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Comparison of Stability of Four Numerical Integration Methods Under Negative Stiffness

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Proceedings of the 2022 International Conference on Green Building, Civil Engineering and Smart City (GBCESC 2022)

Part of the book series: Lecture Notes in Civil Engineering ((LNCE,volume 211))

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Abstract

Numerical Integration Algorithm plays a very important role in real-time hybrid experiments. Based on the Newmark (γ = 1/2, β = 1/4) average constant acceleration algorithm, the stability analysis equations of Chang Algorithm, CR Algorithm and TL Algorithm under the condition of negative stiffness were derived by using the principle of positive stiffness analysis. The stability of the four algorithms under the condition of negative stiffness was analyzed by Matlab, and the stability characteristics of the four algorithms were studied by changing the integral time interval, damping ratio and stiffness ratio. The research findings indicate that when stiffness is negative, the Newmark average constant acceleration algorithm (γ = 1/2, β = 1/4) is no longer unconditionally stable, whearas the other three algorithms are all unconditionally stable. The Chang Algorithm has the best stability, while the CR algorithm is nearly as stable as the TL algorithm. It is suggested that while performing hybrid testing with probable negative stiffness, the numerical integration algorithm should be carefully chosen.

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Authors and Affiliations

  1. Shandong Huake Planning and Architectural Design Co., Ltd., Liaocheng, 252000, China

    Fantao Meng & Xingqun Ruan

  2. Qingdao University of Technology, Qingdao, 266520, China

    Jianfeng Zhao

Authors
  1. Fantao Meng
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  2. Jianfeng Zhao
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  3. Xingqun Ruan
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Correspondence to Fantao Meng .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, China

    Wei Guo

  2. Guilin University of Technology, Guilin, China

    Kai Qian

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Meng, F., Zhao, J., Ruan, X. (2023). Comparison of Stability of Four Numerical Integration Methods Under Negative Stiffness. In: Guo, W., Qian, K. (eds) Proceedings of the 2022 International Conference on Green Building, Civil Engineering and Smart City. GBCESC 2022. Lecture Notes in Civil Engineering, vol 211. Springer, Singapore. https://doi.org/10.1007/978-981-19-5217-3_101

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  • DOI: https://doi.org/10.1007/978-981-19-5217-3_101

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-5216-6

  • Online ISBN: 978-981-19-5217-3

  • eBook Packages: EngineeringEngineering (R0)

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