Steady Periodic Response for A Vibration System With Distributed Order Derivatives to Periodic Excitation

Abstract

Steady-state periodic responses for a vibration system with distributed order derivatives are investigated, where the fractional derivative operator -infinity D-t(beta) is utilized. The response to complex harmonic excitation is derived and the amplitude-frequency and phase-frequency relations are obtained. For a periodic excitation, we decompose it into the Fourier series, and then make use of the principle of superposition and the results of harmonic excitations to obtain the response. Finally, we examine three numerical examples by using the proposed method.