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Impact damage detection in composite laminates using nonlinear acoustics
Composites: Part A 41 (2010) 1084–1092
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Impact damage detection in composite laminates using nonlinear acoustics F. Aymerich a,*, W.J. Staszewski b a b
Department of Mechanical Engineering, University of Cagliari, Piazza d0 Armi, 09123 Cagliari, Italy Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
a r t i c l e
i n f o
Article history: Received 29 May 2009 Received in revised form 27 August 2009 Accepted 8 September 2009
Keywords: A. Carbon fibre B. Delamination B. Impact behaviour D. Ultrasonics
a b s t r a c t The paper demonstrates the application of nonlinear acoustics for impact damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is instrumented with bonded low-profile piezoceramic transducers. A high-frequency acoustic wave is introduced to one transducer and picked up by a different transducer. A low-frequency flexural modal excitation is introduced to the plate at the same time using an electromagnetic shaker. The damage induced by impact is exhibited in a power spectrum of the acoustic response by a pattern of sidebands around the main acoustic harmonic. The results show that the amplitude of sidebands is related to the severity of damage. The study investigates also the effect of boundary conditions on the results. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Composite materials have been widely used in many advanced engineering structures. High specific strength, light weight, resistance to fatigue/corrosion and flexibility in design displayed by these materials have benefited many industries especially in the transportation area. Despite of these benefits the susceptibility of composite materials to incur impact damage is well-known and creates a major concern related to structural integrity [1]. In aerospace structures, low-velocity impacts are often caused for example by tool drops during manufacturing and servicing or runway stones during landing or take off. Such impacts may result in various forms of damage such as indentation, matrix cracking, delamination or fibre fracture, leading to severe reduction in strength and integrity of composite structures. Although structures designed with fail-safe principles can withstand in theory partial system failures, impact damage detection is an important issue in maintenance of aircraft and space structures. While visible damage can be easily detected and remedial action taken to maintain structural integrity, a major concern to end-users is the growth of undetected, hidden damage caused by low-velocity impacts and fatigue. This internal damage is also known in aerospace applications as Barely Visible Impact Damage (BVID), and failure to detect BVIDs may result in a catastrophic collapse of the structure. Many techniques have been developed for impact damage detection in composite structures over the last few decades. These * Corresponding author. Tel.: +39 70 6755727; fax: +39 70 6755717. E-mail addresses: [email protected] (F. Aymerich), w.j.staszewski@sheffield. ac.uk (W.J. Staszewski). 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.09.004
include various Non-Destructive Testing (NDT) methods based on visual inspection, ultrasonic waves, acousto-ultrasonics, acoustic emission or X-rays. Although various research activities are ongoing in order to automate inspection effort (e.g. robot-assisted scanning systems), current NDT techniques used for damage detection are labour-intensive, time-consuming and often expensive. Recent years have shown a range of different Structural Health Monitoring (SHM) techniques developed for damage detection in composite structures. Guided ultrasonic waves and nonlinear acoustic techniques are particularly attractive because of their ability of inspecting large structures with a small number of transducers. Nonlinear vibration and acoustic effects have been also used for damage detection for many years. Application examples include methods based on second harmonic frequency generation [2,3], quasi-static time-of-flight measurements [4], frequency mixing [5,6], resonance spectra [7,8], reverberation analysis [8], modulation analysis [9–12] and investigations of slow dynamic behaviour [13]. The majority of these investigations are related to fatigue crack detection in metallic structures. Applications to composite structures are very limited and include [14–17]. In particular, damage detection techniques based on nonlinear elastic wave spectroscopy were successfully used to detect the damage introduced in the laminated skin of a sandwich panel by penetration with a sharp object [14], and for comparing the responses of a set of composite panels, each characterized by a different impact-induced delamination area [16]. The objective of the paper is to demonstrate the application of nonlinear acoustics for detecting impact damage in composite structures and monitoring its progression under multiple impacts. For the sake of completeness, Section 2 introduces briefly
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nonlinear acoustic principles used for damage detection. Section 3 describes the experimental work performed to impact composite plate and the experimental tests undertaken to detect structural impact damage. Damage detection results are presented in Section 4 and the paper is concluded in Section 5.
