Nonplanar Nonlinear Vibration Phenomenon on the One to One Internal Resonance of the Circular Cantilever Beam

Abstract:

Experimental and theoretical study of the non-planar response motions of a circular cantilever beam subject to base harmonic excitation has been presented in this paper work. Theoretical research is conducted using two non-linear coupled integral-differential equations of motion. These equations contain cubic linearities due do curvature term and inertial term. A combination of the Galerkin procedure and the method of multiple scales are used to construct a first-order uniform expansion for the case of one-to-one resonance. The results show that the nonlinear geometric terms are very important for the low-frequency modes of the first and second mode. The non-linear inertia terms are also important for the high-frequency modes. We present the quantitative and qualitative results for non-planar motions of the dynamic behavior.

• Periodical: Key Engineering Materials (Volumes 326-328)
• Pages: 1641-1644
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.326-328.1641
• Online since: December 2006
• Authors: Myoung Gu Kim, Chong Du Cho, Chang Boo Kim, Ho Joon Cho
• Keywords: Base Harmonic Excitation, Cubic Linearity, Non-Linear Inertia, Non-Planar, One-to-One Internal Resonance, Primary Resonance

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