3D nonlinear variable strain-rate-dependent-order fractional thermoviscoelastic dynamic stress investigation and vibration of thick transversely graded rotating annular plates/discs

• Published in: Applied Mathematical Modelling 2020-08, Vol.84, p.287-323
• Main Authors: Shariyat, M., Mohammadjani, R.
• Format: Article
• Language: English
• Subjects: 3D theory of elasticity; 3D vibration; Annular disc; Annular plates; Damping; Differential equations; Dynamic stress analysis; Finite difference method; Investigations; Mathematical analysis; Nonlinear equations; Strain rate; Stress concentration; Thermoviscoelasticity; Thick plates; Transverse loads; Transverse oscillation; Variable-order fractional viscoelasticity; Vibration analysis
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.03.023

•A novel solution scheme is proposed for fractional-order differential equations.•3D dynamic stress and vibration analyses of the circular/annular discs is made.•The considered fractional-order-viscoelastic disc is under nonuniform loads.•The exact 3D theory of elasticity rather than the approximate plate theories is employed.•A comprehensive sensitivity analysis and quite new results are presented. In the present article, the idea of using the variable-order fractional-derivative thermoviscoelastic constitutive laws in dynamic stress and vibration analysis of the engineering structures, the required implementation backgrounds, and the relevant numerical solution procedures are investigated for the first time. In this regard, dynamic 3D stress and displacement fields and radial/transverse vibrations of transversely graded viscoelastic spinning thick plates/discs exposed to sudden thermoelastic loads are investigated. Instead of using the approximate plate theories, the exact thermoviscoelasticity theory is employed in the development of the governing equations. Since the variable fractional order is dependent on the localized deformation rates, the resulting thermoviscoelastic integro-differential equations are nonlinear. These equations are solved by utilizing a combination of the second-order backward/central/forward finite difference discretization of the spatial and time domains, numerical evaluation and updating of the Caputo-type fractional derivatives, updating the growing number of terms of the governing equations, and Picard's iterations. Various edge conditions are considered. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed regarding the effects of the variable fractional order of the constitutive law, time variations of the nonuniformly distributed transverse loads, and edge conditions on the distributions and damping of the resulting displacement and stress components.