Structural Engineering and Mechanics

  • 제61권4호
  • /
  • Pages.497-510
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Auto-parametric resonance of framed structures under periodic excitations

  • Li, Yuchun (Department of Hydraulic Engineering, College of Civil Engineering, Tongji University) ;
  • Gou, Hongliang (Department of Hydraulic Engineering, College of Civil Engineering, Tongji University) ;
  • Zhang, Long (Department of Hydraulic Engineering, College of Civil Engineering, Tongji University) ;
  • Chang, Chenyu (Department of Hydraulic Engineering, College of Civil Engineering, Tongji University)
  • 투고 : 2016.07.17
  • 심사 : 2016.11.18
  • 발행 : 2017.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

키워드

과제정보

연구 과제 주관 기관 : National Science Foundation of China

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피인용 문헌

  1. Experimental and Numerical Analyses for Auto-Parametric Internal Resonance of a Framed Structure vol.21, pp.1, 2017, https://doi.org/10.1142/s0219455421500127
  2. Stability analysis for parametric resonances of frame structures using dynamic axis-force transfer coefficient vol.34, pp.None, 2017, https://doi.org/10.1016/j.istruc.2021.09.095