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Experimental results and analytical results are presented on chaotic vibrations of a clamped-supported beam with a concentrated mass. The beam is elastically compressed by an axial spring at the simply supported end and is excited by lateral periodic acceleration. In the experiment, periodic and chaotic vibrations are detected under several conditions of the axial compression. In the analysis, the governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses of the beam are examined with the Fourier spectra, the Poincaré projections and the maximum Lyapunov exponents and the principal component analysis. Under a specific axial compression with post-buckled state of the beam, the chaotic vibrations dominated by dynamic snap-through are generated by the ultra-sub-harmonic resonance response of 2/3order of the fundamental vibration mode. The number of pre-dominant vibration modes that contribute to the chaos is found to be three. Decreasing the axial compression, the chaotic vibrations are induced by the internal resonance response between the second and the fundamental mode of vibration. The number of predominant vibration modes that contribute to the chaos is found to be two or three. Both results of the experimental and the analysis agree remarkably with each other in detail.

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Automobile wiper systems provide a clear sight for drivers by creating a very thin layer of water about few dozen nano meters on a windshield. Several studies have been carried out to investigate the dynamic behavior of the wiper systems. However, there are few studies focused on reversal behavior of the wiper blade. Observation was conducted and analytical model is developed from the observation of the real wiper system. A water layer is considered in the analytical model between the wiper blade and the glass surface. The bottom of the model is assumed to always contact the water layer so that the fluid force is always applied. The dimensionless equations, which govern the wiping motion including the reversal behavior, were derived. The equations are discussed neglecting the nonlinear terms to understand the approximate movement and effect of the parameters. Moreover, the equation is solved numerically to obtain the time histories of the wiper blade. As a result, the effect of the fluid force, which acts on the wiper blade on the reversal behavior of the wiper blade, became clear.