Citation :

Yousra El Hankouri, Abdelouafi El Ghoulbzouri, "The Influence of Various Parameters on the MDOF Structure Response to Harmonic Excitation," International Journal of Civil Engineering, vol. 13, no. 5, pp. 86-96, 2026. Crossref, https://doi.org/10.14445/23488352/IJCE-V13I5P107

Abstract

Assessing the dynamic behavior of structures is a highly intricate task, often involving complex and challenging calculations. This complexity is particularly evident when analyzing how Multi-Degree Of Freedom (MDOF) buildings respond to various excitations, such as harmonic forces and seismic forces. These models implicate a coupled set of equations of motion, in which the interaction between various structural components creates more sophisticated dynamic behavior. This work focuses on investigating the impact of several dynamical characteristics on MDOF buildings and examining their performance by systematically varying diverse parameters. A two-step methodology is employed, beginning with analytical solutions and followed by numerical simulations using Newmark-β and Wilson-θ algorithms.

Keywords

MDOF, Damping, Dynamical Characteristics, Seismic Force, Newmark-β, and Wilson-θ algorithms.

References

1. M.B. Vikram, G. P. Chandradhara, and B.S. Keerthi Gowda, “A Study of Effect of Wind on the Static and Dynamic Analysis,” International Journal of Emerging trends in Engineering and Development, vol. 4, no. 3, pp. 885-890, 2014.
   [Google Scholar] [Publisher Link]
2. Ahmet Tüken, “Dynamic Response Analysis of A 3-Story Shear Frame Subjected to Harmonic Loading: An Analytical Approach,” Uludağ University Faculty of Engineering Journal, vol. 24, no. 2, pp. 725-734, 2019.
   [CrossRef] [Google Scholar] [Publisher Link]
3. Robert Jankowski, and Sayed Mahmoud, “Linking of Adjacent Three-storey Buildings for Mitigation of Structural Pounding during Earthquakes,” Bulletin of Earthquake Engineering, vol. 14, pp. 3075-3097, 2016.
   [CrossRef] [Google Scholar] [Publisher Link]
4. Ahmet Tuken, and Yassir M. Abbas, “Dynamic Response of a MDOF System Subjected to Harmonic and Impulsive Loadings and Free Vibration: An Analytical Approach,” Journal of Structural Technology, vol. 3, no. 3, pp. 1-14, 2018.
   [Publisher Link]
5. Yun Xiang Lu et al., “Study on Calculation Method of Dynamic Response of Structure Subjected to Harmonic Load,” Applied Mechanics and Materials, vol. 226-228, pp. 70-75, 2012.
   [CrossRef] [Google Scholar] [Publisher Link]
6. R. Rakshita et al., “Influence of Stiffness and Mass Parameters on Seismic Damping of Structures,” International Journal of Engineering and Advanced Technology, vol. 8, no. 2, pp. 58-62, 2018.
   [Publisher Link]
7. Ahmed Ibrahim, and Hamed Askar, “Dynamic Analysis of a Multistory Frame RC Building with and without Floating Columns,” American Journal of Civil Engineering, vol. 9, no. 6, pp. 177-185, 2021.
   [CrossRef] [Google Scholar] [Publisher Link]
8. A. A. Gholampour, and M. Ghassemieh, “New Practical Approach to Nonlinear Dynamic Analysis of Structures: Refinement of Newmark’s and Wilson’s Classical Methods,” Practice Periodical on Structural Design and Construction, vol. 17, no. 1, pp. 30-34, 2015.
   [CrossRef] [Google Scholar] [Publisher Link]
9. Nathan M. Newmark, “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, vol. 85, no. 3, 1959.
   [CrossRef] [Google Scholar] [Publisher Link]
10. L. Edward Wilson, and Ray W. Clough, “Dynamic Response by Step-by-step Matrix Analysis,” Symposium on the Use of Computers in Civil Engineering, Lisbon, 1962.
    [Google Scholar]
11. Mehdi Babaei, Meysam Jalilkhani, and Somayeh Mollaei, “A Numerical Method for Estimating the Dynamic Response of Structures,” Journal of Civil and Environmental Engineering, vol. 55, no. S1, pp. 1-19, 2025.
    [CrossRef] [Google Scholar] [Publisher Link]
12. Mohit Sharma, and Savita Maru, “Dynamic Analysis of Multistoried Regular Building,” IOSR Journal of Mechanical and Civil Engineering, vol. 11, no. 1, pp. 37-42, 2014.
    [Google Scholar]
13. Rafiqul Islam et al., “Study of Dynamic Behavior of a Three Story Model Frame,” American Journal of Construction and Building Materials, vol. 2, no. 1, pp. 10-15, 2018.
    [CrossRef] [Google Scholar] [Publisher Link]
14. K.J. Bathe, and E.L. Wilson “Stability and Accuracy Analysis of Direct Integration Methods,” Earthquake Engineering and Structural Dynamics, vol. 1, no. 3, p. 283-291, 1972.
    [CrossRef] [Google Scholar] [Publisher Link]
15. Hiroshi Yamakawa, and Tetsuya Ohnishi, “Dynamic Response Analysis of Structures with Large Degrees of Freedom by Step-by-step Transfer Matrix Method,” Bulletin of JSME, vol. 26, no. 211, pp. 109-116, 2021.
    [CrossRef] [Google Scholar] [Publisher Link]
16. Klaus-Jürgen Bathe, Finite Element Procedures, Prentice Hall, pp. 1-1037, 1996.
    [Google Scholar] [Publisher Link]
17. Anil K. Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 3^rd ed., Pearson/Prentice Hall, pp. 1-876, 2007.
    [Google Scholar] [Publisher Link]
18. Ray W. Clough, and Joseph Penzien, Dynamics of Structures, McGraw-Hill, pp. 1-738, 1993.
    [Google Scholar] [Publisher Link]
19. Ted Belytschko, Wing Kam Liu, and Brian Moran, Nonlinear Finite Elements for Continua and Structures, Wiley, pp. 1-650, 2000.
    [Google Scholar] [Publisher Link]
20. Dmitry Ivanov, Supply Chain Management and Structural Dynamics Control, Structural Dynamics and Resilience in Supply Chain Risk Management, Springer, Cham, pp. 1-18, 2018.
    ​​​​​​​[CrossRef] [Google Scholar] [Publisher Link]