A new time fractional wave propagation in a solid cylinder

Abstract eng:
This study considers radial vibration of transversely-isotropic solid cylinders with a view to model the mechanical diffusive waves propagating in the bodies. The effect of finite deformation is investigated. The problem is described by state equation of motion taking into account the Khalil et al. fractional order derivatives. The obtained time fractional wave equation and its solution generalize some results in literature. It is shown that waves in finite deformation exhibit some additional term even in the absence of time fractional operator. Furthermore, the obtained results degenerate to the classical waves in solid cylinders. Finally, this study reinforces the view that factional derivative helps to apprehend processes in-between diffusion and wave propagation.

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