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Computers and Concrete
  Volume 23, Number 5, May 2019 , pages 303-309
DOI: https://doi.org/10.12989/cac.2019.23.5.303
 


Analysis of axisymmetric fractional vibration of an isotropic thin disc in finite deformation
Odunayo O. Fadodun

 
Abstract
    This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy\'s stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.
 
Key Words
    axisymmetric; finite deformation; fractional vibration; thin disc
 
Address
Odunayo O. Fadodun: Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005, Nigeria
 

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