High-order sensitivity analysis of complex modal parameters and their comparison

Zhang, Miao; Xu, Xinxin; Yu, Lie

doi:10.1007/s00419-022-02317-9

Cited by 2 publications

(1 citation statement)

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“…Lei et al (2019) proposed a Lagrange direct method to calculate the second order derivative of modal strain energy of undamped structures. To construct the gradient and Hessian matrices, Zhang and Yu (2020) proposed a method to calculate the first and second order derivatives of the complex mode for an asymmetrical damped linear system, and the proposed method was compared with algebraic method, direct method, full-mode method, and truncated modal method (Zhang et al, 2023). In sensitivity based methods, the response derivatives of the analytical model are usually 1 School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan, China required to be calculated repeatedly.…”

Section: Introductionmentioning

confidence: 99%

Efficient calculation of higher order time history response derivatives by substructuring method

Li,

Wu,

Weng

2024

Advances in Structural Engineering

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Time history response derivatives with respect to the design variables are frequently used in optimization design, damage detection, structural control, etc. This paper proposes a substructuring method for efficient calculation of higher order time history response derivatives of large-scale structures. First, the global structure is disassembled into several small substructures and the substructural displacement is projected onto the range space of a few substructural master eigenvectors. Afterwards, the derivative of substructural master eigenvectors of a few substructures containing the design variables are assembled to form the reduced first, second, and higher order sensitivity equations with a size of the number of master eigenvectors. The equivalent eigenvector which relates the slave and master eigenvectors is derived to compensate for the inertial effect of discarded slave eigenvectors. Finally, the first, second, and higher order time history response derivatives of global large-scale structure are efficiently solved from the reduced sensitivity equations by using Newmark- β method. A numerical one-bay plane frame and a numerical highway bridge are applied to verify the accuracy and efficiency of proposed substructuring method.

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Section: Introductionmentioning

confidence: 99%