Material property estimation in thin plates using focused, synthetic-aperture acoustic beams

Abstract

The method developed here exploits the wide angular range of focused acoustic probes and the large synthetic aperture of scanned transducers to permit a rapid and reliable estimation of material properties in thin plates. It is found in several tests with various materials that estimates of elastic behavior using this method agree with contact measurements to within less than 5%. The method utilizes transmission (or reflection) coefficient reconstruction for an infinite thin plate, across a wide range of frequency and wave number, from which elastic property estimates are made. Data collected over a large synthetic acoustic aperture are processed with temporal and spatial Fourier transforms applied to change the acquired data from the coordinate and time domains to the wave number and frequency domains. Extrinsic real-beam effects on the data are accounted for with a complex transducer point analysis. Transmission measurements yield reconstructed data extending to the mode cutoffs, permitting easy and nearly unambiguous estimation of a subset of the elastic stiffnesses. For anisotropic plates, elastic stiffnesses are estimated with an inversion procedure that uses only limited data carefully selected from different portions of the measured scattering coefficient. Estimates are made by reconstructing in a stepwise fashion, based on sensitivity studies, where only one stiffness is estimated from the data at any one time, restricting the optimization to a robust one-dimensional search.

Air-coupled ultrasonic through-transmission thickness measurements of steel plates

“…[67] used laser based ultrasound measurements of the dispersion curves, applying them to a theoretical model in order to infer the thickness. This technique can be used to measure not only thickness, but also the elastic parameters of a plate [68].…”

Tank measurements of scattering from a resin-filled fiberglass spherical shell with internal flaws

“…If compared to methodologies designed to invert the material properties of plates, [9][10][11]15 the insonification of an object with circular cross section allows the simultaneous excitation of all the elastic waves supported in a certain bandwidth through a single monostatic measurement, without the need for a bistatic measurement system and/or of the insonification at a fan of possible incident angles, as is generally done in the case of a flat interface. The resulting acoustic response is rich in information, but also more complicated to analyze, and, hence, requires model-based inversion.…”

“…Acoustic inversion based on elastic scattering measurements either in air 7,8 or in water [9][10][11] is generally applied to thin plates of various materials, including composite laminates and plastics. Kinra et al 12 presented a method for simultaneous health monitoring and inversion of the properties of the individual thin layers comprising a multilayered medium.…”

Elastic Constants Inversion from Ultrasonic Transmission Spectra Obtained Using a Wide Aperture PVDF Sensor

“…[6] reported successful implementation of two-step inversion -Simplex followed by Newton-Raphson from transmitted ultrasonic fields. Fei and Chimenti [13,14] have successfully implemented reconstruction of elastic stiffness using "targeted stiffness reconstruction" from data obtained from a single scan of plate samples done using focused transducers. The inverse problem has been attempted here using Genetic Algorithm (GA) based optimization technique [15] - [19].…”