Ultra-long beam structure has large vibration frequency span. To control the wide frequency vibration of ultra-long beam structures， amplitude-enhanced dynamic vibration absorbers with damping are arranged periodically on the beam. The amplitude magnification device artificially magnifies the amplitude at the controlled point， thereby increasing the operating ability of the ab sorber. To be able to consider the effect of damping， a complex band structure analysis model is established， and a new complex band structure calculation method is proposed based on the artificial spring model and the energy method. This method is used to analyze the effect of amplification device type， absorber damping and magnification factor on the complex band structure in detail. The effect of the relative position of the connection points of the ungrounded magnification device on its vibration damping perfor mance is studied. The results show that the magnitude amplification device type， absorber damping and magnification factor have great influence on the complex band structure. The suitably relative position can significantly improve the working ability of the un grounded magnification device.