Experiments on Chaotic Vibrations of a Rectangular Plate under an In-Plane Elastic Constraint at Clamped Edges

Abstract

Experimental results are presented on chaotic vibrations of a rectangular plate with in-plane elastic constraint. The plate has initial imperfection. Opposite edges of the plate are clamped and the other edges are simply supported. One side of clamped edges is connected to elastic springs and is movable to in-plane direction. The simply-supported edges are connected to the boundaries with adhesive flexible films. Loading in-plane compressive force to the plate, the plate shows pre-buckled configuration with the type of a softening-and-hardening spring. Under periodic lateral excitation, chaotic responses are obtained in specific frequency regions. Predominant chaotic responses are examined with the Fourier spectra, the Poincaré projections and the maximum Lyapunov exponents. Furthermore, applying the Karhunen-Loéve method, contributions of vibration modes on the chaotic responses are confirmed. It is found that the chaotic responses are generated from the internal resonant vibrations with the first mode of vibration and higher modes of vibration. The chaotic responses are dominated by the lowest mode of vibration. The higher modes of vibration contribute from 11 to 20 percent to the chaos. As the exciting amplitude increases, the amplitude of the chaotic responses increases and frequency regions of the chaotic responses shift. In the larger amplitude of the response, the frequency region shifts to the higher range owing to the resonant response with the type of a hardening spring. In contrast, the frequency region shifts to the lower range when the amplitude of the chaotic response is smaller comparatively. The resonant response with the smaller amplitude corresponds to the type of a softening spring.