Experiments on Nonlinear Vibrations of a Cylindrical Shallow Shell-Panel with Clamped Edges Under an In-Plane Elastic Constraint

Abstract

Experimental results are presented on nonlinear vibrations of a cylindrical shallow shell-panel with a rectangular platform. Opposite cylindrical edges of the shell-panel are clamped and the other opposite straight edges are simply supported. One side of the clamped edges is connected with elastic springs and is movable to an in-plane direction. The simply supported edges are supported by adhesive elastic films. Under the in-plane compressive force over the buckling load, the post-buckled configuration is obtained. In the specific compressive force, the shell-panel has the conditions of internal resonances. By exciting the shell-panel with periodic lateral acceleration, nonlinear periodic and non-periodic responses are observed in specific regions of the excitation frequency. These responses are examined with the Fourier spectra and the principal component analysis. Non-periodic responses are evaluated by the maximum Lyapunov exponent. Under the smaller magnitude of the compressive force, the principal resonance and the sub-harmonic resonance of 1/2 order corresponding to the lowest mode are obtained. Furthermore, the combination resonance dominated by the higher modes of vibration is also obtained. Under the larger magnitude of the compressive force, the chaotic response is generated from internal resonances close to the lowest natural frequency. Applying the principal component analysis, dominant modes of vibration and their contributions are confirmed on the combination resonance and the chaotic response.