Coupled systems mechanics

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Parametric dynamic instability of a suspension bridge deck under dynamic loading along two of its opposite edges

  • Hafid Mataich (Laboratory of Informatics and Interdisciplinary Physics (LIPI), High Normal School, Sidi Mohamed Ben Abdellah University)
  • Received : 2025.03.06
  • Accepted : 2025.07.09
  • Published : 2025.06.25
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Abstract

This paper examines the dynamic instability of a suspension bridge deck, modeling it as a symmetrically laminated rectangular plate made of composite material, featuring an angular fold and subject to various boundary conditions. To simplify the analysis, the instability of this structure is studied under the effect of a dynamic, non-uniform and periodic uni-axial loading applied along its edges. The equations of motion are formulated using Reissner-Mindlin's first-order shear deformation theory (FSDT) and Hamilton's principle. FSDT is based on five degrees of freedom (DOF) modeling per node within a finite element approach. Structural damping, modeled using the Rayleigh method, is incorporated into the system of equations to assess its influence on instability characteristics. A modal analysis is then performed to decouple the partial differential equations (PDEs) into a Mathieu-Hill system of ordinary differential equations (ODEs), thus reducing the problem size. The dynamic instability zones (DIR) of the plate are identified by applying the Bolotin approach, while the dynamic excitation frequencies are determined by solving an eigenvalue problem. Finally, a parametric analysis is carried out to examine the influence of the various parameters on the lower and upper bounds of the instability zones, as well as on the simple parametric resonance phenomenon of the structure representing the deck.

Keywords

Acknowledgement

The support given to this research project by Sidi Mohamed Ben Abdellah University, Fez, is gratefully acknowledged. The authors would also like to thank the profs. ENS Fès for their help in correcting the manuscript.

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