Analyses of oscillators with non-polynomial damping terms

In this paper the properties of the oscillatory motion of the system with non-polynomial damping is investigated. The two limits for damping are the dry friction and linear viscous damping. The mathematical model of the system is a strong nonlinear differential equation with fraction order velocity terms. Using the modified version of Heʹs homotopy perturbation method the approximate analytic solution is obtained. The generating solution is assumed in the form which corresponds to the system with linear viscous damping. Two special cases are considered: first, when the coefficient of the damping force is small and second, when the damping force is close to dry friction. The obtained analytical solutions are compared with numerical ones. They show good agreement.