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New insights into dynamic instability regions of spillway radial gate owing to fluid-induced parametric oscillation

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Abstract

Spillway radial gate, a spatial frame structure, plays an important role in flood prevention and sustainable energy system. Dynamic instability mechanism of the spillway radial gate, excited by quasi-periodic hydrodynamic loads, remains unclear. In this work, an efficient numerical method, for analyzing dynamic stability of discretized model, is developed. Furthermore, a comprehensive investigation on the dynamic instability regions of struts and frame structure in the spillway radial gate, performed in discrete model, is provided. Specifically, the presented discrete finite element model and developed numerical method are validated by using numerical simulation in ANSYS software and definitive works from Bolotin. The out-of-plane vibration of struts and frame structure render dynamic instability of the spillway radial gate. The mode-coupling dynamic instability regions of frame structure are revealed, which is ignored in the dynamic instability analysis of struts and the analytical solution of radial gate structure as well. Long-term quasi-stable state exists in parametric resonance response, threatening the reliability of structural health diagnosis based on monitoring data for radial gates structure. From the comparison of strut and frame structure, it is shown that the dynamic instability regions of frame structure are more dense and complicated, close to the dominant frequency of external hydrodynamic loads during water discharging. The proposed insights highlight the importance of analyzing frame structure’s dynamic stability in evaluating the safety of radial gate structure, as the corresponding dynamic stability characteristics are generally ignored in current works.

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

Abbreviations

L girder, L strut :

Length

m :

Mass per unit length

E :

Elastic modulus

θ :

Excitation frequency of external periodic load

λ cr :

Buckling load factor

P cr :

Buckling load

P 0 :

Static load in buckling analysis

k :

Dimension of the solution

Ω:

Characteristic exponent

Δ:

Difference value

φ i :

i-Th vibration mode

P(t):

External dynamic load

P s :

Static component in dynamic load

P d :

Dynamic component in dynamic load

K, b 0, a k, b k :

Constants

w i :

i-Th order natural frequency

Δ{δ}:

Buckling mode

β :

Dynamic load factor

f u :

Critical instability frequency

Q :

Nodal displacement vector

I :

Identity matrix

Q(t):

Solution of equation

M, M e :

Mass matrices

K :

Stiffness matrices

K E, K e E :

Elastic stiffness matrices

K G, K e G :

Geometric stiffness matrices

\({\mathbf{K}}_{G}^{s}\) :

Geometric stiffness matrices by static component

\({\mathbf{K}}_{G}^{t}\) :

Geometric stiffness matrices by dynamic component

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Acknowledgements

This work has been supported by funding from the National Natural Science Foundation of China (Grant No. 51179164), and Natural Science Foundation of Shaanxi province of China (Grant No. 2022JM-234). These supports are gratefully acknowledged. The first author (Dr. Chao Xu) would like to express appreciation to his beloved family and Yandan Wang for their support of this manuscript. The authors thank Dr. Huijun Li, Dr. Baohui Li, and Dr. Dongfeng Li for their kind help. The authors appreciate the editor and anonymous reviewers for their constructive comments in improving the quality of the manuscript.

Funding

This work has been supported by funding from the Key Programme (Grant No. 51179164), and Natural Science Foundation of Shaanxi Province (Grant No. 2022JM-234).

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Authors and Affiliations

  1. Department of Hydropower Engineering, School of Water Resources and Hydropower Engineering, North China Electric Power University, 2 Beinong Road, Changping, Beijing, 102206, China

    Chao Xu

  2. College of Water Resources and Architectural Engineering, Cold and Arid Regions Water Engineering Safety Research Center, Northwest A&F University, Yangling, Shaanxi, 712100, China

    Chao Xu & Zhengzhong Wang

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Chao Xu contributed to conceptualization, methodology, software, validation, formal analysis, investigation, writing—original draft, writing—review & editing, and funding acquisition. Zhengzhong Wang contributed to writing—review & editing, methodology and funding acquisition.

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Correspondence to Chao Xu.

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Xu, C., Wang, Z. New insights into dynamic instability regions of spillway radial gate owing to fluid-induced parametric oscillation. Nonlinear Dyn 111, 4053–4070 (2023). https://doi.org/10.1007/s11071-022-08040-y

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