A Multi-step Interpolated-FFT procedure for full-field nonlinear modal testing of turbomachinery components

Abstract

Model updating for lightweight structures featuring geometrical nonlinearities has long been a goal in the aerospace industry, which requires spatially detailed measurement of the structure vibrating at large amplitudes. Performing such a measurement for lightweight structure is an extremely challenging task due to its low mass-to-area ratio, complex spatial deformation shapes, and geometrically nonlinear behaviours. Indeed, the current full-field measurements of nonlinear structural dynamics are mostly limited to flat, small-scale, academic structures such as beams or plates. To enable full-field measurement of nonlinear responses of large-scale industrial structures, a procedure based on the Three-Dimensional Scanning Laser Doppler Vibrometry (3D SLDV) is developed in this paper, in which full-field, multi-harmonic operating deflection shapes are measured when the structure is vibrating at its resonance. More specifically, a super-short sampling interval is used for each scan point to achieve a significant reduction in measurement duration. A novel Multi-step Interpolated-Fast Fourier Transform (Multi-step Interpolated-FFT) procedure is proposed to refine the coarse frequency resolution and suppress the severe spectral leakage of the signal spectra. In the procedure, the instantaneous driving frequency is first interpolated using the force signal and then used to perform a fixed-frequency interpolation for each harmonic of the response signals. In such a way, it allows accurate estimations of the frequencies, magnitudes and phase lags of the constituent harmonics in the measured signal sets. Numerical validations of the proposed procedure are carried out to investigate its accuracy and robustness with regard to different signal frequencies and noise levels before it is applied to experimental data of an industrial-scale fan blade. Results have shown that it allows, for the first time, to capture full-field, multi-harmonic operating deflection shapes of a large-scale, geometrically-nonlinear structure vibrating at its resonance. These spatially-detailed operating deflection shapes are advantages in describing local deformation patterns of a nonlinear structure, allowing essential ingredients in model updating algorithms, such as the Modal Assurance Criterion (MAC) values, to be correlated with exceptionally high quality.