Laser-vibrometric measurement of oscillating piezoelectric actuators and of Lamb waves in CFRP plates for structural health monitoring Jürgen Pohl a, Gerhard Mook a, Rolf Lammering b and Sven von Ende b a Otto-von-Guericke-University Magdeburg, Germany Institute of Materials and Joining Technology (IWF) b Helmut-Schmidt-University/University of the Federal Armed Forces Hamburg, Germany Institute of Mechanics Abstract. The use of Lamb waves is attractive for structural health monitoring of plate and shell structures since their propagation in thin-walled structures is disturbed at damage locations especially at high frequencies. Lamb waves can easily be generated by thin piezoelectric plates which are attached to the surface of the structure. For the observation of the oscillating actuator as well as the propagating Lamb waves laser vibrometry is a powerful tool. Examples of vibrations of free and bonded piezoelectric actuators are given with special regard to the influences of contacts and other parameters, affecting the effectiveness of the wave generation. The determination of important features of Lamb wave propagation in carbon fibre reinforced plastics includes the measurement of dispersion curves and the estimation of attenuation and anisotropy. The interactions of Lamb waves with defects represented by reflections, transmissions and mode conversions are visualised and are easily to interpret. Keywords: Structural Health Monitoring, Lamb waves, laser-doppler-vibrometry. PACS: 62.30.+d, 81.05.Qk, 83.60.Uv 1. STRUCTURAL HEALTH MONITORING Structural Health Monitoring (SHM) is a new, rapidly developing technology for damage detection in technical structures. Especially lightweight structures and designs, which are highly sensitive to damage development, require new, sophisticated technologies for damage detection and characterisation. Typical examples for such structures are fibre reinforced materials, e. g. Carbon Fibre Reinforced Plastics (CFRP), which are used more and more in aerospace structures and other areas. SHM allows for permanent and automatic assessment of the structural integrity by built-in devices such that nondestructive testing becomes an integral part of the structure [1, 2, 3, 4]. This monitoring technique allows adjusting the maintenance intervals in accordance to the real requirements so that a reduction of the operating costs is expected. Disadvantages of conventional maintenance concepts (time based with fixed inspection intervals) are overcome by introducing condition based maintenance. Direct damage detection and evaluation by SHM substitute assumptions for damage initiation, damage progress and its effects thus making damage tolerance concepts more efficient. Among different approaches, the application of ultrasonic Lamb waves is an attractive method for structural health monitoring of plate and shell structures made of fibre reinforced material. Excitation and reception of Lamb waves are provided by actuators and sensors, respectively, which are integrated into the structure or attached to its surfaces. Thin piezoelectric plates are particularly suitable and cost-effective for transducer purposes. Application of Lamb waves requires knowledge of the function of the piezoelectric plates as transmitters and receivers of the waves, of the velocity and attenuation behaviour of Lamb modes as well as their interactions with defects. For the observation of propagating Lamb waves as well as defect detection, optical measurement techniques are particularly beneficial. Besides the scanning Laser Vibrometry which is under consideration in the following Sections, speckle interferometry has proven its suitability, cf. [5].
2. LAMB WAVES In the case of an unbounded elastic medium it is well known that two and only two types of waves are propagating, namely the compression (P-) wave and the shear (S-) wave. These types of waves are fundamental to the following considerations. In the case of elastic semi-infinite media the existence of a boundary comes into play and distinguishes this problem from the previous. The analysis leads to the phenomenon of mode conversion that occurs when waves encounter a free boundary. This means that in the case of an incident P- or S-wave, both a P-wave as well as an S- wave may be reflected. The result of the respective mathematical problem, i.e. differential equations including boundary condition, is interpreted as a surface wave. This Rayleigh wave is a third type of wave. It is nondispersive. Like in the case of the elastic semi-infinite media the Lamé-Navier differential equations are solved with respect to the boundary conditions for plate and shell problems. The existence of two parallel free surfaces entails a new type of wave, so-called Lamb waves or guided plate waves. In contrast to the unbounded or semi-infinite elastic media an infinite number of modes may emerge in plates and shells. The formation of Lamb waves may be considered as a consequence of P- and S- wave reflections at the surfaces of plates and shells. Many textbooks, e.g. [3], deal with the Lamb wave theory. Lamb waves can propagate over long distances and offer potentials for damage detection, localisation and further characterisation by their interaction with defects. They offer the possibility to detect superficial as well as internal flaws in structures. 