Homotopy Perturbation–Based Dynamic Analysis of Structural Systems
Publication: Journal of Engineering Mechanics
Volume 146, Issue 12
Abstract
This paper presents the dynamic analysis of structural systems using the homotopy perturbation method (HPM). HPM was applied to the first-order differential equations of motion defined by the state vector. This approach is in the framework of time-history matrix analyses. According to the formulas obtained from HPM, response of the system was achieved by sequential product of the characteristic matrix of the system. This method was theoretically compared with the exponential matrix method (EMM). Based on the obtained formulas, nonlinear structural analysis was performed in addition to the linear method. The applicability and efficiency of the proposed method were tested with the classical and nonclassical damping structures and with different dynamic behaviors. Solutions of this method were compared with solutions of EMM and the time-integration method (TIM). The results of the proposed method were in good agreement with those of the two other methods in linear and nonlinear analyses.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request. The list of items includes the numerical models of the linear and nonlinear structural analysis using HPM, TIM, and EMM with capability of the torsional behavior and various stiffness irregularity in height, as well as with a base isolation system and tuned mass damping.
Acknowledgments
The authors would like to thank Professor Kamy Sepehrnoori and Dr. Chowdhury K. Mamun for their help in completing this research and preparing the manuscript.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 12 • December 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jun 7, 2019
Accepted: Jun 12, 2020
Published online: Sep 30, 2020
Published in print: Dec 1, 2020
Discussion open until: Feb 28, 2021
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