J. Luis Deán

Determination of thickness and elastic constants of aluminum plates from full-field wavelength measurements of single-mode narrowband Lamb waves

A method based on fitting the theoretical dispersion curves of Lamb waves to experimental data is presented to determine the thickness and two independent elastic constants of aluminum plates a few millimeters thick. The waves are generated by means of the wedge method using a narrowband source, selecting the wedge angle and the acoustic frequency f so that mainly one mode is excited. A self-developed pulsed electronic speckle pattern interferometry system renders a two dimensional map of the out-of-plane acoustic displacement field at the plate surface, which allows an accurate measurement of the acoustic wavelength lambda(1). For any mode, the relation between lambda(1) and f depends on the three unknown parameters, so at least three experimental measurements (lambda(1i),f(i)) with different frequencies and/or different modes are required to calculate them. The suitability of different Lamb modes to determine each parameter when the others are known is studied, as well as the conditions that the experimental set of values must fulfill to calculate all three parameters. Numerous Lamb modes at different frequencies are generated in each plate, and a fitting is made based on the minimization of the error function, resulting in an accuracy better than 1%.

Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method.

The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.

Measurement of Lamb waves dispersion curves under narrowband monomode excitation using TV holography

Ultrasonic Lamb waves provide a useful means for the nondestructive determination of the material elastic constants of shell structures such as plates, pipes, cans and many others. A new optical technique is described for the measurement of the dispersion curves of Lamb wave modes. The experimental system employs the wedge method for the excitation of Lamb modes in aluminum plates of thickness in the range of a few millimetres. Long tone-bursts are used in order to ensure the generation of narrowband ultrasonic waves. Furthermore, an appropriate selection of the wedge angle allows one to generate only the desired individual Lamb mode. The detection of the surface out-of-plane displacements is performed by our self-developed pulsed TV holography system, which evaluates the optical phase by the Spatial Fourier Transform Method. Inasmuch as a whole-field measurement is realized, the wavelength of the excited mode can be precisely measured from the TV holography displacement maps. On the other hand, the wave frequency is measured by a pointwise method, namely a Michelson speckle interferometer. The phase velocity is directly obtained as the product of these two values. Measurements are done for several frequencies and several Lamb modes, thus yielding a collection of experimental points. By fitting these results to the theoretical Rayleigh-Lamb frequency spectrum, values of the shear wave velocity and the Poissons ratio of the plate material are obtained. For a better accuracy in the measurements, the longitudinal phase velocity was directly determined by the pulse-echo method. The additional knowledge of the mass density allows one to calculate the Youngs modulus.

Numerical reconstruction of acoustic bulk waves in aluminium from TV holography surface displacement measurements

The paper describes a hybrid technique, aimed at nondestructive inspection of materials, that combines whole-field optic measurements, acoustic excitation and a numerical reconstruction method. The interior of a thick specimen is probed by short bursts of narrowband ultrasonic bulk waves. The acoustic wavefronts that constitute the burst emerge at the opposite face of the sample and induce periodic displacements of its surface. These displacements are measured by TV holography, a whole-field optical technique, also known as electronic speckle pattern interferometry (ESPI). The measurement process yields the complex amplitude (i.e., amplitude and phase) of the acoustic wavefronts at the plane of the surface as a series of 2-D, complex-valued maps. Lastly, a numerical reconstruction algorithm that uses the Rayleigh-Sommerfeld diffraction formula is employed to calculate the amplitude and phase of the acoustic wavefronts at any other plane in the interior of the specimen. This procedure is analogous to the numerical reconstruction of optical object wavefronts in digital holography (with light and free space taking the place of acoustic waves and the material medium, respectively), so the present method could also be designated as digital opto-acoustic holography. If the wavefronts are affected by the presence of inhomogeneities in the medium, information about the shape and position of such defects could be retrieved from the reconstructed wavefront at the appropriate depth. The technique herein proposed was successfully tested in an alluminium specimen with an artificial defect.

