Thin-walled structures are crucial components in large-scale aerospace applications, where the inherent low stiffness due to minimal thickness frequently induces self-excited vibration during machining. For addressing severe vibration and deformation at milling points, a mechanism of integrating local stiffness supplement with targeted vibration reduction through resonance is proposed for the first time. Accordingly, a semi-active electromagnetic vibration attenuation device, leveraging magnetic follow-up support technology, is reasonably designed and systemically studied for non-magnetic thin-walled workpieces. The adjustment regulation, dynamics and modal properties are analytically investigated and experimentally validated, and the nonlinear characteristics are investigated by harmonic balance method with arc length continuation. The six machining cases involve three spindle speeds and two machining paths, which demonstrate that the proposed device effectively cooperates with follow-up support fixtures and functions at multiple spindle speeds and milling positions. This facilitates notable enhancement in machining quality, evidenced by an average reduction of 29.85% in RMS vibration signals and 51.52% in resonance-peak amplitudes. Improvements in surface roughness and machining depth are also observed. Characterized by its compact structure, extensive adjustable ranges, and robust vibration suppression capabilities, the device has unique advantages to adapt to position-dependent parameters across broad spindle speed ranges. Therefore, it provides a flexible and feasible solution for further improving machining stability, and has practical potential in mechanical processing and manufacturing.