Mechanical energy and mean equivalent viscous damping for SDOF fractional oscillators

TL;DR

This paper derives an expression for the total mechanical energy of a fractional oscillator, analyzes energy flow during vibration, and introduces a new concept of mean equivalent viscous damping based on fractional damping properties.

Contribution

It presents the first formulation of total mechanical energy for fractional oscillators and proposes a novel mean equivalent viscous damping concept.

Findings

Energy regeneration and loss during vibration are quantified.

A new method to evaluate damping coefficient in fractional oscillators.

The concept of mean equivalent viscous damping is introduced.

Abstract

This paper addresses the total mechanical energy of a single degree of freedom fractional oscillator. Based on the energy storage and dissipation properties of the Caputo fractional derivatives, the expression for total mechanical energy in the single degree of freedom fractional oscillator is firstly presented. The energy regeneration due to the external exciting force and the energy loss due to the fractional damping force during the vibratory motion are analyzed. Furthermore, based on the mean energy dissipation of the fractional damping element in steady-state vibration, a new concept of mean equivalent viscous damping is suggested and the value of the damping coefficient is evaluated.