An analytical criterion for jump phenomena in fractional Duffing oscillators

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.