3. LASER-DOPPLER-VIBROMETRY Scanning-laser-Doppler-vibrometry is an interferometric method with high sensitivity for non-contact detection of small displacements of wave fields or oscillations [6, 7]. It is based on the modulation of the phase of the laser light by the vibrating surface of the subject. A point-by-point detection of surface velocity or displacement combined with scanning of the subjects surface provides information on mode shapes of vibrations or the propagating wave modes. In the present case, a Polytec PSV-300 scanning-laser-vibrometer is utilized and the out-of-plane component of the particle velocity is recorded up to a frequency of 1 MHz. The general arrangement for the experimental work is given in Figure 1. A piezoceramic actuator is attached to the plate-like object and is driven by a suitable electrical signal produced and amplified by a generator and an amplifier respectively. The Lamb waves generated in this way are picked up by the moving laser beam emitted from the scanning head of the vibrometer system. The scanning area is formed by a grid of measuring points, definable in different ways. FIGURE 1. Arrangement for experimental detection of Lamb waves with scanning-laser-vibrometer Laser-vibrometry has the advantages of a non-contact measurement technique. The only conditions are that the laser beam has unhindered access to the object and that the amount of backscattered laser light is adequate. The detection of the laser light modulation requires a sufficient reflectivity of the specimens surface. Blank metallic materials and the surface of CFRPs may be not ideal for this. CFRP is in this sense often regarded as a noncooperative surface [8]. Whitening with the developer powder of penetrant testing systems or the use of a retroreflective foil create appropriate measuring conditions in these cases.
Laser-Doppler-vibrometry is a powerful tool in the development of SHM systems since these interferometric measurement techniques allow for the visualization of Lamb wave propagation and their interaction with defects. Furthermore, this measurement technique permits the characterisation of piezoelectric actuators as Lamb wave sources. 4. LASER-VIBROMETRIC MEASUREMENT OF OSCILLATING PIEZOELECTRIC PLATES Oscillating piezoceramic plates, surface-attached or embedded into a structure act as a source of elastic waves and are designated as piezo-actuators in the following. The different modes of vibration which are possible for such plates will produce different Lamb wave modes in plate-like structures accordingly. Laser-vibrometric measurements help to identify the vibration modes by visualisation of their mode shapes and estimation of their frequency behaviour by determination of the typical spectrum. Figure 2 presents mode shapes of free vibrations of a circular piezo-actuator, showing the typical fundamental out-of-plane modes in the low frequency range. FIGURE 2. Mode shapes of free vibrations of a circular piezo-actuator (diameter 40 mm, thickness 0.5 mm, material PIC 151 from PI Ceramics) Soldering contacts of the piezo-actuator influence the vibration modes by introducing additional mass and stiffness [9]. Figure 3 shows two identical disc-shaped piezo-actuators (diameter 10 mm, thickness 0.5 mm, material PIC 181 from PI Ceramics) with different soldering contacts. Case a) represents typical contacts; case b) one soldering point with about twice the mass. The comparison of the two spectra of free vibrations, averaged over the area of the piezo-actuator, shows distinct changes in the higher frequency region, starting from about 100 khz. The corresponding examples of identical mode shapes in Figure 4 indicate this by the differences in the frequencies. FIGURE 3. Piezo-actuators with different soldered contacts and their spectra: a) typical soldering contacts, b) soldering contacts with greater mass
