Determination of the frequency spectrum of Lamb waves from a sequence of maps of the instantaneous acoustic displacement obtained with TV holography

A novel approach to an established method to calculate the frequency spectrum of Lamb waves is introduced. Lamb wavetrains are generated with the wedge method in aluminium plates, and a sequence of instantaneous acoustic out-of-plane displacement fields at the plate surface is measured with a self-developed double-pulsed TV holography system. This is achieved by emitting two laser pulses synchronized with the piezoelectric transducer that generates the waves and conveniently delayed. As a result, a 2D optical phase-change map, proportional to the aforementioned acoustic displacement field, is obtained for the instant of emission of the second laser pulse. Then, a series of maps is acquired under repeatability conditions by successively delaying the second laser pulse, so that the resulting sequence of maps records successive instants of the propagation of the wavetrain. The frequency spectrum of the wavetrain is obtained from a 3D spatio-temporal Fourier transform of the whole sequence of optical phase-change maps, as the relation between the temporal frequency and the spatial frequency along the principal propagation direction of the wavetrain. The use of a 3D Fourier transform permits to calculate the frequency spectrum regardless of the propagation direction of the wavetrain, with non-perfectly plane wavefronts and also increases the signal to noise ratio with respect to the 2D spatio-temporal Fourier transform approach. Experiments show that the resulting branches for the Lamb modes existing in the wavetrain are in agreement with the theoretical frequency spectrum of Lamb waves in aluminium.