The performance of time reversal in elastic chaotic cavities as a function of volume and geometric shape of the cavity.

Time reversal is used as an energy-focusing technique in nondestructive evaluation applications. Here, it is often of interest to evaluate small samples or samples that do not lend themselves to the bonding of transducers to their surfaces. A reverberant cavity, called a chaotic cavity, attached to the sample of interest provides space for the attachment of transducers as well as an added reverberant environment, which reverberation is critical to the quality of time reversal focusing. The goal of this research is to explore the dependence of the quality of the time reversal focusing on the size and geometric shape of the chaotic cavity used. An optimal chaotic cavity will produce the largest focusing amplitude, best spatial resolution, and linear focusing of the time reversed signal. Ultrasonic elastic-wave experiments are performed on a rectangular, cylindrical, and three-dimensional Sinai billiard prism samples, and experiments are repeated each time these samples are successively cut down to smaller volumes. As the size of the cavity decreases, the peak amplitude may increase or decrease depending on the normalization scheme employed. The higher the degree of ergodicity of the cavity, the higher the amplitude and quality focusing achieved.

A comparison of impulse response modification techniques for time reversal with application to crack detection.

Time reversal (TR) focusing used for nonlinear detection of cracks relies on the ability of the TR process to provide spatially localized, high-amplitude excitation. The high amplitude improves the ability to detect nonlinear features that are a signature of the motion of closed cracks. It follows that a higher peak focal amplitude than what can be generated with the traditional TR process will improve the detection capability. Modifying the time-reversed impulse response to increase the amplitude of later arrivals in the impulse response, while maintaining the phase information of all arrivals, increases the overall focal signal amplitude. A variety of existing techniques for increasing amplitude are discussed, and decay compensation TR, a technique wherein amplitude is increased according to the inverse of the amplitude envelope of the impulse response decay, is identified as the best modification technique for nonlinear crack detection. This technique increases the focal signal amplitude with a minor introduction of harmonic content, a drawback in two other methods studied, one-bit TR and clipping TR. A final study employs both decay compensation TR and traditional TR, focusing on a rod with stress corrosion cracking, and compares the merits of each in detecting nonlinearity from cracks in a real system.