Modelling for characterizing defects in plates using two-dimensional maps of instantaneous ultrasonic out-of-plane displacement obtained by pulsed TV-holography

It has been demonstrated that non-destructive inspection of plates can be performed by using two-dimensional maps of instantaneous out-of-plane displacements obtained with a self-developed pulsed TV-holography system. Specifically, the interaction of guided elastic waves with defects produces scattering patterns that contain information about the defects (position, dimensions, orientation, etc.). For quantitative characterization on this basis, modeling of the wave propagation and interaction with the defects is necessary. In fact, the development of models for scattering of waves in plates is yet an active research field in which the most reliable approach is usually based on the rigorous formulation of elasticity theory. By contrast, in this work the capability of a simple two-dimensional scalar model for obtaining a quantitative description of the output two-dimensional maps associated to artificial defects in plates is studied. Some experiments recording the interaction of narrowband Rayleigh waves with artificial defects in aluminum plates are presented, in which the acoustic field is obtained from the TV-holography optical phase-change maps by means of a specially developed two-step spatio-temporal Fourier transform method. For the modeling, harmonic regime and free-stress boundary conditions are assumed. Comparisons between experimental and simulated maps are included for defects with different shapes.

Video visualization of the dispersive behaviour of Rayleigh and Lamb wavetrains by double-pulsed TV holography

In this work we present an application of TV holography to the generation of movies showing the propagation of acoustic guided waves in aluminium plates. Each movie shows a wavetrain whose envelope (i.e., the acoustic amplitude) and carrier wave move at the group and phase velocities, respectively. In particular, we use the S0 Lamb mode and the Rayleigh wave to illustrate the behaviour of dispersive and non-dispersive waves. Both wavetrains were generated by means of the classical wedge method and detected with our double-pulsed TV holography system, which renders 2D maps of the instantaneous out-of-plane displacement fields of the plate surface. The snapshots of the movie are obtained from a set of these 2D measurements, taken under repeatability conditions by successively increasing the delay between generation and detection. Then, a processing based on the 3D-FFT is applied to the set; the result is a new set of complex maps that permits to characterize the evolution of the positions of the envelope centre and of a point with a given value of the phase, so that it is possible to compare the phase and group velocities of the wavetrain.

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.

Scanner of dynamic deflections (SCADD): a new approach for field data acquisition of the vibration of civil structures

We describe a novel instrument for the remote measurement of dynamic deflection shapes of structures several tens of meters long, based on geometrical optics techniques with scanned laser illumination, which we have named Scanner of Dynamic Deflections (SCADD). A set of aligned control points is measured in each scan, each point being defined by a retroreflector attached to the structure. By measuring the delay of the optical signal reflected from each point, the system renders a component of the displacement of that point which is transverse to the illumination direction. The intended application of SCADD is the field data acquisition for diagnosing the structural health of civil infrastructures, either as a stand-alone instrument or integrated in a non-destructive structure testing system comprising several data sources, typically an array of accelerometers and a SCADD unit. The foreseen measurement accuracy and the spatial and temporal sampling density of SCADD are adequate to the application of modal analysis techniques. For the purpose of locating our proposal in its technological context, we include firstly a brief description of the most usual methods (optical and non-optical) for the field measurement of vibrations of civil structures. Then, the SCADD principle of measurement and architecture are detailed. In the experimental section we describe a SCADD prototype and a series of measurements of a control point located 18 m away from the SCADD head, from which we extract the repeatability and a calibration curve of the prototype. Finally, the main advantages of SCADD are detailed.

Full-field localization of plate-thickness inhomogeneities through the local changes in the wavenumber of Lamb waves measured with pulsed TV holography

A new capability of TV holography, also known as electronic speckle pattern interferometry (ESPI), is presented for locating and imaging slightly thinned or thickened areas in metallic plates. It is based on the measurement of the wavenumber variation of narrowband Lamb waves as they propagate through these plate-thickness inhomogeneities. The relation between frequency and phase velocity of all Lamb modes depends on the elastic constants of the material the plate is made of (two parameters in isotropic materials) and on the plate thickness. Therefore, the associated dispersion curve of each mode present wavenumber changes that are sensitive to a thickness reduction. We have formerly developed a double-pulsed TV holography system which allows the full-field measurement of the instantaneous out-of-plane displacement field induced by surface acoustic waves and, by further processing, to calculate maps of the acoustic amplitude and phase. A method based on further analysis of the acoustic complex-displacement map is therefore proposed to locate and characterize such smooth thickness reductions. In particular, we calculate a map of the local wavenumber of the acoustic wave as the modulus of the two-dimensional gradient of the mechanical phase. Hence, as the variations in the wavenumber correspond to variations in the plate thickness, the local thickness reductions and increments can be detected in this map. Within the resolution limits imposed by the wavelength of the Lamb wave, this method allows also to contour the shape of the inhomogeneities. The technique is demonstrated herein by imaging a X-shaped recess machined on an aluminium plate.