Time reversal focusing of elastic waves in plates for an educational demonstration

Restricting angles of incidence to improve super resolution in time reversal focusing that uses metamaterial properties of a resonator array

Focusing waves with a spatial extent smaller than a half wavelength (i.e., super resolution or sub diffraction limit) is possible using resonators placed in the near field of time reversal (TR) focusing. While a two-dimensional (2D) Helmholtz resonator array in a three-dimensional reverberant environment has limited ability to produce a high-resolution spatial focus in the TR focusing of audible sound, it is shown that acoustic waves propagating out-of-plane with the resonator array are not as strongly affected by the smaller effective wavelength induced by the resonator array, partially negating the effect of the resonators. A physical 2D waveguide is shown to limit the out-of-plane propagation, leading to improved resolution. It is also shown that post processing using an orthogonal particle velocity decomposition of a spatial scan of the focusing can filter out-of-plane particle motion in the near field of the array, which bypasses the effect of the unwanted third spatial dimension of propagation. The spatial resolution in a reverberant environment is shown to improve in the presence of a 2D Helmholtz resonator array and then further improve by adding a 2D waveguide. The resolution among the resonator array is better still without using a waveguide and instead using the partial-pressure reconstruction.

Numerical modeling of Mach-stem formation in high-amplitude time-reversal focusing

In acoustics, time-reversal processing is commonly used to exploit multiple scatterings in reverberant environments to focus sound to a specific location. Recently, the nonlinear characteristics of time-reversal focusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), 3603-3614 (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both finite difference and finite-element models, it is shown that nonlinear interactions between high-amplitude waves lead to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of the focus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high-amplitude time-reversal focusing.

Nonlinear characteristics of high amplitude focusing using time reversal in a reverberation chamber

Time reversal (TR) signal processing is an effective tool to exploit a reverberant environment for the intentional focusing of airborne, audible sound. A previous room acoustics TR study found preliminary evidence that above a certain focal amplitude the focal waveform begins to display signs of nonlinearity [Willardson, Anderson, Young, Denison, and Patchett, J. Acoust. Soc. Am. 143(2), 696-705 (2018)]. This study investigates that nonlinearity further by increasing the focal peak amplitudes beyond that previously observed. This increases the nonlinear characteristics, allowing for a closer inspection of their properties. An experiment is conducted using eight horn loudspeaker sources and a single receiver in a reverberation chamber. A maximum peak focal amplitude of 214.8 kPa (200.6 dB_pk) is achieved. The focus signal waveforms are linearly scaled to observe and characterize the nonlinear amplification of the waveform. Frequency spectra of the peak focal amplitudes are plotted to observe changes in frequency content as the signals become nonlinear. A one-dimensional spatial scan of the focal region is conducted to observe properties of the converging and diverging waves. A proposal for a possible explanation involving free-space Mach stem formation is given.

The physics of knocking over LEGO minifigures with time reversal focused vibrations for use in a museum exhibit

Time reversal (TR) is a method of focusing wave energy at a point in space. The optimization of a TR demonstration is described, which knocks over one selected LEGO minifigure among other minifigures by focusing the vibrations within an aluminum plate at the target minifigure. The aim is to achieve a high repeatability of the demonstration along with reduced costs to create a museum exhibit. By comparing the minifigure's motion to the plate's motion directly beneath its feet, it is determined that a major factor inhibiting the repeatability is that the smaller vibrations before the focal event cause the minifigure to bounce repeatedly and it ends up being in the air during the main vibrational focal event, which was intended to launch the minifigure. The deconvolution TR technique is determined to be optimal in providing the demonstration repeatability. The amplitude, frequency, and plate thickness are optimized in a laboratory setting. An eddy current sensor is then used to reduce the costs, and the impact on the repeatability is determined. A description is given of the implementation of the demonstration for a museum exhibit. This demonstration illustrates the power of the focusing acoustic waves, and the principles learned by optimizing this demonstration can be applied to other real-world applications.

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.

