Nonlinear nonclassical elasticity applied to the analysis of low frequency flexural vibrations: theory and experiments.

Motivated by the increasing interest on nonlinear nondestructive damage detection, a comparison of the nonlinear elastic behavior of damaged samples and their intact state is presented. Flexural vibration is induced in thin glass plates with laser thermal shock induced micro-cracks by means of two thin piezo-ceramic patches glued in a bimorph configuration. The cases of direct excitation of a resonance and excitation of an internal resonance cases are considered. The resulting nonlinear vibrations exhibit the main features of quadratic hysteresis: linear variation of the resonance frequency and quadratic production of the third harmonic. A theoretical model for nonlinear resonant flexural vibrations based on the Preisach-Mayergoyz constitutive relations is proposed for damage quantification. Experimental comparison between the intact and damaged sample indicates an increase in the relevant nonlinearity parameter, indicating a widening of the hysteresis loop due to damage.