145 Analysis on Nonlinear Vibrations of a Cantilevered Beam with Initial Deflection Elastically Constrained by Stretched String at the Beam End

Abstract

Analytical results are presented on nonlinear vibrations of a cantilevered beam with initial deflection elastically constrained by stretched string at the beam end. The beam is subjected to periodic lateral acceleration. Nonlinear responses are obtained by the harmonic balance method and by the numerical integration. Results of analysis show that the chaotic responses are generated in the frequency region near the lowest natural frequency. The frequency regions of chaos are narrowed by the increase of initial deflection. The number of modes generated in the chaos is counted as two by the Lyapunov dimension. The principal component analysis shows the predominant contribution of the lowest mode of vibration.