Experiments on Chaotic Vibrations of an Outer-Free and Inner-Clamped Annular Plate with Initial Deflection

Abstract

This paper presents experimental results on chaotic vibrations of an annular plate with initial deflection. The effect of modal interaction on chaotic vibrations is main scope in this paper. The plate is free on the outer edge and clamped on the inner edge. The initial deflection of the plate is nine thousandth times to the difference between the outer radius and the inner radius. The lowest and the third modes with one nodal-diameter have different natural frequencies due to the initial deflection. The second mode corresponds to the mode without nodal-diameter. The fourth and fifth modes have two cross nodal-diameters. The linear natural frequencies of the second and the third modes coincide with a slight deviation. The plate is subjected to lateral periodic acceleration. Sweeping the excitation frequency, nonlinear response curves of the plate are recorded. In the wide frequency ranges, non-periodic responses are generated. The responses are inspected by the Fourier spectrum, the Poincaré projection, the maximum Lyapunov exponent and the principal component analysis. The predominant non-periodic response is confirmed as the chaotic response generated from one-to-one and two-to-three internal resonances. The lowest, the second and the third modes are coupled in the internal resonances. The principal component analysis is applied to the chaotic response selected with short-time intervals sequentially collected from the long-time response. It is found that exchanges of the contribution ratio are observed among the lowest, the second and the third modes. Furthermore, the nodal diameters of the fourth and the fifth modes are fluctuated along the circumferential direction in the chaotic response.