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http://dx.doi.org/10.5050/KSNVN.2008.18.2.160

Stability of Nonlinear Oscillations of a Thin Cantilever Beam Under Parametric Excitation  

Bang, Dong-Jun (건국대학교 대학원 기계공학과)
Lee, Gye-Dong (건국대학교 대학원 기계공학과)
Jo, Han-Dong (건국대학교 대학원 기계공학과)
Jeong, Tae-Gun (건국대학교 공과대학 기계공학부)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.18, no.2, 2008 , pp. 160-168 More about this Journal
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.
Keywords
Parametric Excitation; Perturbation Analysis; Mathieu Equation; Method of Multiple Scales; Combination Resonance;
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