A new optimized quality factor Q for a general class of the Zener viscoelastic model

The modeling of wave propagation in viscoelastic media often depends on the choice of appropriate relaxation functions. The latter describe the energy decay constraint in the time domain and approximate the quality factor, Q, in terms of rational functions. Thus, the challenge is to obtain physically significant relaxation functions depending on the optimal Q. In this paper, we propose a new Generalized Fractional Zener Model (GFZM) to simulate an almost constant Q. The new method is based on nonlinear constrained optimization methods with fractional order optimization. As a result, we obtain an optimal approximation of the quality factor Q. It will be shown that the method is efficient as the almost constant Q approaches the function of frequency.