title: A fractional calculus model of anomalous dispersion of acoustic waves.
abstract: An empirical formula based on viscoelastic analysis techniques that employs concepts from the fractional calculus that was used to model the dielectric behavior of materials exposed to oscillating electromagnetic fields in the radiofrequency, terahertz, and infrared bands. This work adapts and applies the formula to model viscoelastic behavior of materials that show an apparent increase of phase velocity of vibration with an increase in frequency, otherwise known as anomalous dispersion. A fractional order wave equation is derived through the application of the classic elastic-viscoelastic correspondence principle whose analytical solution is used to describe absorption and dispersion of acoustic waves in the viscoelastic material displaying anomalous dispersion in a specific frequency range. A brief discussion and comparison of an alternative fractional order wave equation recently formulated is also included.
authors.affiliation: 711th Human Performance Wing, Airman Systems Directorate, Bioeffects Division, Optical Radiation Bioeffects Branch, 4141 Petroleum Road, JBSA, Fort Sam Houston, Texas 78234, USA.
authors.forename: Andrew W
authors.initials: AW
authors.lastname: Wharmby