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A causal fractional derivative model for acoustic wave propagation in lossy media

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Abstract

This study proposes a dissipative acoustic equation in time-space domain including fractional derivative to describe the characteristic impedance and the propagation coefficient, which has been observed in an experimental study on the fibrous absorbent materials by Delany and Bazley. The parameters of characteristic impendence are obtained by fitting experimental data. The present fractional derivative model can be deduced by characteristic impendence, continuity equation, and state equation, of which the fractional order possesses clear physical meaning of the acoustical properties for porous materials. The attenuation and dispersion functions of the present model obey the Kramers–Kronig relation and agree well with the experimental results, where the fractional order is found to be 0.63 via data fitting. Finally, the proposed model is applied to normal incidence energy absorption aiming at investigating the effect of fractional order on the absorption coefficient with respect to the wave frequency. According to the power-law dissipative relationship, the fractional order in the present wave model ranges from 0 to 1.

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Acknowledgments

This work was supported the National Science Funds for Distinguished Young Scholars (11125208) and the 111 Project (Grant No. B12032).

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 210098, People’s Republic of China

    Wen Chen, Shuai Hu & Wei Cai

  2. China Construction Steel Structure Co. Ltd., Shenzhen, 518040, Guangdong, People’s Republic of China

    Shuai Hu

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  1. Wen Chen
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  2. Shuai Hu
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  3. Wei Cai
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Correspondence to Wen Chen.

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Chen, W., Hu, S. & Cai, W. A causal fractional derivative model for acoustic wave propagation in lossy media. Arch Appl Mech 86, 529–539 (2016). https://doi.org/10.1007/s00419-015-1043-2

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