Free vibration of summation resonance of suspended-cable-stayed beam

Chunguang Dong; Zhuojie Zhang; Xiaoxia Zhen; Mu Chen; Chunguang Dong; Zhuojie Zhang; Xiaoxia Zhen; Mu Chen

doi:10.3934/mbe.2019363

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7230-7249. doi: 10.3934/mbe.2019363

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Free vibration of summation resonance of suspended-cable-stayed beam

1.
Poly ChangDa Engineering Co., Ltd., Guangzhou511431, PR China
2.
School of Civil Engineering, Shi Jiazhuang Tiedao University, Shijiazhuang050043, PR China
3.
Innovation Center for Wind Engineering and Wind Energy Technology of Hebei Province, Shijiazhuang, Hebei 050043, PR China
4.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou510640, PR China

Received: 29 April 2019 Accepted: 01 July 2019 Published: 08 August 2019

Free vibration of summation resonance of suspended-cable-stayed beam is investigated in the article. A 3-DOF model of the coupled structure is built, with the main cable and sling (vertical cable) considered to be geometrically nonlinear, and the beam is taken as linear Euler beam. Hamilton's principle is used to derive the dynamic equilibrium equations of the coupled structure. Then, the dynamic equilibrium equations are solved by means of multiple scales method, the second order approximation solutions of single-modal motion of the coupled structure are obtained. Numerical examples are presented to discuss time history of free vibration of the summation resonance, with and without damping. Additionally, fourth-order Runge-Kutta method is directly used for the dynamic equilibrium equations to complement and verify the analytical solutions. The results show that the coupled structure performs strongly nonlinear and coupled characteristics, which is useful for engineering design.
- free vibration,
- summation resonance,
- multiple scales method,
- fourth-order Runge-Kutta method
Citation: Chunguang Dong, Zhuojie Zhang, Xiaoxia Zhen, Mu Chen. Free vibration of summation resonance of suspended-cable-stayed beam[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7230-7249. doi: 10.3934/mbe.2019363

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Abstract

Free vibration of summation resonance of suspended-cable-stayed beam is investigated in the article. A 3-DOF model of the coupled structure is built, with the main cable and sling (vertical cable) considered to be geometrically nonlinear, and the beam is taken as linear Euler beam. Hamilton's principle is used to derive the dynamic equilibrium equations of the coupled structure. Then, the dynamic equilibrium equations are solved by means of multiple scales method, the second order approximation solutions of single-modal motion of the coupled structure are obtained. Numerical examples are presented to discuss time history of free vibration of the summation resonance, with and without damping. Additionally, fourth-order Runge-Kutta method is directly used for the dynamic equilibrium equations to complement and verify the analytical solutions. The results show that the coupled structure performs strongly nonlinear and coupled characteristics, which is useful for engineering design.

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