Typical turbofan engine-support-structure systems having a high thrust-to-weight ratio are light, and the structure primarily comprises a plate and shells. The local vibration response of the support structure is excessively large when different frequency loads are applied. A structural vibration response control method based on dry friction damping is proposed to control the excessive vibration response. A dry friction damper with dynamic suction was designed to enhance the damping characteristics of the rotor supporting structure system in the wide frequency domain, without sacrificing the dynamic stiffness of the structure. The system is designed to effectively control the vibration response of the supporting structure at the working-speed frequency. Through theoretical modeling and simulation analyses, the influence of friction contact and damper structure characteristics on the damping effect is described quantitatively. Furthermore, the design idea and the damping process of the supporting structure are described. The calculation results show that the contact friction of the dry friction damper can consume the vibration energy of the supporting frame. A reasonable design of the contact characteristics and geometric configuration parameters of the damper can further optimize the vibration-reduction effect, and thereby improve the vibration response control design of the supporting structure system of aeroengines.