2. Nonlinear acoustics It is well-known that NDT applications based on ultrasonic techniques use linear amplitude and/or phase variations of reflected, transmitted or scattered ultrasonic waves to reveal material damage. In contrast, nonlinear acoustics uses different nonlinear phenomena to detect damage. These phenomena can be related to either various imperfections of atomic lattices or non-symmetric thermo-elastic behaviour of interfaces such as opening–closing cracks, rubbing surfaces or other contacts. The first type of nonlinearity is well-known [18,19] and often called material (or intrinsic) nonlinearity. Various techniques have been developed since the early 1960s to detect material imperfections and application examples include work on micro-cracks in materials [20–22]. The second type of nonlinearity is a local phenomenon arising from the interaction of ultrasonic waves with contact-type interfaces [23,24]. This phenomenon has demonstrated a great interest of theoretical and applied research for the last 15 years. The majority of theoretical investigations are related to various models of nonlinear elastic, thermal and acoustic interactions, as reported in [22]. The exploitation of this nonlinear effect for damage detection has resulted in numerous inspection techniques based on generation of higherharmonics, frequency mixing, analysis of slow dynamics, reverberation analysis and signal modulations [2–13]. It is the latter effect which is of interest in the current investigations. The focal point of the nonlinear acoustic technique when used for damage detection is the combined vibro-acoustic interaction of a high-frequency ultrasonic wave and a low-frequency vibration excitation. The entire technique can be illustrated using Fig. 1. An ultrasonic wave (high-frequency range) is introduced to a structure using actuator A, while the structure is simultaneously excited modally at position B. One of the modal frequencies – for example the frequency f1 of the first bending mode – can be used as the lowfrequency excitation, in order to generate a flexural vibration wave in the structure. The intact or undamaged structure acts as a ‘‘linear carrier” for the ultrasonic propagating wave. In other words the
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spectrum around the high-frequency response captured in position C displays only the major frequency component f0 of the propagating acoustic wave. When the structure is cracked, the high-frequency ‘‘weak” ultrasonic wave is modulated by the low-frequency ‘‘strong” vibration wave. As a result, frequency sidebands f0 ± nf1 (where n = 1, 2, 3, . . .) can be observed around the main acoustic harmonic in the spectrum of the ultrasonic signal acquired in position C. The intensity of modulation strongly relates to the crack size. Often additional effects – such as frequency shift, amplitude reduction and/or generation of higher-harmonics – can also be observed. However, these effects are not used in the current investigations. It is important to note that the theoretical understanding of the modulation mechanism is still not clear and various models are available, as reported in [22]. Nevertheless, it is widely accepted that the modulation of the acoustic wave relates to the nonlinear contact dynamics. Using this approach, different nonlinear models of modulation mechanisms are possible following the nonlinear relationship between the stress r and strain e as:
r¼
Z
gðe; e_ Þde
ð1Þ
where g is a nonlinear function. The normal stiffness of the interface formed by two crack surfaces which are in contact can be modeled using a nonlinear elasticity, as demonstrated in [23]. An acoustically-driven clapping between crack interfaces can be modeled using a nonlinear piece-wise stress–strain function [23]. A different nonlinear mechanism can be used to model energy dissipation due to friction or adhesion between crack interfaces, as also shown in [23]. Delaminated and damaged regions in composite materials are in fact weak areas where all the above nonlinear effects, i.e. local nonlinear elasticity, clapping, energy dissipation between internal fractured surfaces or delaminated interfaces, are possible, leading to modulations of the acoustic wave. It is important to note that non damage-related contact effects, such as those occurring at boundaries (due to the support between the monitored structure and external bodies) and lose elements (joints, rivets), or those inherently related to material deformation (e.g. molecular or fibre/matrix internal friction in composites) are likely to produce similar nonlinear phenomena, as pointed out in [12] and observed experimentally for example in [10,25].
3. Impact tests on composite panel This section reports impact tests performed in the damage detection experiments. In what follows, the composite specimen, experimental set-up and procedure are described in detail. This is complemented by the description of X-ray tests performed to assess the severity of impact damage. 3.1. Composite specimen
Fig. 1. Schematic layout demonstrating the principle of nonlinear acoustics used for damage detection.
The specimen used in the current study, shown graphically in Fig. 2, was a rectangular 420 120 2 mm laminated composite plate with [0/+45/45]2s stacking sequence. The plate was cut from a laminate made up from Seal TexipregÒ HS160/REM carbon/epoxy prepreg layers (0.17 mm nominal thickness) and consolidated in an autoclave at a maximum temperature of 160 °C. The nominal fibre fraction of prepreg layers was 61.5% in weight. The panel was instrumented with two PI Ceramic PIC 151 lowprofile piezoceramic transducers (6.35 mm diameter, 0.25 mm thickness) positioned as shown in Fig. 2. The transducers were surface bonded using a two-component epoxy adhesive and wired using additionally bonded connectors. The composite plate was
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Fig. 3. X-radiographs of impact damage for 2.04 J and 10.1 J impacts.
