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To reveal the failure mechanism of resonance effect on long-periodic structures, the spectrum characterization of nonlinear and non-stationary long-periodic ground movements are studied. Firstly, the period and energy characterizations about IMFs (intrinsic mode functions) of ground movements are analyzed. Then, an energy-weighted average period is proposed to indicate the long-periodic characterization on different types of ground movements. Lastly, the simplified method on the low-frequency time history for long-periodic ground movements is proposed and verified. The research conclusions show that, various Hilbert amplitude spectra analysis can expose all the inherent information of nonlinear and non-stationary long-periodic ground movement accurately and comprehensively. The proposed periodic parameter that characterizes different earthquake classifications can help to efficiently and conveniently filter out long-period ground movements, and it also can be used as a quantitative indicator to identify long-period ground movements. The suggested simplified method can facilitate in-depth and accurate analysis of the low-frequency components of long-periodic ground movements. Effective and accurate evaluation on the low-frequency components of long-periodic ground movements plays the key role to uncover the nonlinear dynamic behavior of long-periodic structures, and it is of great scientific research significance in the field of earthquake engineering and structural engineering. • The spectrum characterizations of long-periodic ground movement can make up for the deficiencies of linear signals analysis. • The suggested periodic parameter can be used as a quantitative indicator to identify long-period ground movements. • The proposed simplified method can facilitate in-depth and accurate analysis on the long-periodic ground movements. [ABSTRACT FROM AUTHOR]