Developing Inelastic Jerk Spectra for Pulse-Like Earthquakes

Document Type : Original Article

Authors

1 Department of Civil Engineering, Faculty of Engineering, University of Jiroft, Jiroft, Kerman, Iran

2 Department of Civil Engineering, Geological and Mining Engineering, Polytechnique Montreal, Montreal, QC, Canada

Abstract

Jerk, or jolt, is defined as the time derivative of acceleration. This study investigates the jerk response of inelastic single-degree-of-freedom (SDOF) systems subjected to pulse-like near-fault ground motions. Compared with ordinary non–pulse-like records, pulse-like motions can impose significantly higher demands on structures. In this work, constant-strength spectra for the jerk response of inelastic SDOF systems are developed using a set of 91 pulse-like earthquakes. The influence of key structural parameters, including strength reduction factor, hysteretic behavior, and viscous damping ratio, is examined. The results show that jerk demands exhibit slightly higher sensitivity to viscous damping in the short, normalized period region than in the long-period region. Furthermore, an analytical equation is proposed to estimate jerk demand as a function of the ratio of elastic vibration period to pulse period and the strength reduction factor, for various hysteretic models and damping ratios.

Keywords

Main Subjects

References

  1. Hayati, H., Eager, D., Pendrill, A. M., Alberg, H. Jerk within the Context of Science and Engineering—A Systematic Review. Vibration, 2020; 3: 371-409. doi:10.3390/vibration3040025.
  2. Nemes, A., Mester, G. Energy Efficient Feasible Autonomous Multi-Rotor Unmanned Aerial Vehicles Trajectories. In: Proceedings of the 4th International Scientific Conference on Advances in Mechanical Engineering; 2016 Oct 15-16; Debrecen, Hungary. p. 369-376.
  3. Pendrill, A.-M. Rollercoaster loop shapes. Physics Education, 2005; 40: 517-521. doi:10.1088/0031-9120/40/6/001.
  4. Eager, D., Pendrill, A.-M., Reistad, N. Beyond velocity and acceleration: jerk, snap and higher derivatives. European Journal of Physics, 2016; 37: 065008. doi:10.1088/0143-0807/37/6/065008.
  5. Gierlak, P., Szybicki, D., Kurc, K., Burghardt, A., Wydrzyński, D., Sitek, R., Goczał, M. Design and dynamic testing of a roller coaster running wheel with a passive vibration damping system. Journal of Vibroengineering, 2018; 20: 1129–1143. doi:10.21595/jve.2017.18928.
  6. Sicat, S., Woodcock, K., Ferworn, A. Wearable technology for design and safety evaluation of rider acceleration exposure on aerial adventure attractions. In: Proceedings of the Annual Occupational Ergonomics and Safety Conference; 2018 Jun 7-8; Pittsburgh, Pennsylvania. p. 74-79.
  7. Vaisanen, A. Design of Roller Coasters (Master Thesis). Espoo (FI): Aalto University; 2018.
  8. Pendrill, A.-M., Eager, D. Velocity, acceleration, jerk, snap and vibration: forces in our bodies during a roller coaster ride. Physics Education, 2020; 55: 065012. doi:10.1088/1361-6552/aba732.
  9. Bae, I., Moon, J., Seo, J. Toward a Comfortable Driving Experience for a Self-Driving Shuttle Bus. Electronics, 2019; 8: 943. doi:10.3390/electronics8090943.
  10. Coats, T. W., Haupt, K. D., Murphy, H. P., Ganey, N. C., Riley, M. R. A Guide for Measuring, Analyzing, and Evaluating Accelerations Recorded During Seakeeping Trials of High-Speed Craft. Bethesda (MD): Naval Surface Warfare Center Carderock West Bethesda United States; 2016. Report No.: NSWCCD-80-TR-2016/003.
  11. Sosa, L., Ooms, J. A Comfort Analysis of an 86 m Yacht Fitted with Fin Stabilizers Vs. Magnus-Effect Rotors. In: 24th International HISWA Symposium on Yacht Design and Yacht Construction; 2016 Nov 14-15; Amsterdam, Netherlands. p. 1-13.
  12. Werkman, J. Determining and Predicting the Seakeeping Performance of Ships Based on Jerk in the Ship Motions (Master Thesis). Delft (NL): Delft University of Technology; 2019.