Fig. 2. Schematic diagram of the composite specimen.
ultrasonically C-scanned prior to testing to assess the quality of the laminate and to exclude the presence of manufacturing defects. 3.2. Impact tests A drop-weight impact testing tower with a 2.2 kg impactor was used in order to introduce damage onto the composite plate. The impactor was provided with a hemispherical indentor of 12.5 mm diameter and instrumented with a semiconductor strain-gauge bridge for dynamic load acquisition. A pneumatic catch mechanism was used to capture the impactor after the rebound in order to prevent multiple impacts on the specimens. The energy dissipated during the impact was evaluated from the impact and rebound velocities, as measured by an infra-red sensor. During testing, the laminate was simply supported on a steel plate with a rectangular opening measuring 87.5 mm (along the 0° direction of the laminate) by 65 mm and subjected to impact on the centre of the 300 mm by 120 mm area (Fig. 2). Impact energies of 2.04 and 10.1 J, obtained by varying the drop height of the impactor, were used to progressively introduce different levels of damage in the laminated panel.
across the thickness of the laminate, together with a dense network of 0° and ±45° matrix cracks. Short fibre fracture paths may also be seen on the impact side of the plate in the proximity of the contact area, while only a shallow indentation (about 0.08 mm in depth) may be noticed at the impact location on the surface of the laminate. Extensive delaminated areas, major fibre fracture (on both the tensile and compressive sides of the panel) and a much larger indentation (0.85 mm) are on the other hand observed for the 10.1 J impact energy. Such an energy level may be therefore approximately assumed as the energy threshold indicating the onset of laminate penetration [26]. A summary of the main indicators of the damage response of the panel to impact energies of 2.04 and 10.1 J is reported in Table 1. 4. Impact damage detection with nonlinear acoustics Damage detection experimental work using nonlinear acoustics is described in this section. The experimental modal analysis was performed initially to estimate the best frequency values for modal and ultrasonic excitation. The undamaged plate was then monitored using nonlinear acoustics. This was followed by a series of damage detection nonlinear acoustic tests performed after each impact in order to reveal possible damage. In what follows, the entire experimental procedure and results are presented.
3.3. Inspection for impact damage 4.1. Experimental modal analysis Non-destructive penetrant-enhanced X-ray inspections were carried out after each impact to identify and characterize internal damage. Radiographic analyses were performed with a HP Faxitron cabinet, using a 20 kV voltage, 3 mA current, and 100 s exposure time to produce X-ray images on an AGFA NDT D4 film. After processing, digital images of the negative were acquired by an optical scanner for direct observation of damage and measurement of projected delaminated areas. Fig. 3 shows X-ray pictures of internal damage after 2.04 J and 10.1 J impacts. Damage induced by the 2.04 J impact mainly consists of multiple delaminations developing along several interfaces
Simple modal analysis experiments were preliminary performed in order to establish frequencies for the modal excitation in nonlinear acoustics. As shown in Fig. 4, the plate was clamped between two steel plates, using a Galdabini SUN 500, 5 kN servoelectric testing machine in order to control the clamping level. The clamped area of the plate is indicated graphically in Fig. 2. The clamping load adopted during the analyses was equal to 5 kN. The composite plate was excited modally using a Bruel & Kjaer 4809 electrodynamic vibration shaker, as visible in Fig. 4. The position of the excitation was selected to avoid possible nodal points of
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F. Aymerich, W.J. Staszewski / Composites: Part A 41 (2010) 1084–1092 Table 1 Damage indicators characterizing the response of composite plate to 2.04 J and 10.1 J impacts. Impact energy (J)
Absorbed energy (J)
Peak force (N)
Indentation depth (mm)
Projected delamination area (mm2)
2.04 10.1
0.28 7.73
2010 6790
0.08 0.85
104.4 558.4
Fig. 4. Experimental clamping arrangement for the composite specimen.
