sound Absorption of Polyfelt Fibrous Materials for Acoustical Applications - Article Example Empirical models do not require detailed knowledge of the internal structure of the material nor are they derived from theoretical considerations. Delany and Bazley [1] showed that the values of the characteristic acoustic impedance and propagation coefficient for a range of fibrous materials, normalized as a function of frequency divided by flow resistivity could be presented as simple power law functions. Model for Impedance The model is based on numerous impedance tube measurements and is good for determining the bulk acoustic properties at frequencies higher than 250 Hz, but not at low frequencies [2,3]. The validity of this model for lower and higher frequencies was further extended by Bies and Hansen [4].Dunn and Davern [5] calculated new regression coefficients between characteristic acoustic impedance and propagation coefficient for low airflow resistivity values of polyurethane foams and multilayer absorbers. To that effect, engineers can obtain the absorption coefficient of sound at normal incidence by using the equation below: ZR = P0 * C0 (1 + C1 ((P0f)/r)-c2) The final model which comes as a derivative of the first model is Zt = (ZR + iZl)[coth(a + iB) * l] Zt = ZIR + iZIl Qunli [6] later extended this work to cover a wider range of flow resistivity values by considering porous plastic open-cell foams.Miki [7, 8] generalized the empirical models developed by Delany and Bazley for the characteristics acoustic impedance and propagation coefficient of porous materials with respect to the porosity, tortuosity, and the pore shape factor ratio. Moreover, he showed that the real part of surface impedance computed by the Delany’s model converges to negative values at low frequencies. Therefore, he modified the model to give it real positive values even in wider frequency ranges. Other empirical models include those of Allard and Champoux [9]. These models are based on the assumption that the thermal effects are dependent on frequency. The models wor k well for low frequencies. The Voronina model [10] is another simple model that is based on the porosity of a material. This model uses the average pore diameter, frequency and porosity of the material for defining the acoustical characteristics of the material. Voronina [11] further extended the empirical model developed for porous materials with rigid frame and high porosity, and compared it with that of Attenborough's theory. A significant agreement was found between their empirical model and Attenborough's theoretical model. Recently, Gardner et al. [12] implemented a specific empirical model using neural networks for polyurethane foams with easily measured airflow resistivity. The algorithm embedded in the neural networks substitutes the usual power-law relations. The phenomenological models are based on the essential physics of acoustic propagation in a porous medium such as their universal features and how these can be captured in a model [13]. Biot [14] established the theo retical explanation of saturated porous materials as equivalent homogeneous materials. His model is believed to be the most accurate and detailed description till now. Among the significant refinement made to Biot theory, Johnson et al. [15] gave an interpolation formula for â€Å"Dynamic tortuosity† of the medium based on limiting behavior at zero and infinite frequency. The dynamic tortuosity employed by Johnson et al. is equivalent to the structure factor introduced by Zwikker and Kosten [16] and therefore