Influences of temporal evolution of ground motion frequency content on developed dynamic ratcheting in SDOF systems

Document Type: Full Length Article


1 MSc Ministry of Roads & Urban Development, Kermanshah, Iran

2 Associate Professor Department of Civil Engineering, Razi University, Kermanshah, Iran



Dynamic Ratcheting (DR) is a nonlinear dynamic phenomenon occurring in hysteretic damping systems. It means the structural plastic deformation increases asymmetrically in successive cycles under an earthquake excitation. Although it is generally recognized that DR is closely related to the frequency contents of an earthquake excitation applied to the
structure, no targeted analysis has been conducted on the influence of time- varying frequency content on occurrence and development of DR. This manuscript aims to analyze the influence of time evolution of DR-inducing ground motion frequency content on developed DR phenomenon in the Single Degree-Of-Freedom (SDOF) system with the Elastic-Perfectly-Plastic (EPP) hysteretic behavior. To survey the influence of time evolution of ground motion frequency
content on the developed DR: In the first step, the three DR-inducing ground motion records were selected as excitations input of EPP SDOF systems. In the second step, time-varying frequency of ground motions were changed by shifting their
frequency content  forward or backward in time using wavelet transform to produce altered versions records. In the final step, the displacement responses of EPP SDOF systems under selected records and their altered versions were compared. By analyzing the displacement response of EPP SDOF systems excited by selected ground motions and their altered versions, it can be found that the time-varying frequency content considerably influences the developed DR behavior in SDOF systems. In the selection of records for dynamic analysis of structures, time-varying frequency content could be further considered as an important characteristic variable for ground motion records.


  • SDOF hysteretic damping with EPP behavior is defined for systems under earthquake excitation.
  • Wavelet analysis is used to identify active frequencies and temporal localization of excitation.
  • Effect of ground motions on the DR behavior is investigated using the time shift technique.
  • Temporal localization of active frequencies is found having significant effects on DR behavior.


Main Subjects

[1] C.-H. Yeh, Y.K. Wen, Modeling of nonstationary ground motion and analysis of inelastic structural response, Structural Safety, 8 (1990) 281-298.

[2] J.P. Conte, K.S. Pister, S.A. Mahin, Nonstationary ARMA modeling of seismic motions, Soil Dynamics and Earthquake Engineering, 11 (1992) 411-426.

[3] W.u. Zuo-ju, Z. Jian-jing, W. Zhi-jia, W. Xing-xu, W. Ming-yuan, Time-frequency analysis on amplification of seismic ground motion, ROCK AND SOIL MECHANICS, 38 (2017) 685-695.

[4] X. Li, Z. Li, E. Wang, J. Feng, X. Kong, L. Chen, B. Li, N. Li, Analysis of natural mineral earthquake and blast based on Hilbert–Huang transform (HHT), Journal of Applied Geophysics, 128 (2016) 79-86.

[5] D. Wang, Z. Fan, S. Hao, D. Zhao, An evolutionary power spectrum model of fully nonstationary seismic ground motion, Soil Dynamics and Earthquake Engineering, 105 (2018) 1-10.

[6] D. Sun, Q. Ren, Seismic damage analysis of concrete gravity dam based on wavelet transform, Shock and Vibration, 2016 (2016).

[7] H. Cao, M.I. Friswell, The effect of energy concentration of earthquake ground motions on the nonlinear response of RC structures, Soil Dynamics and Earthquake Engineering, 29 (2009) 292-299.

[8] Y.N. Li, J.P. Conte, M. Barbato, Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems, Earthquake Engineering & Structural Dynamics, 45 (2016) 1271-1291.

[9] S. Yaghmaei-Sabegh, Time–frequency analysis of the 2012 double earthquakes records in North-West of Iran, Bulletin of earthquake engineering, 12 (2014) 585-606.

[10] S. Yaghmaei-Sabegh, J. Ruiz-García, Nonlinear response analysis of SDOF systems subjected to doublet earthquake ground motions: A case study on 2012 Varzaghan–Ahar events, Engineering Structures, 110 (2016) 281-292.

[11] I.-S. Ahn, S.S. Chen, G.F. Dargush, Dynamic ratcheting in elastoplastic single-degree-of-freedom systems, Journal of Engineering Mechanics, 132 (2006) 411-421.

[12] N. Challamel, C. Lanos, A. Hammouda, B. Redjel, Stability analysis of dynamic ratcheting in elastoplastic systems, Physical Review E, 75 (2007) 026204.

[13] I.-S. Ahn, S.S. Chen, G.F. Dargush, An iterated maps approach for dynamic ratchetting in sdof hysteretic damping systems, Journal of Sound and Vibration, 323 (2009) 896-909.

[14] I.-S. Ahn, S.S. Chen, G.F. Dargush, L. Cheng, Dynamic ratcheting in SDOF hysteretic damping systems induced by earthquake excitations, Engineering Structures, 100 (2015) 665-673.


[16] A. Kaveh, A.A. Aghakouchak, P. Zakian, Reduced record method for efficient time history dynamic analysis and optimal design, Earthquake and Structures, 35 (2015) 637-661.

[17] E. Salajegheh, A. Heidari, Optimum design of structures against earthquake by wavelet neural network and filter banks, Earthquake engineering & structural dynamics, 34 (2005) 67-82.

[18] A. Yazdani, T. Takada, Wavelet‐Based Generation of Energy‐and Spectrum‐Compatible Earthquake Time Histories, Computer‐Aided Civil and Infrastructure Engineering, 24 (2009) 623-630.

[19] D.E. Newland, Wavelet analysis of vibration: part 1—theory, Journal of vibration and acoustics, 116 (1994) 409-416.

[20] D.E. Newland, Wavelet analysis of vibration, Part 2: Wavelet maps, Transactions of the ASME-L-Journal of Vibration and Acoustics, 116 (1994) 417-424.

[21] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE transactions on information theory, 36 (1990) 961-1005.

[22] J.J. Bommer, A. Martinez-Pereira, Strong-motion parameters: definition, usefulness and predictability, in:  Proc. of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.