Abstract
By extension of the generalized Lord-Shulman (LS) theory to multi-rational-order thermo-viscoelastic spinning annular discs with fractional-order constitutive and heat conduction models, the propagation and interference of the temperature, displacement, and stress waves are studied here under various thermomechanical boundary conditions. A novel finite-element-based numerical iterative time marching technique is developed for the solution of the resulting nonlinear coupled multi-rational-order integrodifferential equations with accumulated terms whose number grows within each time step. The wave interference phenomenon due to simultaneous opposite shocks has not been investigated so far, even for the integer-order thermo-viscoelastic models. Results of the present multi-rational-order thermo-viscoelasticity are compared with those of the integer-order classical and LS thermo-viscoelastic models. Results show that the traction-type tensile and compressive shocks lead to local temperature reduction and rise, respectively, at the wavefront location. Although the thermal and constitutive fractional orders both increase the inertia and damping of the resulting system, the former affects the temperature rise and overshoot, and thermal memory effect and wave lag, whereas the latter affects the mechanical damping and oscillatory nature of the displacements and stresses more remarkably. Indeed, the thermal fractional-order represents an integrated thermal inertia-damping combination whereas the constitutive fractional-order leads to an integrated damping-stiffness combination.
Published Version
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