Resolution improving filter for time-reversal (TR) with a switching TR mirror in a halfspace

This paper addresses the issue of using a switching time-reversal (TR) mirror for wave energy focusing to subsurface targets. The motivation stems from applications in geophysics, hydro-geology, environmental engineering, and even in therapeutic medicine. Using TR concepts, wave-focusing is straightforward and efficient, but only under ideal conditions that are, typically, unattainable in practice. The unboundedness of the subsurface that hosts the target, the TR mirror's limited aperture, and, worse, the practical need for a switching TR mirror, where recorded Dirichlet data are time-reversed as Neumann data (switching mirror), all contribute to the deterioration of the focusing resolution at the target. Herein, the development of a data filter is discussed, which is shown to be capable of overcoming the switching mirror's shortcoming, leading to improved focusing resolution. The filter's effect is demonstrated with numerical examples.

Nonlinearity from stress corrosion cracking as a function of chloride exposure time using the time reversed elastic nonlinearity diagnostic

The Time Reversed Elastic Nonlinearity Diagnostic (TREND) has a long history of successful nondestructive detection of cracks in solids using nonlinear indicators. Recent research implemented TREND to find stress corrosion cracking (SCC) in the heat-affected zone adjacent to welds in stainless steel. SCC development around welds is likely to occur due to the temperature and chemical exposure of steel canisters housing spent nuclear fuel. The ideal SCC detection technique would quantify the size and extent of the SCC, rather than just locating it, as TREND has been used for in the past. The current paper explores TREND's ability to detect an assumed increase in SCC over time using 13 samples exposed to a magnesium chloride (MgCl₂) bath for different lengths of time. The samples are then scanned with TREND and nonlinearity is quantified for each scan point and each sample. The results suggest that TREND can be used to not only locate SCC in the heat-affected zone, but also track an increase in nonlinearity, and thereby an increase in damage, in samples exposed to the MgCl₂ solution for a longer duration.

Time reversal acoustics applied to rooms of various reverberation times

Time Reversal (TR) is a technique that may be used to focus an acoustic signal at a particular point in space. While many variables contribute to the quality of TR focusing of sound in a particular room, the most important have been shown to be the number of sound sources, signal bandwidth, and absorption properties of the medium as noted by Ribay, de Rosny, and Fink [J. Acoust. Soc. Am. 117(5), 2866-2872 (2005)]. However, the effect of room size on TR focusing has not been explored. Using the image source method algorithm proposed by Allen and Berkley [J. Acoust. Soc. Am. 65(4), 943-950 (1979)], TR focusing was simulated in a variety of rooms with different absorption and volume properties. Experiments are also conducted in a couple rooms to verify the simulations. The peak focal amplitude, the temporal focus quality, and the spatial focus clarity are defined and calculated for each simulation. The results are used to determine the effects of absorption and room volume on TR. Less absorption increases the amplitude of the focusing and spatial clarity while decreasing temporal quality. Dissimilarly, larger volumes decrease focal amplitude and spatial clarity while increasing temporal quality.

Time reversal focusing of high amplitude sound in a reverberation chamber

Time reversal (TR) is a signal processing technique that can be used for intentional sound focusing. While it has been studied in room acoustics, the application of TR to produce a high amplitude focus of sound in a room has not yet been explored. The purpose of this study is to create a virtual source of spherical waves with TR that are of sufficient intensity to study nonlinear acoustic propagation. A parameterization study of deconvolution, one-bit, clipping, and decay compensation TR methods is performed to optimize high amplitude focusing and temporal signal focus quality. Of all TR methods studied, clipping is shown to produce the highest amplitude focal signal. An experiment utilizing eight horn loudspeakers in a reverberation chamber is done with the clipping TR method. A peak focal amplitude of 9.05 kPa (173.1 dB peak re 20 μPa) is achieved. Results from this experiment indicate that this high amplitude focusing is a nonlinear process.

The effect of transducer directivity on time reversal focusing

This letter explores the effect of the directivity of a source on time reversal acoustic focusing of energy. A single loudspeaker produces an airborne focus of sound in a reverberation chamber and in a classroom. Individual foci are created at microphone positions that surround the loudspeaker. The primary axis of the loudspeaker is then rotated and experiments are repeated to average out the room response. Focal amplitude, temporal quality of the foci, and spatial focusing quality are compared to determine the optimal angle to aim a directional source axis relative to the desired focal position.