No Access

Dynamic Analysis of a Double-Cable-Stayed Shallow Arch Model Under Multi-Frequency Excitation by IHB Method

State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures, Guangxi University, 530004 Guangxi, P. R. China

Scientific Research Center of Engineering Mechanics, Guangxi University, 530004 Guangxi, P. R. China

Search for more papers by this author

Shiyu Jin

https://orcid.org/0009-0002-1295-260X

State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures, Guangxi University, 530004 Guangxi, P. R. China

Scientific Research Center of Engineering Mechanics, Guangxi University, 530004 Guangxi, P. R. China

Search for more papers by this author

, and

Houjun Kang

https://orcid.org/0000-0002-2452-9844

State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures, Guangxi University, 530004 Guangxi, P. R. China

Scientific Research Center of Engineering Mechanics, Guangxi University, 530004 Guangxi, P. R. China

E-mail Address: HJKang@gxu.edu.cn

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219455425500336Cited by:0 (Source: Crossref)

Abstract

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.

Keywords:

Remember to check out the Most Cited Articles!
Remember to check out the structures

References

1. G.-Q. Zhang, Y.-L. Xu, B. Wang and Q. Zhu, Turbulence effects on vortex-induced dynamic response of a twin-box bridge and ride comfort of the vehicle, Int. J. Struct. Stab. Dyn. 23 (2023) 2340023. Link, Web of Science, Google Scholar
2. H. Xiang, W. Ren, C. Shang, J. Zhu and Y. Li, Dynamic response analysis of train–vehicle–bridge system under train-induced winds, Int. J. Struct. Stab. Dyn. 23 (2023) 2350132. Link, Web of Science, Google Scholar
3. Y. Duan, S. Wu, S. Wang, J. Yau, Y. Ni and C. Yun, Train-induced dynamic behavior and fatigue analysis of cable hangers for a tied-arch bridge based on vector form intrinsic finite element, Int. J. Struct. Stab. Dyn. 22(12) (2022) 2250136. Link, Web of Science, Google Scholar
4. F. Benedettini and G. Rega, Planar non-linear oscillations of elastic cables under superharmonic resonance conditions, J. Sound Vib. 132(3) (1989) 353–366. Crossref, Web of Science, Google Scholar
5. C. M. Chin and A. H. Nayfeh, Three-to-one internal resonances in hinged-clamped beams, Nonlinear Dyn. 12 (1997) 129–154. Crossref, Web of Science, Google Scholar
6. W. M. Tien, N. S. Namachchivaya and A. K. Bajaj, Non-linear dynamics of a shallow arch under periodic excitation — I. 1:2 internal resonance, Int. J. Non-Linear Mech. 29(3) (1994) 349–366. Crossref, Google Scholar
7. M. H. Wei, Y. Q. Xiao, H. T. Liu and K. Lin, Nonlinear responses of a cable-beam coupled system under parametric and external excitations, Arch. Appl. Mech. 84(2) (2013) 173–185. Crossref, Google Scholar
8. S. Lenci and L. Ruzziconi, Nonlinear phenomena in the single-mode dynamics of a cable-supported beam, Int. J. Bifurcation Chaos 19(3) (2009) 923–945. Link, Web of Science, Google Scholar
9. Y. Cong, H. Kang and T. Guo, Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge, Mech. Syst. Signal Process. 120 (2019) 505–523. Crossref, Web of Science, Google Scholar
10. R. H. Plaut and J. C. Hsieh, Oscillations and instability of a shallow arch under two-frequency excitation, J. Sound Vib. 102(2) (1985) 189–201. Crossref, Google Scholar
11. Y. Zhao, Z. Guo, C. Huang, L. Chen and S. Li, Analytical solutions for planar simultaneous resonances of suspended cables involving two external periodic excitations, Acta Mech. 229(11) (2018) 4393–4411. Crossref, Web of Science, Google Scholar
12. C. Cai, Y. Shen and S. Wen, Primary and super-harmonic simultaneous resonance of van der Pol oscillator, Int. J. Non-Linear Mech. 147 (2022) 104237. Crossref, Web of Science, Google Scholar
13. H. Kang, Y. Cong and G. Yan, Theoretical analysis of dynamic behaviors of cable-stayed bridges excited by two harmonic forces, Nonlinear Dyn. 102(2) (2020) 965–992. Crossref, Web of Science, Google Scholar
14. Y. Cong, H. Kang and G. Yan, Investigation of dynamic behavior of a cable-stayed cantilever beam under two-frequency excitations, Int. J. Non-Linear Mech. 129 (2021) 103670. Crossref, Web of Science, Google Scholar
15. A. H. Nayfeh, The response of two-degree-of-freedom systems with quadratic non-linearities to a parametric excitation, J. Sound Vib. 88(4) (1983) 547–557. Crossref, Google Scholar
16. R. R. Pušenjak and M. M. Oblak, Incremental harmonic balance method with multiple time variables for dynamical systems with cubic non-linearities, Int. J. Numer. Methods Eng. 59(2) (2003) 255–292. Crossref, Google Scholar
17. J. L. Huang, R. K. L. Su, Y. Y. Lee and S. H. Chen, Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities, J. Sound Vib. 330(21) (2011) 5151–5164. Crossref, Web of Science, Google Scholar
