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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn


Nonlinear Dynamics and Sensitivity to Imperfections in Guyed Mast

Journal of Vibration Testing and System Dynamics 9(2) (2025) 109--121 | DOI:10.5890/JVTSD.2025.06.002

Diego Orlando$^{1}$, Paulo B. Gon\c{c}alves$^{2}$, Stefano Lenci$^{3}$, Giuseppe Rega$^{4}$

$^{1}$ Department of Mechanics and Energy -- FAT, State University of Rio de Janeiro, Resende, 27537-000, Brazil

$^{2}$ Department of Civil and Environmental Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, 22451-900, Brazil

$^{3}$ Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Ancona, 60131, Italy

$^{4}$ Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, 00197, Italy

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Abstract

Stay cable systems present a complex nonlinear behavior under static and dynamic loads. The prevention of buckling and undesirable nonlinear vibrations of these structures is a major concern in engineering design. In this paper the stability analysis of a simplified two-degree-of-freedom model of a guyed tower is studied. The results show that the system displays a strong modal coupling, resulting in several unstable post-buckling solutions, thus leading to high imperfection sensitivity. For applied loads lower than the theoretical buckling load, the system is supposedly in a safe position, according to the classical theory of elastic stability. However, this is not completely true. The system may buckle at load levels much lower than the critical value due to the simultaneous effects of imperfections and dynamic disturbances. For systems liable to unstable post-buckling behavior, the safe pre-buckling well is bounded by the manifolds of the saddles associated with the unstable post-buckling paths. Here, the homoclinic orbits emerging from these saddles define the safe region. The geometry and size of the safe region is here analyzed using the mathematical methods of classical mechanics, in particular Lagrangian or Hamiltonian mechanics and numerical tools for nonlinear vibrations such as bifurcation diagrams, stability boundaries and basins of attraction. This is a first step in the evaluation of the integrity of the real dynamical system.

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