Ferdowsi Civil Engineering

Ferdowsi Civil Engineering

A quantitative study of the accuracy of the 3rd order acceleration method compared to other numerical methods for harmonic loading - A case study of a two-degree-of-freedom softening structure

Document Type : Original Article

Authors
masoud mahmoudabadi 1
fateme ansari 2
fateme hatefi ardakani 2
1 Department of Civil Engineering, University of Qom, Qom, Iran.
2 Faculty of Engineering, Qom University, Qom, Iran
10.22067/jfcei.2025.91623.1337
Abstract
In this paper, the displacement response of a nonlinear softening two-degree-of-freedom system under a range of sinusoidal loadings with different frequencies and force amplitudes has been investigated. The stiffness changes of this system had a quadratic relationship with the displacement value. Eight numerical methods including the 3rd-order acceleration method, the 2nd-order acceleration method, the Newmark method (linear acceleration method), the Newmark method (average acceleration method), the Wilson-Theta method, the central difference method, the Jennings method and the innovative method were used to calculate the displacement response of this system. Using the innovative method and using t∆ equal to 0.001 seconds, the displacement response of the system was calculated and was considered as the exact response of the system. Then, for t∆s of 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, and 0.007, and using the 8 numerical methods introduced above, the displacement response of this system was calculated for PGAs of 1, 2, 3, 4, and 5 meters per second squared, and the values ​​of the root mean square error and the coefficient of variation of the error of these 8 methods were calculated for the t∆s defined above. The results of the work are presented in the form of bar graphs in the article.
Keywords
3rd order acceleration method
numerical methods in structural dynamics
softening system
root mean square error
error coefficient of variation
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