18. D. Zhang and J. Huang, Nonlinear vibration of a thin plate subjected to multi-force excitation, J. Vib. Shock 35(23) (2016) 174–179 (in Chinese). Google Scholar
19. J. L. Huang, W. J. Zhou and W. D. Zhu, Quasi-periodic motions of high-dimensional nonlinear models of a translating beam with a stationary load subsystem under harmonic boundary excitation, J. Sound Vib. 462 (2019) 114870. Crossref, Web of Science, Google Scholar
20. Y. Hui, Q. Ruan, Z.-Q. Yang and B. Chen, A generic pre-processing technique of IHB method for continuum system to improve calculation efficiency, Int. J. Appl. Mech. 15(10) (2023) 2350091. Link, Web of Science, Google Scholar
21. Y. Hui, S.-S. Law and W. Zhu, Efficient algorithm for the dynamic analysis of large civil structures with a small number of nonlinear components, Mech. Syst. Signal Process. 152 (2021) 107480. Crossref, Web of Science, Google Scholar
22. Y. Hui, S.-S. Law, W. Zhu and Q. Yang, Extended IHB method for dynamic analysis of structures with geometrical and material nonlinearities, Eng. Struct. 205 (2020) 110084. Crossref, Web of Science, Google Scholar
23. Y. Hui, P. Xie, Q. Ruan, W. Zhu and L. Xu, An efficient extended IHB method for non-linear dynamic analysis with multi-frequency harmonic excitations using an auto adapted truncation technique, Acta Mech. 234(12) (2023) 6271–6295. Crossref, Web of Science, Google Scholar
24. V. Gattulli and A. Paolone, A parametric analytical model for non-linear dynamics in cable-stayed beam, Earthq. Eng. Struct. Dyn. 31 (2002) 1281–1300. Crossref, Web of Science, Google Scholar
25. N. Malhotra and N. S. Namachchivaya, Chaotic dynamics of shallow arch structures under 1:2 resonance, J. Eng. Mech. 123(6) (1997) 612–619. Crossref, Google Scholar
26. V. Gattulli and M. Lepidi, Nonlinear interactions in the planar dynamics of cable-stayed beam, Int. J. Solids Struct. 40(18) (2003) 4729–4748. Crossref, Web of Science, Google Scholar
27. M. Guskov and F. Thouverez, Harmonic balance-based approach for quasi-periodic motions and stability analysis, J. Vib. Acoust. 134(3) (2012) 031003. Crossref, Web of Science, Google Scholar
28. Y. K. Cheung, S. H. Chen and S. L. Lau, Application of the incremental harmonic balance method to cubic non-linearity systems, J. Sound Vib. 140(2) (1990) 273–286. Crossref, Web of Science, Google Scholar
29. A. Y. T. Leung and S. K. Chui, Non-linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method, J. Sound Vib. 181(4) (1995) 619–633. Crossref, Web of Science, Google Scholar
30. C. S. Hsu, Impulsive parametric excitation: Theory, J. Appl. Mech. 39(2) (1972) 551–558. Crossref, Google Scholar
31. C. S. Hsu and W.-H. Cheng, Applications of the theory of impulsive parametric excitation and new treatments of general parametric excitation problems, J. Appl. Mech. 40(1) (1973) 78–86. Crossref, Google Scholar
32. C. S. Hsu, On approximating a general linear periodic system, J. Math. Anal. Appl. 45(1) (1974) 234–251. Crossref, Google Scholar
33. P. Friedmann, C. E. Hammond and T. H. Woo, Efficient numerical treatment of periodic systems with application to stability problems, Int. J. Numer. Methods Eng. 11(7) (2010) 1117–1136. Crossref, Google Scholar
34. R. Geier, G. De Roeck and R. Flesch, Accurate cable force determination using ambient vibration measurements, Struct. Infrastruct. Eng. 2(1) (2006) 43–52. Crossref, Web of Science, Google Scholar
35. H. Nam and N. Nghia, Estimation of cable tension using measured natural frequencies, Procedia Eng. 14 (2011) 1510–1517. Crossref, Google Scholar
36. Y. Fujino, P. Warnitchai and B. M. Pacheco, An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam, Nonlinear Dyn. 4 (1993) 111–138. Crossref, Google Scholar
37. X. Su, H. Kang, J. Chen, T. Guo, C. Sun and Y. Zhao, Experimental study on in-plane nonlinear vibrations of the cable-stayed bridge, Nonlinear Dyn. 98(2) (2019) 1247–1266. Crossref, Web of Science, Google Scholar
38. Y. Wang, H. Kang, Y. Cong, T. Guo and W. Zhu, Vibration suppression of a cable under harmonic excitation by a nonlinear energy sink, Commun. Nonlinear Sci. Numer. Simul. 117 (2023) 106988. Crossref, Web of Science, Google Scholar
39. Y. Cong and H. Kang, Planar nonlinear dynamic behavior of a cable-stayed bridge under excitation of tower motion, Eur. J. Mech. A, Solids 76 (2019) 91–107. Crossref, Web of Science, Google Scholar
40. H. J. Kang, Q. Hu, X. Su and Y. Cong, Study on vibration suppression of an inclined cable with a nonlinear energy sink under the axial excitation, Int. J. Struct. Stab. Dyn. 23 (2023) 2350111. Link, Web of Science, Google Scholar
41. R. Ju, W. Fan, W. D. Zhu and J. L. Huang, A modified two-timescale incremental harmonic balance method for steady-state quasi-periodic responses of nonlinear systems, J. Comput. Nonlinear Dyn. 12(5) (2017) 051007. Crossref, Web of Science, Google Scholar