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Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method

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Abstract

Cable-stayed bridge is one of the most popular bridges in the world and is always the focus in engineering field. In this work, the in-plane free vibration of a multi-cable-stayed beam, which exists in cable-stayed bridge, has been studied. The general expressions are conducted for the multi-cable-stayed beam based on basic principle of the transfer matrix method. A double-cable-stayed beam is taken as an example and solved according to governing differential equations considering axial and transverse vibrations of cables and beam. Then, numerical analyses are implemented based on carbon fiber-reinforced polymer cables. The dynamic characteristics including natural frequencies and mode shapes are investigated and compared with those obtained by finite element model. Meanwhile, parametric analyses are carried out in detail aiming to explore the effects of parameters on natural frequencies of a two-cable-stayed beam. Finally, some interesting phenomena are revealed and a few interesting conclusions are also drawn.

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Acknowledgements

The program is funded by the National Natural Science Foundation of China (11572117, 11502076 and 11872176) and Hunan Provincial Communications Department Project (201428). Interesting comments and criticism by the reviewers are also gratefully acknowledged.

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Authors and Affiliations

  1. College of Civil Engineering, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Xiaoyang Su, Houjun Kang, Tieding Guo & Yunyue Cong

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Appendix A

Appendix A

The elements of the matrix \(\mathbf{U}^{b}\) in Eq. (59) are given as follows:

$$\begin{aligned} U_{\mathrm{11}}^b= & {} \sin (\beta _b x_b ), U_{\mathrm{12}}^b =\cos (\beta _b x_b ), U_{\mathrm{23}}^b =\sin (\delta _b x_b ), U_{24}^b =\cos (\delta _b x_b ), U_{25}^b =\sinh (\varepsilon _b x_b ), \\ U_{26}^b= & {} \cosh (\varepsilon _b x_b ), U_{33}^b =\delta _b \cos (\delta _b x_b ), U_{34}^b =-\delta _b \sin (\delta _b x_b ), U_{35}^b =\varepsilon _b \cosh (\varepsilon _b x_b ), \\ U_{36}^b= & {} \varepsilon _b \sinh (\varepsilon _b x_b ), U_{43}^b =-E_b I_b \delta _b ^{2}\sin (\delta _b x_b ), U_{44}^b =-E_b I_b \delta _b ^{2}\cos (\delta _b x_b ), \\ U_{45}^b= & {} E_b I_b \varepsilon _b ^{2}\sinh (\varepsilon _b x_b ), U_{46}^b =E_b I_b \varepsilon _b ^{2}\cosh (\varepsilon _b x_b ), U_{53}^b =-E_b I_b \delta _b ^{3}\cos (\delta _b x_b ), \\ U_{54}^b= & {} E_b I_b \delta _b ^{3}\sin (\delta _b x_b ), U_{55}^b =E_b I_b \varepsilon _b ^{3}\cosh (\varepsilon _b x_b ), U_{56}^b =E_b I_b \varepsilon _b ^{3}\sinh (\varepsilon _b x_b ), \\ U_{61}^b= & {} E_b A_b \beta _b \cos (\beta _b x_b ), U_{62}^b =-E_b A_b \beta _b \sin (\beta _b x_b ) \end{aligned}$$

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Su, X., Kang, H., Guo, T. et al. Dynamic analysis of the in-plane free vibration of a multi-cable-stayed beam with transfer matrix method. Arch Appl Mech 89, 2431–2448 (2019). https://doi.org/10.1007/s00419-019-01587-0

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