This paper examines the oscillatory behavior of complex viscoelastic systems with power law like relaxation behavior. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot… Click to show full abstract
This paper examines the oscillatory behavior of complex viscoelastic systems with power law like relaxation behavior. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which produces a power-law creep behavior and a relaxation law following the Mittag-Leffler function. The fractional dashpot is characterized by a parameter β, continuously moving from the pure viscous behavior when β = 1 to the purely elastic response when β = 0. In this work, we study the general response function and focus on the oscillatory behavior of a fractional Maxwell system in four regimes: Stress impulse, strain impulse, step stress, and driven oscillations. The solutions are presented in a format analogous to the classical oscillator, showing how the fractional nature of relaxation changes the long-time equilibrium behavior and the short-time transient solutions. We specifically test the critical damping conditions in the fractional regime, since these have a particular r...
               
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