Improvement of Euler-Bernoulli Beam Theory for Free Vibration and Buckling Analyses via Saint-Venant's Principle

생브낭 원리를 이용한 고전 보 이론의 고유진동수 및 좌굴하중 예측 개선

  • Jeong, Yong-Min (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology) ;
  • Kim, Jun-Sik (Dept. of Mechanical System Engineering, Kumoh Nat'l Institute of Technology)
  • 정용민 (금오공과대학교 기계시스템공학과) ;
  • 김준식 (금오공과대학교 기계시스템공학과)
  • Received : 2016.01.27
  • Accepted : 2016.02.13
  • Published : 2016.04.01


In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.


Saint-Venant's Principle;Free Vibration Analysis;Buckling Analysis


Supported by : 금오공과대학교


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