Free damped vibrations of a viscoelastic oscillator based on Rabotnov’s model

Abstract

Free damped vibrations of a linear viscoelastic oscillator based on Rabotnov’s model involving one fractional parameter and several relaxation (retardation) times are investigated. The analytical solution is obtained in the form of two terms, one of which governs the drift of the system’s equilibrium position and is defined by the quasi-static processes of creep occurring in the system, and the other term describes damped vibrations around the equilibrium position and is determined by the systems’s inertia and energy dissipation. The drift is governed by an improper integral taken along two sides of the cut of the complex plane. Damped vibrations are determined by two complex conjugate roots of the characteristic equation, which are located in the left half-plane of the complex plane. The behaviour of the characteristic equation roots as function of the system’s parameters is shown in the complex plane.