Generalized Berry conjecture and mode correlations in chaotic plates

Extracting guided waves from cross-correlations of elastic diffuse fields: applications to remote structural health monitoring

Due to their apparent complexity, diffuse fields are not commonly used by conventional structural health monitoring methodologies. However, recent theoretical and experimental studies have demonstrated that local Green's functions (GFs) can be estimated from the cross-correlation of elastic diffuse fields (CDFs) recorded between any points of a sensor grid and generated by sources located remotely from the monitoring area. Hence, this CDF technique effectively transforming each measurement point into a virtual elastic source, thus allowing to measure the local structural response (or GF). Theoretical and experimental studies are conducted to assess the broadband performance of the CDF technique for the extraction of low-frequency coherent Lamb waves (4-90 kHz) propagating in a thin aluminum plate of complex geometry using a scanning laser Doppler vibrometer. The coherent signal-to-noise ratio and the accuracy of the phase and group velocity measurements of the coherent A(0) mode obtained from CDF are also measured to quantify the influence of the spatio-temporal characteristics of the recorded diffuse field, the number and spatial configuration of the remote ultrasonic sources, and the influence of incoherent measurement noise (e.g., sensor noise). In addition, a criterion to assess the emergence rate of late coherent coda arrivals from CDF is also formulated.

Statistical properties of experimental coherent waves in microcavity lasers: analogous study of quantum billiard wave functions

We use a microcavity laser to explore the properties of experimental coherent waves as an analogous study of the chaotic wave functions in quantum billiards. With the eigenstate expansion method, the experimental high-order chaotic coherent waves are well reconstructed. The reconstructed wave functions are employed to calculate the field and intensity correlations. It is found that the spreading of k-space (momentum space) distribution leads to not only wave localization in coordinate space but also enhancement of long-range correlations.

Wave-vector resonance in a nonlinear multiwavespeed chaotic billiard

Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multiwavespeed chaotic billiards, the average coupling strength can exhibit sharp discontinuities as a function of frequency related to wave-vector coincidences between constituent waves of different wavespeeds. The phenomenon is investigated numerically for an ensemble of two-dimensional square two-wavespeed billiards with rough boundaries and quadratic nonlinearity representative of elastodynamic waves. Results of direct numerical simulations are compared with theoretical predictions.