On Frequency Dependence of Stability in Materials with Fractional Viscosity

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Abstract

Material instability refers to the tendency of materials to undergo alterations in their properties in loading. The concept of instability is governed by the constitutive equation of solids. Our analysis uses the entire set of equations describing the motion of solids, including the kinematical equation and Cauchy’s equations of motion. Damping, or rate-dependence, plays a crucial role in stability. A potential generalization involves the utilization of fractional-order derivatives of the strain or stress tensors. The stability analysis primarily focuses on periodic perturbations. The mechanism of loss of stability on various parts of the stability boundary is under consideration.

Keywords:

applied fractional calculus, material instability, dynamical systems

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