Research Papers

Attenuated Fractional Wave Equations With Anisotropy

[+] Author and Article Information
Mark M. Meerschaert

Department of Statistics and Probability,
Michigan State University,
East Lansing, MI 48824
e-mail: mcubed@stt.msu.edu

Robert J. McGough

Department of Electrical
and Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: mcgough@egr.msu.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 18, 2013; final manuscript received October 24, 2013; published online July 25, 2014. Assoc. Editor: Thomas J. Royston.

J. Vib. Acoust 136(5), 050902 (Jul 25, 2014) (5 pages) Paper No: VIB-13-1115; doi: 10.1115/1.4025940 History: Received April 18, 2013; Revised October 24, 2013

This paper develops new fractional calculus models for wave propagation. These models permit a different attenuation index in each coordinate to fully capture the anisotropic nature of wave propagation in complex media. Analytical expressions that describe power law attenuation and anomalous dispersion in each direction are derived for these fractional calculus models.

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