FIGURE 4. Frequency shift of modes for cases a) above and b) beneath Figure 5 indicates the significant influence of the bonding to the structure for the vibrations of a piezo-actuator. A polystyrene plate with 4.75 mm thickness was chosen as an isotropic subject. Recorded mode shapes and spectra for the free and the bonded condition are compared. To create reversible bonding, paraffin was used as the coupling medium. As a result of the bonding, the amplitudes generally decrease. The frequencies of resonant vibrations shift to higher values and peaks in the spectrum are extinguished. Mode shapes in the bonded state are not in every case marked by a distinct peak in the spectrum. 1.6E-06 1.2E-06 u [m] 8.0E-07 4.0E-07 0.0E+00 0 50 100 150 200 250 300 f [khz] FIGURE 5. Spectrum (gray = free, black = bonded) and mode shapes (free above, bonded beneath) of a piezo-actuator (diameter 10 mm, thickness 2 mm, material PIC 181 from PI Ceramics)
5. LASER-VIBROMETRIC MEASUREMENT OF LAMB WAVES Recording of Lamb Wave Fields Laser-vibrometic measurements provide a direct view of the propagation of Lamb waves. Thus the features of the wave field become evaluable. Figure 6 shows an example for a Lamb wave field in polymethylmethacrylate as an isotropic material. The source was a circular shaped piezo-actuator. Even in the case of geometric and material isotropy, the resulting wave field is remarkably anisotropic. This behaviour is frequency-dependent and can be explained by the control of the wave field by the different mode shapes of the piezo-actuator s vibrations [10]. FIGURE 6. Lamb wave field in a PMMA plate generated by a circular piezoelectric actuator at 207.5 khz (scanning area 140 x 140 mm 2 ) The same effects are visible for a quasi-isotropic laid-up CFRP plate without defects in Figure 7. Here, anisotropy of the CFRP-material is superimposed on the anisotropic radiation of the source. At certain frequencies the energy propagation direction of the wave will follow the fibre direction of distinct material layers. The recorded wave fields reflect the amplitude characteristics as a function of distance. In this way the influence of the material on attenuation can be detected and measured quantitatively by the material s attenuation coefficient. This value is of great importance for an effective design of the SHM-system, because attenuation is a limiting factor for the maximal achievable distances between sensors and actuators. FIGURE 7. Lamb wave field in a CFRP plate generated by a circular piezoelectric actuator at 50 khz (scanning area 500 x 500 mm 2 )
Laser vibrometer scans can reveal the interaction of the Lamb waves with defects. Transmission, reflection and mode conversion are marking effects, which require further description. Figure 8 gives an example for the interaction of the S 0 -wave, produced by an embedded piezo-actuator in a CFRP plate with natural defects. The plate was damaged by sequential impacts, causing delaminations with diameters from 10 to 13 mm, evaluated by separate ultrasonic testing. The reflected signals of the mode-converted A 0 -mode can be clearly seen. FIGURE 8. Lamb wave field in a CFRP plate generated by a circular piezoelectric actuator at 350 khz with reflections at impact defects Measurement of Dispersion Curves The Lamb wave modes exhibit a pronounced frequency dependence of their velocity. The knowledge of this dispersion behaviour is essentially for SHM-purposes. Knowledge of velocity helps to distinguish the different wave modes from each other. For transient signals, a frequency region with low dispersion has to be chosen to prevent additional attenuation. The exact velocity is directly needed for the locating procedure of the defects. Experimental determination of the dispersion relation of Lamb waves is useful for this all. One possibility for dispersion measurement by laser-vibrometry is the use of a chirp-signal, covering a broad frequency region. The method of signal processing is schematically displayed in Figure 9. The wave fields of the produced modes are recorded and displayed as C-scan (amplitude versus coordinates x and y). Processing with a double Fourier transform (time and space) delivers the dispersion curves of the wave number k over frequency and inverting gives the dispersion relation in the desired manner of phase velocity c versus frequency [11]. For transient signals, (commonly burst signals are used) this method of applying a double Fourier transformation is described in [12, 13, 14]. FIGURE 9. Processing of Lamb wave data to obtain dispersion curves
