Experiments on chaotic vibrations of a post-buckled cantilevered beam connected by a string to an axial spring

Abstract

Experimental results are presented on chaotic vibrations of a post-buckled cantilevered beam constrained by a string. The string is stretched between the top end of the beam and an axial spring. The axial spring consists of a leaf spring with an attached mass and is fixed on a base frame close to the clamped end of the beam. The length of the string is less than that of the beam. The beam is excited by lateral periodic acceleration. By increasing the attached mass on the axial spring, nonlinear responses of the beam are examined. Nonperiodic response is observed in a typical frequency region. The response is examined by the Fourier spectrum, maximum Lyapunov exponents, Poincaré projection, and principal component analysis. Predominant chaotic response is generated by the internal resonance with a frequency ratio of one-to-three. The fundamental mode and the second mode of vibration are strongly coupled in the chaotic response. When the attached mass of the axial spring is increased, the natural frequency of the axial spring approaches the region of chaotic response. Therefore, the number of vibration modes that contribute to the chaos increases. Furthermore, the Poincaré projection of the chaotic response shows more scattered figures.