Dynamic Response Calculation of Inertial Coupled Nonlinear Systems Based on Real Modal Analysis and P-T Method

Linyan Li, Yundong Li (), Yumei Luo and Zhongxiang Li
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Linyan Li: School of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Yundong Li: School of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Yumei Luo: School of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Zhongxiang Li: School of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China

Mathematics, 2025, vol. 13, issue 20, 1-26

Abstract: The development of efficient and accurate numerical methods forms a crucial foundation for revealing complex dynamic evolution in nonlinear dynamical systems. Focusing on nonlinear inertia-coupled systems, this paper constructs a semi-analytical method that integrates the mathematical framework of real modal analysis with the piecewise constant arguments and Taylor series (P-T) method. This method first conducts symmetric preprocessing on the second-order term coefficient matrix of the system to construct the proportional damping decoupling form. Then, it realizes the linear term decoupling corresponding to this proportional damping form by using the mathematical framework of real modal analysis. Finally, the P-T method is applied to solve the dynamic response of the nonlinear system. Numerical validation using a two-dimensional aeroelastic system demonstrates that, under the premise of achieving the same computational accuracy as the time-domain minimum residual method (TMRM), the computational efficiency of the proposed method is significantly better than that of TMRM.

Keywords: real modal analysis; P-T method; dynamic system; inertial coupling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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