Archive of Applied Mechanics

, Volume 88, Issue 4, pp 573–586 | Cite as

Nonlinear dynamic analysis of cable-stayed arches under primary resonance of cables

  • Jiangen Lv
  • Houjun Kang


In this paper, the one-to-one interaction of a cable-stayed arch structure under the cable’s primary resonance is investigated. Based on the coupling condition at the arch tip, the partial differential equations governing the planar motion of the system are derived using the extended Hamiltonian principle, while with the application of the Galerkin method, these equations are transformed into a set of ordinary equations. Applying the method of multiple scales to these ordinary equations, the first approximated solutions and solvability condition are obtained. The one-to-one interaction between the cable and the arch is investigated under simultaneous internal and external resonances for an actual cable-stayed arch structure. Based on the shooting method and the pseudo-arclength algorithm, the dynamic solutions of the system are obtained, and a period-doubling route to chaos is analyzed. The effects of the cable’s initial tension, inclination angle, the arch’s rise-to-span ratio and intersection angle between the cable and the arch are explored, and the results show that the interaction response mainly depends on specific parameters.


Cable-stayed arch 1:1 interaction Nonlinear response Chaos 



This work is supported by the National Science Foundation of China under Grant No. 11572117.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.College of Urban ConstructionZhongkai University of Agriculture and EngineeringGuangzhouChina
  2. 2.College of Civil EngineeringHunan UniversityChangshaChina

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