This paper investigates the primary and subharmonic simultaneous resonance of a fractional cerebral aneurysm model with double-frequency excitation proposed in [16]. Using the multiple scale method, the amplitude-frequency equation of simultaneous resonance is obtained. Comparison between approximate analytical solution and numerical solution is discussed. The influence of parameters on the system response is analyzed, especially the influence of damping coefficient on the simultaneous resonance is discussed. It is further verified that the new parameter \(\kappa\) , a combination of the nonlinear stiffness coefficients and the linear natural frequency, plays an important role in creating typical hardening or softening characteristics.
