Comparison and assessment of time integration algorithms for nonlinear vibration systems
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A corrected explicit method of double time steps (CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-α method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn’t unconditionally stable for the precise integration method, the Newmark method and the generalized-α method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step (Δt≤T min/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large (Δt≥0.3T min) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.
Key wordsnonlinear vibration conservative system explicit algorithm accuracy
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- Zhai Wan-ming, Xia He. Train-track-bridge dynamic interaction: Theory and engineering application [M]. Beijing: Science Press, 2011. (in Chinese)Google Scholar
- Masuri S U, Hoitink A, Zhou X, Tamma K K. Algorithms by design: A new normalized time-weighted residual methodology and design of a family of energy-momentum conserving algorithms for non-linear structural dynamics [J]. International Journal for Numerical Methods in Engineering, 2009, 79: 1094–1146.MathSciNetCrossRefMATHGoogle Scholar
- Yang C, Xiao S, Lu L, Zhu T. Two dynamic explicit methods based on double time steps [J]. Proc IMechE, Part K: Journal of Multi-body Dynamics, 2014, 228(3): 330–337.Google Scholar
- Zhang Xiong, Wang Tian-shu. Computational dynamics [M]. Beijing: Tsinghua University Press, 2007: 147–184. (in Chinese)Google Scholar
- Leontiev V A. Extension of LMS formulations for L-stable optimal integration methods with U0-V0 overshoot properties in structural dynamics: The level-symmetric (LS) integration methods [J]. International Journal for Numerical Methods in Engineering, 2007, 71: 1598–1632.MathSciNetCrossRefMATHGoogle Scholar
- Shao Hui-ping, Cai Cheng-wen. A three parameters algorithm for numerical integration of structural dynamic equations [J]. Chinese Journal of Applied Mechanics, 1988, 5(4): 76–82. (in Chinese)Google Scholar
- Lu He-xiang, Yu Hong-jie, Qiu Chun-hang. An integral equation of nonlinear dynamics and its solution method [J]. Acta Mechanica Solida Sinica, 2001, 22(3): 303–308. (in Chinese)Google Scholar
- Yang Chao, Xiao Shou-ne, Yang Guang-wu, Zhu Tao, Yang Bing. Non-dissipative explicit time integration methods of the same class [J]. Journal of Vibration Engineering, 2015, 28(3): 441–448. (in Chinese)Google Scholar