Estimation of Lamb wave propagation by means of Fourier spectral frequency response function

Considering the frequency dispersion and the scale sensitivity in wave propagation, the central frequency and bandwidth should be carefully selected in Lamb wave-based structural health monitoring. These crucial parameters are hardly determined without the prior knowledge. Therefore, massive trials should be conducted before the formal test. A Fourier spectral Frequency Response Function (FRF) method is proposed to address this problem. As the FRF contains wide-band information on the relationship between excitation and output, the Lamb wave responses in a wide frequency range can be estimated by using an arbitrary virtual input within the frame of single FRF test, being free from the massive experimental works. The theoretical FRF can be obtained from the unit impulse response of a linear system, but this path is impracticable due to the difficulty of exciting the ideal impulse. Considering the integral relationship and Fourier differential properties between step excitation and the ideal impulse, a robust approximation of wave signal by FRF is developed. Synthetic data tests and experiments both verified that the present method can accurately extract the response in isotropic and anisotropic materials for the specifically designed excitation signal in a wide parameter range.