  13. Geoffrey Chase, J., Barroso, L. R., Hunt, S. Quadratic jerk regulation and the seismic control of civil structures. Earthquake Engineering & Structural Dynamics, 2003; 32: 2047-2062. doi:10.1002/eqe.314.
  14. He, Z., Xu, Y. Correlation between global damage and local damage of RC frame structures under strong earthquakes. Structural Control and Health Monitoring, 2017; 24: e1877. doi:10.1002/stc.1877.
  15. Taushanov, A. Jerk Response Spectrum. In: Proceedings of the International Jubilee Scientific Conference “75th Anniversary of UACEG”; 2017 Nov 1-3; Sofia, Bulgaria. p. 39-50.
  16. Tong, M., Wang, G.-Q., Lee, G. C. Time derivative of earthquake acceleration. Earthquake Engineering and Engineering Vibration, 2005; 4: 1-16. doi:10.1007/s11803-005-0019-6.
  17. Papandreou, I., Papagiannopoulos, G. On the jerk spectra of some inelastic systems subjected to seismic motions. Soil Dynamics and Earthquake Engineering, 2019; 126: 105807. doi:10.1016/j.soildyn.2019.105807.
  18. He, H., Li, R., Chen, K. Characteristics of jerk response spectra for elastic and inelastic systems. Shock and Vibration, 2015; 2015: doi:10.1155/2015/782748.
  19. Yaseen, A. A., Ahmed, M. S., Al-Kamaki, Y. S. S. The Possibility of Using Jerk Parameters as Seismic Intensity Measure. In: 3rd international conference on recent innovations in engineering (ICRIE); 2020 Sep 9-10; Duhok, Iraq. p. 254-277.
  20. Wakui, M., Iyama, J., Koyama, T. Estimation of plastic deformation of vibrational systems using the high-order time derivative of absolute acceleration. In: Proceedings of the 16th World Conference on Earthquake Engineering; 2017 Jan 9-13; Santiago, Chile. p. 3932.
  21. Vukobratović, V., Ruggieri, S. Jerk in earthquake engineering: State-of-the-art. Buildings, 2022; 12: 1123. doi:10.3390/buildings12081123.
  22. Amiri, S., Di Sarno, L., Garakaninezhad, A. On the aftershock polarity to assess residual displacement demands. Soil Dynamics and Earthquake Engineering, 2021; 150: 106932. doi:10.1016/j.soildyn.2021.106932.
  23. Amiri, S., Garakaninezhad, A., Bojórquez, E. Normalized residual displacement spectra for post-mainshock assessment of structures subjected to aftershocks. Earthquake Engineering and Engineering Vibration, 2021; 20: 403-421. doi:10.1007/s11803-021-2028-5.
  24. Amiri, S., Di Sarno, L., Garakaninezhad, A. Correlation between non-spectral and cumulative-based ground motion intensity measures and demands of structures under mainshock-aftershock seismic sequences considering the effects of incident angles. Structures, 2022; 46: 1209-1223. doi:10.1016/j.istruc.2022.10.076.
  25. Amiri, S., Koboevic, S. Inelastic spectra under mainshock-multiple aftershock sequences. In: 3rd European Conference on Earthquake Engineering & Seismology; 2022 Sep 4-9; Bucharest, Romania. p. 1-22.
  26. Garakaninezhad, A., Amiri, S., Noroozinejad Farsangi, E. Effects of Ground Motion Incident Angle on Inelastic Seismic Demands of Skewed Bridges Subjected to Mainshock–Aftershock Sequences. Practice Periodical on Structural Design and Construction, 2023; 28: 04023006. doi:10.1061/PPSCFX.SCENG-1218.
  27. Amiri, S., Koboevic, S. On the necessary number of aftershocks for seismic collapse risk assessment of buildings. In: 18th World Conference on Earthquake Engineering (WCEE2024); 2024 Jun 30-Jul 5; Milan, Italy. p. 1-9.
  28. Somerville, P. G., Smith, N. F., Graves, R. W., Abrahamson, N. A. Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity. Seismological Research Letters, 1997; 68: 199-222. doi:10.1785/gssrl.68.1.199.
  29. Baker, J. W. Identification of near-fault velocity pulses and prediction of resulting response spectra. 1st ed. Reston (VA): 2008. doi:10.1061/40975(318)4.
