Approximate Solutions and Stability Analysis of Single and Two Degree of Freedom Systems With Fractional Damping

Abstract

In this study, the two frequency excitation oscillations of system having quadratic nonlinearities with fractional damping is considered via Riemann-Liouville fractional derivative. The system is assumed under the effect of external harmonic force. The approximated first-order uniform expansion of the dynamic response is derived for nonlinear forced oscillations of systems by employing a perturbation technique; that is, the method of multiple scales. The damping term is also assumed in a linear form. Perturbation is a well-known technique gives approximate analytical solutions [1-3]. It is frequently preferred for equations that cannot be found analytically solutions, such as equations involving nonlinearity and fractional derivatives. In this research, perturbed solutions are examined for the system. The effects of the coefficient of a fractional damping term on the approximate solution are observed by graphs.