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Structural Engineering and Mechanics
  Volume 73, Number 3, February10 2020 , pages 271-286

Generalized complex mode superposition approach for non-classically damped systems
Huating Chen, Yanhui Liu and Ping Tan

    Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.
Key Words
    non-classical damping; complex mode superposition approach; critical damping; overcritical damping; modal corrected method
1Guangdong Provincial Key Laboratory of Earthquake Engineering and Applied Technology, Guangzhou University,
Guangzhou, 510006, China
2Key Laboratory of Earthquake Resistance, Earthquake Mitigation and Structural Safety, Ministry of Education, Guangzhou University,
Guangzhou, 510405, China

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