Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Stability of Nonlinear Oscillations of a Thin Cantilever Beam Under Parametric Excitation

매개 가진되는 얇은 외팔보의 비선형 진동 안정성

  • 방동준 (건국대학교 대학원 기계공학과) ;
  • 이계동 (건국대학교 대학원 기계공학과) ;
  • 조한동 (건국대학교 대학원 기계공학과) ;
  • 정태건 (건국대학교 공과대학 기계공학부)
  • Published : 2008.02.20
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Abstract

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

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References

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