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Earthquakes and Structures
  Volume 13, Number 5, November 2017, pages 465-471
DOI: http://dx.doi.org/10.12989/eas.2017.13.5.465
 


Fractional wave propagation in radially vibrating non-classical cylinder
Odunayo O. Fadodun, Olawanle P. Layeni and Adegbola P. Akinola

 
Abstract
    This work derives a generalized time fractional differential equation governing wave propagation in a radially vibrating non-classical cylindrical medium. The cylinder is made of a transversely isotropic hyperelastic John\'s material which obeys frequency-dependent power law attenuation. Employing the definition of the conformable fractional derivative, the solution of the obtained generalized time fractional wave equation is expressed in terms of product of Bessel functions in spatial and temporal variables; and the resulting wave is characterized by the presence of peakons, the appearance of which fade in density as the order of fractional derivative approaches 2. It is obtained that the transversely isotropic structure of the material of the cylinder increases the wave speed and introduces an additional term in the wave equation. Further, it is observed that the law relating the non-zero components of the Cauchy stress tensor in the cylinder under consideration generalizes the hypothesis of plane strain in classical elasticity theory. This study reinforces the view that fractional derivative is suitable for modeling anomalous wave propagation in media.
 
Key Words
    fractional wave; non-classical cylinder; radial vibration
 
Address
Odunayo O. Fadodun, Olawanle P. Layeni and Adegbola P. Akinola: Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005, Nigeria
 

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