High amplitude vibrations induce amplitude dependence of the characteristic resonance parameters (i.e., resonance frequency and damping factor) in materials with microscopic damage features as a result of the nonlinear constitutive relation at the damage location. This paper displays and quantifies results of the nonlinear resonance technique, both in time (signal reverberation) and in frequency (sweep) domains, as a function of sample crack density. The reverberation spectroscopy technique is applied to carbon fiber reinforced plastic (CFRP) composites exposed to increasing thermal loading. Considerable gain in sensitivity and consistent interpretation of the results for nonlinear signatures in comparison with the linear characteristics are obtained. The amount of induced damage is quantified by analyzing light optical microscopy images of several cross-sections of the CFRP samples using histogram equalization and grayscale thresholding. The obtained measure of crack density is compared to the global macroscopic nonlinearity of the sample and explicitly confirms that the increase in nonlinearity is linked to an increased network of cracks. A change from 1% to 3% in crack density corresponds to a tenfold increase in the signature of nonlinearity. Numerical simulations based on a uniform distribution of a hysteretic nonlinear constitutive relation within the sample support the results.

In this paper, two methods to acquire the dispersion of bending waves in beams are compared: the spatial Fourier transform and inhomogeneous wave correlation. Two examples of beams with non-standard dynamic properties are given: layered beams made out of wood (cross laminated timber) and beams with a periodically varying thickness profile. Dynamic testing, such as modal analysis or wave speed measurements, can be used to determine the elastic properties of materials. A direct measurement of the dispersion facilitates an easy assessment of the stiffness parameters over a wide frequency range for layered beams made out of orthotropic layers. The efficiency of structural metamaterials, elastic structures engineered to exhibit band gaps in which waves are quickly attenuated, can also be addressed through the dispersion relation.

In view of emerging imaging technologies based on the combination of Time Reversed Acoustics (TRA) with Nonlinear Elastic Wave Spectroscopy (NEWS) for the detection and localization of micro-damage in solids, we have investigated the benefits of chirped source signal excitation, inverse filtering techniques, and the implementation of chaotic cavity transducers to improve the quality of energy focusing, especially for weakly reverberant media. Chaotic cavity transducer focusing is defined as the hardware-software combination of a piezoelectric ceramic glued on a cavity of chaotic shape on the one hand with the reciprocal Time Reversal (or Inverse Filter) technique on the other hand. Experimental data for reverberant and nonreverberant composite plates show that the use of chirps, inverse filtering and chaotic cavity transducers significantly enhances the focusing process, and enables focusing in a nonreverberant medium using only one transducer. As a potential exploitation, the application of the chaotic cavity transducer concept for synthetic imaging is examined, revealing several properties similar to phased arrays.