Interpretation of bimodal interference in and optimized operational modal analysis for long-range continuously scanning laser Doppler vibrometer measurements with a beam under white noise excitation

This paper explains the phenomenon of a dominant frequency in the spectrum of a raw response measured by a long-range continuously scanning laser Doppler vibrometer (LCSLDV) system being symmetrically shifted into two sharp peaks. This phenomenon is referred to as bimodal interference in this work, which gradually becomes obvious when the scanning length is greater than 0.5 m. Bimodal interference is significant because it makes natural frequencies unable to be estimated in LCSLDV measurements and this paper analyzes its nature. Natural frequencies and mode shapes of a structure under white noise excitation can be estimated by analysis of its responses measured by the LCSLDV system. The effect of bimodal interference has been ignored in previous LCSLDV and continuously scanning laser Doppler vibrometer (CLSDV) measurement studies, but its appearance makes the value of the dominant frequency not to be accurately identified. By deducing mathematical inter-pretation of bimodal interference with analysis of incidence and reflection of a continuously scanning laser beam in a tiny time interval and comparing experimental results with 21 groups of different conditions, it is concluded that bimodal interference is caused by signal coupling between the scanning frequency of the mirror and the vibration frequency of the measured structure. There is a positive correlation between the scanning frequency and the magnitude of the symmetric frequency shifts centered at the dominant frequency generated by bimodal interference. In experimental results of LCSLDV measurements with a distance of 60 m, the frequency shift ratio compared to the dominant frequency can be reduced to 0.06% when the scanning frequency is lower than 0.01 Hz. In this case, bimodal interference is not noticeable in the spectrum. The experiment was carried out on a cantilever beam machined based on a prescribed design. Modal parameters of the cantilever beam estimated by white noise excitation were successfully estimated by the LCSLDV system with a distance of 60 m. The maximum difference between the first four natural frequencies of the cantilever beam from the finite element model and the LCSLDV system was 2.97% and the minimum difference was 1.1%.

Automated summary

This paper explains the phenomenon of bimodal interference in a long-range continuously scanning laser Doppler vibrometer (LCSLDV) system, where the dominant frequency in the spectrum is symmetrically shifted into two sharp peaks. The bimodal interference affects the estimation of natural frequencies in LCSLDV measurements, and this paper analyzes its nature.