Nonplanar Nonlinear Vibration Phenomenon on the One to One Internal Resonance of the Circular Cantilever Beam
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.
Soon-Bok Lee and Yun-Jae Kim
M. G. Kim et al., "Nonplanar Nonlinear Vibration Phenomenon on the One to One Internal Resonance of the Circular Cantilever Beam", Key Engineering Materials, Vols. 326-328, pp. 1641-1644, 2006