Comparison of lock-in correlation and a novel periodogram method for experimental multi-harmonic thermoelastic analysis

Abstract

Lock-in correlation is a simple, efficient and widely employed method for thermoelastic stress analysis under cyclic loading. Frequency domain analysis of the thermoelastic signal using the Fourier transform has been also valuable for researchers, even though it presents some drawbacks. In this paper, a new frequency-domain method for thermoelastic analysis through periodograms using Welch’s averaging method has been developed. This method supplies the lack of phase shift information of the simple Fourier transform for thermoelastic signals and considerably reduce the data size. This work evaluates its performance against lock-in correlation through two experiments with opposite features for multi-harmonic analysis. One experiment consisted in the analysis of the thermoelastic signal in a plate with a centred hole, exhibiting a stress concentration and using the second harmonic as an indicator of the non-linearities. The second experiment consisted in the characterisation of mode shapes thermal maps during the simultaneous excitation of multiple specimen resonances. In comparison with the stress concentrator experiment, here the level of the thermal signal is lower and the number of frequencies to analyse is higher. The analysis of the thermal maps by both methods revealed that they yield practically identical results for any experiment. However, the evaluation of the computation efficiency highlights that the periodogram method has fewer memory requirements whereas, in terms of computation time, lock-in correlation is more efficient to analyse fewer frequencies in short image sequence tests, being the periodogram method more efficient for the opposite case.