Abstract: The amplitude-frequency response characteristic of SD oscillator with fractional damping under harmonic excitation is studied，compared with the SD oscillator with integral damping. The Fourier equivalent model is proposed to solve the nonlinear stiffness of the differential equation of system motion，the problem of the nonlinear stiffness non-integrability of the differential motion equation of the system is solved. The expression of amplitude-frequency response is obtained by solving the differential equation of system motion using the average method. The stability of periodic solution is determined based on the Lyapunov stability theory and the Routh criterion. The correctness of the analytical method for amplitude-frequency response is verified by comparing with the numerical results. The result shows that the Fourier transform equivalent model of the nonlinear stiffness term of the SD oscillator can be applied to the motion characteristic of the system with large amplitude，which greatly improves the calculation accuracy. With the same damping coefficient，the amplitude-frequency response of the fractional damping system is different from that of the integral damping system，the resonance frequency and amplitude of the fractional damping system vary greatly. Changing the fractional coefficient will change the amplitude-frequency response backbone curve of the fractional damping system，but the integral damping system is not affected. When the fractional order is changed，the amplitude of the fractional damping system changes oppositely on both sides of the cut-off point.