Stress and power as a response to harmonic excitation of a fractional anti-Zener and Zener type viscoelastic body

Abstract

The stress as a response to strain prescribed as a harmonic excitation is examined in both transient and steady state regime for the viscoelastic body modeled by thermodynamically consistent fractional anti-Zener and Zener models by the use of the Laplace transform method. Assuming strain as a sine function, the time evolution of power per unit volume, previously derived as a sum of time derivative of a conserved term, which represents the rate of change of stored energy, and a dissipative term, which represents dissipated power, is investigated when expressed through the relaxation modulus and creep compliance. Further, two forms of energy and two forms of dissipated power per unit volume are examined in order to see whether they coincide.