固定辺で面内弾性拘束を受ける長方形板のカオス振動実験(<特集>D&D 2008)

Abstract

Experimental results are presented on chaotic vibrations of a rectangular plate with an in-plane elastic constraint. Opposite edges of the plate are clamped and the other edges are simply supported. One of the clamped edges is connected with elastic springs and is movable to an in-plane direction. The simply-supported edges are composed with adhesive elastic thin films. Under the specified in-plane compressive force, the plate shows the type of a softening-and-hardening spring. Moreover, the plate has the condition of the two to three internal resonance between the second and third modes. Under periodic lateral excitation, non-periodic responses are obtained in specific frequency regions. The non-periodic responses are examined with the Fourier spectra, the Poincare projections and the maximum Lyapunov exponents. It is found that two types of chaotic responses are generated from the internal resonances dominated by the first mode and higher modes of vibration. Appying the Karhunen Loeve method, contributions of vibration modes on the chaotic responses are confirmed. The first mode contributes to the chaotic responses dominantly. The higher three modes including the second, third and fourth modes have 10 to 20 percent of contribution. As exciting amplitude increases, the lower frequency region of chaotic response with large amplitude shifts to the higher frequency range owing to the hardening nonlinearity of the plate, while the higher region of chaotic response with small amplitude shifts to the lower frequency range.