Analysis on Nonlinear Coupled Vibrations of a System of a Rigid Rod Supported by Parallel Strings(<Special Issue>Dynamics & Design Conference 2009)

Abstract

Analytical results are presented on nonlinear coupled vibrations of a system of a rigid rod supported by parallel strings. The governing equation of the system includes nonlinear coupling between in-plane, out-of-plane and pitching motions. Nonlinear periodic responses are calculated with the harmonic balance method. Time responses of the system are calculated by direct numerical integration with the Runge-Kutta method. As the excitation frequency is increased, vibration form changes from in-plane periodic vibration to whirling, and then quasi-periodic responses appear accompanied by whirling and pitching motion. At the specific frequencies in the region of quasi-periodic responses, chaotic responses are also observed. As the excitation frequency is increased further, the vibration form transits to periodic pitching vibration with the jump phenomenon. It is found that the frequency region of the quasi-periodic response is narrowed as the eccentricity of the rod is increased. Furthermore, the region of the quasi-periodic response is slightly enlarged by the increase of the distance between the two strings. The variation of the frequency region of the quasi-periodic response has close relation with that of the periodic response of pitching motion.