Dynamics of a mechanical system with a spherical pendulum subjected to fractional damping: analytical analysis

Abstract In the paper, nonlinear vibrations of a system with three degrees freedom having spherical pendulum are considered. The comprises mass element suspended from linear spring and viscous damper, swung element. It is assumed that fractional damping occurs in damper at pivot point. viscoelastic properties to be described using Riemann–Liouville derivative. derivative an order $$ 0 < \alpha \le 1$$ 0 < α ≤ 1 assumed. near internal external resonances analyzed. equations motion analyzed solved multiple-scale method. steady-state approximate solution studied. effect fractional-order on examined.