中心に円孔を有する外周固定の薄肉円板のカオス振動実験

抄録

This paper presents experimental results on chaotic vibrations of a thin circular plate with a circular center hole. The plate is clamped around the outer edge by rigid rings. Asymmetric deflection of the plate is induced by initial imperfection and in-plane compressive stress due to thermal elongation of the plate. Two natural modes of vibration with one nodal diameter are generated in each natural frequency. These nodal diameters are perpendicular to each other. Under periodic excitation, a dominant chaotic response generated due to the type of one-to-two internal resonance in a specific frequency range. The chaotic response is inspected by the Fourier spectrum, the Poincare projection and the maximum Lyapunov exponent. The principal component analysis is adapted on the chaotic response to confirm modal contributions. The multiple time responses of the plate are measured at four positions simultaneously for long-time interval. The modes of vibration without nodal diameter and the two modes with one nodal diameter contribute to the chaotic response, predominantly. Furthermore, changing the calculation of principal component with short-time interval, the chaotic response of the plate shows the motion of irregular traveling waves.