  30. Rupakhety, R., Sigurdsson, S. U., Papageorgiou, A. S., Sigbjörnsson, R. Quantification of ground-motion parameters and response spectra in the near-fault region. Bulletin of Earthquake Engineering, 2011; 9: 893-930. doi:10.1007/s10518-011-9255-5.
  31. Ezzodin, A., Ghodrati Amiri, G., Raissi Dehkordi, M. A Random Vibration-Based Simulation Model for Nonlinear Seismic Assessment of Steel Structures Subjected to Fling-Step Ground Motion Records. Journal of Vibration Engineering & Technologies, 2022; 10: 2641-2655. doi:10.1007/s42417-022-00509-9.
  32. Bray, J. D., Rodriguez-Marek, A. Characterization of forward-directivity ground motions in the near-fault region. Soil Dynamics and Earthquake Engineering, 2004; 24: 815-828. doi:10.1016/j.soildyn.2004.05.001.
  33. Iervolino, I., Chioccarelli, E., Baltzopoulos, G. Inelastic displacement ratio of near-source pulse-like ground motions. Earthquake Engineering & Structural Dynamics, 2012; 41: 2351-2357. doi:10.1002/eqe.2167.
  34. Khoshnoudian, F., Ahmadi, E. Effects of pulse period of near-field ground motions on the seismic demands of soil–MDOF structure systems using mathematical pulse models. Earthquake Engineering & Structural Dynamics, 2013; 42: 1565-1582. doi:10.1002/eqe.2287.
  35. Khoshnoudian, F., Ahmadi, E. Effects of inertial soil–structure interaction on inelastic displacement ratios of SDOF oscillators subjected to pulse-like ground motions. Bulletin of Earthquake Engineering, 2015; 13: 1809-1833. doi:10.1007/s10518-014-9693-y.
  36. Baker, J. W. Quantitative Classification of Near-Fault Ground Motions Using Wavelet Analysis. Bulletin of the seismological society of America, 2007; 97: 1486-1501. doi:10.1785/0120060255.
  37. Zhai, C., Li, S., Xie, L., Sun, Y. Study on inelastic displacement ratio spectra for near-fault pulse-type ground motions. Earthquake Engineering and Engineering Vibration, 2007; 6: 351-355. doi:10.1007/s11803-007-0755-x.
  38. Dong, H., Han, Q., Du, X., Liu, J. Constant ductility inelastic displacement ratios for the design of self-centering structures with flag-shaped model subjected to pulse-type ground motions. Soil Dynamics and Earthquake Engineering, 2020; 133: 106143. doi:10.1016/j.soildyn.2020.106143.
  39. Ghanbari, B., Akhaveissy, A. H. Constant-damage residual ratios of SDOF systems subjected to pulse type ground motions. AUT Journal of Civil Engineering, 2020; 4: 145-154. doi:10.22060/ajce.2019.14984.5510.
  40. Dong, H., Han, Q., Qiu, C., Du, X., Liu, J. Residual displacement responses of structures subjected to near-fault pulse-like ground motions. Structure and Infrastructure Engineering, 2022; 18: 313-329. doi:10.1080/15732479.2020.1835997.
  41. Garakaninezhad, A., Amiri, S. Inelastic acceleration ratio of structures under pulse-like earthquake ground motions. Structures, 2022; 44: 1799-1810. doi:10.1016/j.istruc.2022.08.102.
  42. OpenSees Effects of Hysteretic-Material Parameters. 2006. Available online: https://opensees.berkeley.edu/OpenSees/manuals/usermanual/4052.htm (accessed on December 2025).
  43. Di Sarno, L., Amiri, S. Period elongation of deteriorating structures under mainshock-aftershock sequences. Engineering Structures, 2019; 196: 109341. doi:10.1016/j.engstruct.2019.109341.
  44. Mazzoni, S., McKenna, F., Scott, M. H., Fenves, G. L. OpenSees Command Language Manual. Pacific Earthquake Engineering Research (PEER) Center, 2006; 264: 137-158.
  45. Scott, M., Filippou, F. Hysteretic Material. 2016. Available online: https://opensees.berkeley.edu/wiki/index.php/Hysteretic_Material (accessed on December 2025).
  46. PEER ground motion database. Pacific Earthquake Engineering Research Center. 2010. Available online: https://ngawest2.berkeley.edu/ (accessed on December 2025).

Files

History

  • Receive Date: 06 October 2025
  • Revise Date: 20 October 2025
  • Accept Date: 24 October 2025
  • First Publish Date: 25 October 2025

Share

How to cite

Statistics