Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Non-linear modal interactions in free-edge thin spherical shells: measurements of a 1:1:2 internal resonance

Olivier Thomasa,*, Éric Luminais, Cyril Touzéb
aStructural Mechanics and Coupled Systems Laboratory, CNAM, 2 rue Conté, 75003 Paris, France bENSTA-UME, Chemin de la Hunière, 91761 Palaiseau cedex, France

  Full Text
This study is devoted to the experimental validation of a theoretical model of large amplitude vibrations of thin spherical shells described in Thomas et al. [1]. A specific mode coupling due to a 1:1:2 internal resonance between an axisymmetric mode and two companion asymmetric modes is especially addressed. The structure is forced with a sinusoidal signal of frequency close to the natural frequency of the axisymmetric mode. The experimental setup, which allows precise measurements of the vibration amplitudes of the three involved modes, is presented. Experimental resonance curves showing the amplitude of the modes as functions of the driving frequency are compared to the theoretical ones. A good qualitative agreement is obtained with the predictions given in the model. The quantitative discrepancies are discussed and an improvement of the model is proposed.

Keywords:  Shallow spherical shells; Geometric non-linearities; Internal resonances; Non-linear vibrations; Experiments

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