On the theoretical limitations in estimating thickness of a plate-like structure from a full-field single-tone response Lamb wave measurement

Nicholas Stull; Eric Flynn; Matthew Mascarenas

doi:10.1016/j.ultras.2020.106230

On the theoretical limitations in estimating thickness of a plate-like structure from a full-field single-tone response Lamb wave measurement

Ultrasonics. 2020 Dec:108:106230. doi: 10.1016/j.ultras.2020.106230. Epub 2020 Jul 31.

Authors

Nicholas Stull¹, Eric Flynn², Matthew Mascarenas³

Affiliations

¹ Los Alamos National Laboratory, 4200 West Jemez Rd., Los Alamos, NM 87545, USA. Electronic address: nstull@lanl.gov.
² Los Alamos National Laboratory, 4200 West Jemez Rd., Los Alamos, NM 87545, USA. Electronic address: eflynn@lanl.gov.
³ University of California - San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA.

PMID: 32805572
DOI: 10.1016/j.ultras.2020.106230

Abstract

A persistent question in wavenumber analysis in the estimation of thickness from a steady-state wave field is identifying the theoretical sensitivity of the system. A well-known trade-off between spatial frequency/wavenumber resolution and thickness resolution exists. The current work presents a calculation of the Cramer-Rao Lower bound (CRLB), specifically as applied to thickness estimates, for a 2-dimensional multi-mode waveform in Gaussian noise. Cases of near-field and far-field excitation are considered, and transducer position with respect to the scan area is also varied. Additionally, we consider the CRLB in a plate with multiple sources, simulated as sources placed on the boundary of the plate. We conclude by presenting the CRLB values in terms of frequency for various thicknesses, and by presenting optimal excitation frequencies for a nominal thickness, based on the CRLB.

Keywords: Cramer-Rao lower bound; Lamb waves; Laser Acoustic Wavenumber Spectroscopy.