On Frequency Dependence of Stability in Materials with Fractional Viscosity

Material instability refers to the tendency of materials to undergo alterations in its 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 by adding 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 strain or stress tensors. The stability analysis primarily focuses on periodic perturbations. The way of the loss of stability on various parts of the stability boundary is under consideration.