Time-Dependent Decay Rate and Frequency for Free Vibration of Fractional Oscillator

Abstract

This paper presents an investigation on the free vibration of an oscillator containing a viscoelastic damping modeled by fractional derivative (FD). Based on the fact that the vibration has slowly changing decay rate and frequency, we present an approach to analytically obtain the initial decay rate and frequency. In addition, ordinary differential equations governing the decay rate and frequency are deduced, according to which accurate approximation is obtained for the free vibration. Numerical examples are presented to validate the accuracy and effectiveness of the presented approach. Based on the obtained results, we analyze the decay rate and the frequency of the free vibration. Emphasis is put on their time-dependence, indicating that the decay rate decreases but the frequency increases with time increasing.

Damage Detection in a Fibre Reinforced Polymer Component by the Vibration Decay Rate

“…Where f is the mid frequency of a third octave band in Hz, RT 60 is the decay rate for each third octave mid frequency in s. The value of 2, 2 can be derived from the energy drop to the one millionth of the initial value [21,22].…”