Fractional damping in a monoatomic chain with cubic nonlinearity

Abstract

In this communication, we show the model of a nonlinear periodic chain with fractional-order damping included. The model includes point masses connected through cubic nonlinear and linear springs and fractional spring-pot elements. The motion equation is solved by using the first-order multiple scales perturbation analysis. The case with weak nonlinearity and damping is observed and the corresponding dispersion equation derived. A parametric study is performed to examine the effects of different parameters on dispersion curves. Given the wavenumber, the cubic nonlinearity and fractional damping parameter have shown to produce lower frequencies than the corresponding undamped linear system.