4500 4000 3500 3000 c [m/s] 2500 2000 1500 1000 500 0 0 100 200 300 400 500 600 f [khz] FIGURE 10. Dispersion curves for basic symmetric and antisymmetric Lamb modes in a glass fibre reinforced plastic plate Figure 10 gives an example of the measured dispersion curves for the first two basic modes in a glass fibre reinforced plastic (GFRP) plate with 2 mm thickness. The dispersion curves obtained reflect the conditions of generation and propagation of the wave modes. Dispersion curves are only acquired where the signals of the wave field collected by the vibrometer are adequate in amplitude. For example, the basic symmetric mode S 0 is better recorded at higher frequencies, because the attached piezo-actuator produces this mode only weakly and in the low frequency region the out-of-plane displacements of this wave are very small. The basic antisymmetric mode A 0, on the other hand, is strongly attenuated at higher frequencies and consequently the dispersion curve cannot be obtained in this frequency range. c [m/s] 6000 5000 4000 3000 2000 1000 0 0 0.5 1 1.5 2 f x t [Mhz mm] FIGURE 11. Dispersion curves of Lamb modes in a CFRP plate Figure 11 displays the recorded modes in a quasi-isotropic plate of CFRP with 2 mm thickness. The plate consists of 7 plies in a [(0/90) f /+45/-45/(0/90) f] S layup. The basic antisymmetric mode A 0 is observable even at higher frequencies, indicating less attenuation than in GFRP, but for both modes the curves show interruptions. An additional explanation for gaps in the dispersion curves are anisotropy effects. Anisotropy causes deviations of the wave field direction so that the necessary plane wave status for evaluation is not valid anymore. 6. CONCLUSIONS In this work, the beneficial use of laser vibrometry is shown with regard to various phenomena in structural health monitoring. First, the mode shapes of thin, penny-shaped piezoelectric actuators were studied at two different boundary conditions. It was shown that the mode shape influences strongly the Lamb wave which is generated in the host structure. This is considered as an important result in the interpretation of propagating Lamb waves in thinwalled structures. Furthermore, attenuation and anisotropy of Lamb wave propagation become estimable, and flaws are detected and may be evaluated qualitatively as well as quantitatively. Finally, an experimental procedure is presented which allows the generation of dispersion diagrams. This is an important issue since the material properties of the structure under investigation are often not known exactly,
especially in the case of layered composite materials. The proposed procedure allows for the determination of these diagrams directly from experimental data avoiding the solution of the Rayleigh-Lamb equations. ACKNOWLEDGMENT The financial support of the Deutsche Forschungsgemeinschaft (German Research Foundation, DFG) is gratefully acknowledged (grant numbers MO 553/9-1 and LA 1067/8-1). REFERENCES 1. Boller, C.; Chang, F.-K.; Fujino, Y.: Encyclopedia of Structural Health Monitoring. Wiley & Sons, Chichester, (2009) 2. Su, Z.; Ye, L.; Lu, Y. 2006 Guided Lamb waves for identification of damage in composite structures: A review. J. of Sound and Vibration 295, 753-780. 3. Giurgiutiu, V. 2008 Structural Health Monitoring with Piezoelectric Wafer Active Sensors, Academic Press, ISBN 9780120887606. 4. Raghavan, A.; Cesnik, C. E. S.: Review of guided-wave structural health monitoring. Shock Vib. Dig. 39 91 114 (2007). 5. Lammering, R.: Observation of Piezoelectrically Induced Lamb Wave Propagation in Thin Plates by Use of Speckle Interferometry. Experimental Mechanics, 50 (3), 377-387, (2010). 6. Köhler, B., Schubert, F.; Barth, M.; Frankenstein, B.: Selective Excitation and Detection of Lamb Waves for SHM Applications. Proceedings of the Fourth European Workshop on Structural Health Monitoring held at Krakow, Poland July 2 4, 706-714 (2008). 7. Staszewski, W.J., Lee, B.; K. Mallet, Scarpa, F.: Structural health monitoring using scanning laser vibrometry; I. Lamb wave sensing. Smart Materials and Structures 14 (2), 251-260, (2004). 8. Kalms, M. K.; Osten, W.; Jüptner, W.; Bisle, W.; Scherling, D.; Tober, G.: NDT on Wide Scale Aircraft Structures with Digital Speckle Shearography. SPIE Vol. 3824, Optical Measurement Systems for Industrial Inspection, 1999, 280-286. 9. Willberg, C., Vivar-Perez, J.M., Ahmad, Z., Gabbert. U.: Simulation of Piezoelectric induced Lamb waves in plates, in Fu- Kuo Chang (Ed.): Proceedings of the 7th International Conference on Structural Health Monitoring 2009 From Systems Integration to Autonomous Systems, DEStech Publications Inc., 2009, 2299-3006. 10. Huang, H.; Pamphile, T.; Derriso, M.: 2008 The effect of actuator bending on Lamb wave displacement fields generated by a piezoelectric patch. Smart Materials and Structures 17, 1-13. 11. Pohl, J.; Szewieczek, A.; Hillger, W.; Mook, G.; Schmidt, D. 2010 Determination of Lamb wave dispersion data for SHM. 5th European Workshop SHM. 12. Alleyne, D.; Cawley, P. 1991 A two-dimensional Fourier transform method for the measurement of propagating multimode signals. J. Acoust. Soc. Am. Volume 89, Issue 3, 1159-1168. 13. Li, J.; Liu, S. 2008 The Application of Time-Frequency Transform in Mode Identification of Lamb Waves. 17th World Conference on Nondestructive Testing, 25-28 Oct, Shanghai, China. 14. Köhler, B. 2006 Dispersion Relations in Plate Structures Studied with a Scanning Laser Vibrometer. 9th European NDT Conference, ECNDT, Berlin, paper Mo.2.1.4.