Synthesis of Inhomogeneous Waves Using the Least-squares Method

Trevor A Kyle, Purdue University


The aim of the work presented in this document is to demonstrate the versatility and applicability of least-squares reconstruction of acoustic waves. Appropriately tailored, certain kinds of acoustic waves are able to thermomechanically excite energetic materials in a safe, reliable manner. This allows for easier and more effective detection than current methods are able to offer. Typically, due to the large impedance difference between any given fluid and solid, it is exceedingly difficult to transmit energy between the two dissimilar media. However, it has been shown that certain spatially decaying plane waves, called inhomogeneous waves, are able to breach the fluid--solid barrier and transfer most of their energy into the second medium. However, as inhomogeneous acoustic waves cannot be easily generated from a single source, they must be reconstructed as a superposition of several waves from independent sources. This approach was studied through the lens of the least-squares method, which tunes a discrete number of sources to produce a desired waveform on a target surface. The simulations presented in this document analyze the range of parameters for which the least-squares method of sound field reconstruction provides an acceptable and physically feasible output. The conditions of these simulations were tested with real sources to determine the extent to which irregularities in the sources affected the reconstruction accuracy. By constructing an array of sources and an array of receivers, the effects of varying the standoff distance, source spacing, and level of inhomogeneity were analyzed. While empirical adjustments to the established model were not able to reduce the reconstruction error to the theoretical levels, they did allow for accurate reconstruction over a wide range of excitation parameters. This document provides the framework for further tests of least-squares reconstruction over a wide span of parameters. Utilizing the methods discussed here, progress can be made towards the eventual goal of inducing a temperature increase in a mock energetic material utilizing inhomogeneous acoustic waves.




Bolton, Purdue University.

Subject Area

Mechanical engineering|Acoustics

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