An analytical criterion for jump phenomena in fractional Duffing oscillators

Abstract

This paper presents an analytical study on a general kind of fractional Duffing oscillators subjected to harmonic excitations. The Caputo-type fractional derivatives are transformed into improper double integrals by employing a memory-free principle. The integrals and the cubic stiffness are further handled by equivalent linearization. An equivalent linear equation is then deduced, based on which amplitude–frequency responses can be obtained analytically. According to the attained amplitude–frequency curve, we present an analytical criterion for jump phenomena of the oscillating amplitude due to varying excitation frequency. The analytical results are validated by numerical examples.