the plate in order to guarantee good signal responses. A sweep sine signal starting at 1 Hz and crossing 3200 Hz in 2 s was used to excite the plate. The excitation signal was generated using a Wavetek FG3B, 2 MHz function generator and amplified using a Bruel & Kjaer 2706 power amplifier. The acoustic response was acquired using a National Instruments NI 5112, 100 MSa/s High-Speed Digitizer operated in a WinXP – LabViewÒ environment. During both the preliminary modal analyses and the subsequent damage detection tests, the level of modal vibration was monitored by acquiring the signal of a Bruel & Kjaer 4393 piezoelectric charge accelerometer, located on the front face of the laminate along the axis of shaker excitation. The accelerometer signal was amplified by a Bruel & Kjaer 2635 charge amplifier and acquired using an HP 54520 digital oscilloscope. Fig. 5 shows the main equipment used in the experimental investigations. The excitation (electromagnetic shaker at position B, as indicated in Fig. 2) and response signals (from transducer C) were used to obtain the vibration Frequency Response Function (FRF). The level of the excitation, as measured by the maximum acceleration in B, was equal to 6 m/s2 peak-to-peak. Twenty sets of data were used
to calculate the average FRF amplitude in order to increase the signal-to-noise ratio. The FRF amplitude, presented in Fig. 6a, reveals a number of vibration modes of the plate. The 77, 262 and 2934 Hz frequencies were selected for modal excitation in damage detection tests. These frequencies correspond to the lowest, strongest and highest analysed vibration mode, respectively. A similar procedure was applied to obtain the best ultrasonic frequencies in nonlinear acoustic tests. This time, bonded piezoceramic transducers were used to introduce the ultrasonic wave (transducer A) and to measure the ultrasonic response (transducer C). Positions for the transducers were selected in line with the impact location following previous investigations (e.g. [11,25]). A sweep sine signal starting at 3 kHz and crossing 210 kHz in 3 s was used to excite the plate acoustically. The excitation signal was generated using a TTI TGA1241 40 MHz function generator. The peak-to-peak amplitude of excitation was equal to 20 V. The excitation and response signals were again acquired using the NI 5112 digitizer and used to obtain the acoustical transfer function as the average spectrum of twenty data-sets. The transfer function amplitude, presented in Fig. 6b, reveals a number of vibration modes of the plate. The 17.63 and 98.04 kHz frequencies were selected for ultrasonic excitation in subsequent nonlinear acoustics tests. These frequencies were selected by trial-and-error from the acoustic transfer function as the best two local acoustical modes exhibiting relatively strong signal-tonoise ratio responses. 4.2. Experimental set-up and procedure for damage detection Nonlinear acoustic tests were then performed, with the experimental equipment described in the previous section, first on the undamaged, intact panel and subsequently on the same panel after damaging the laminate with 2.04 J and 10.1 J low-velocity impacts. The composite panel was loaded between the clamping plates with a 5 kN force applied by the servoelectric testing machine. An ultrasonic sine wave (peak-to-peak amplitude = 20 V) was introduced to the low-profile piezoceramic actuator at location A (Fig. 2) and, at the same time, the plate was vibrated using the electromagnetic shaker at location B. The study was performed for the modal (f1) and ultrasonic (f0) frequencies established in Section 4.1 and applying levels of modal excitation (as measured by acceleration signals recorded at location B) ranging between 1 and 5 m/s2 peak-to-peak. The response signal from the piezoceramic trans-
Fig. 5. Experimental equipment used in modal analysis and nonlinear acoustics tests.
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Fig. 6. Modal analysis results: (a) vibration Frequency Response Function (FRF) and (b) acoustic transfer function.
ducer at location C was acquired by the NI 5112 digitizer using 125 kpoints and a 125 kSa/s sampling rate for the 17.63 kHz acoustic excitation, and 500 kpoints and 1 MSa/s sampling rate for the 98.04 kHz acoustic excitation. The resulting frequency resolutions of the signal spectra were thus 1 Hz and 2 Hz for the 17.63 kHz and 98.04 kHz acoustic excitation frequencies, respectively. Averaged power spectra were finally calculated from 10 datasets of the response signal using a specifically written LabView code, and then zoomed on the fundamental harmonic of the acoustic wave in order to reveal possible modulations sidebands. 4.3. Damage detection results and discussion Fig. 7–9 show examples of power spectra from acoustical responses for the 17.63 kHz ultrasonic excitation and three different modal excitation frequencies. The acoustical harmonic dominates all analysed spectra. From Fig. 7, which shows the results for the
77 Hz modal excitation, we may see that spectra recorded after 2.04 and 10.1 J impacts (Fig. 7b and c) exhibit a clear pattern of sidebands around the acoustical frequency component. The frequency of these sidebands corresponds to multiple values of the 77 Hz modal frequency and their amplitude increases with the impact energy (Fig. 10) and thus with the entity of laminate damage. In particular, the average amplitude of the first pair of sidebands increases approximately by 2 dB and 8 dB after 2.04 and 10.1 J impacts, respectively. It is worth noting that one small 77 Hz sideband is also present on the left hand side of the acoustical main component for the undamaged plate, as visible in Fig. 7a. Similar features can be observed in Figs. 8 and 9, where the results for the 262 and 2934 Hz modal excitation are presented. However, the patterns of sidebands for the undamaged specimen in Fig. 8a and 9a are relatively strong if compared with those in Fig. 7a. This time the amplitude of sidebands increases by 4 dB and by 0.4 dB after 2.04 J impact for the 262 and 2934 modal
Fig. 7. Power spectra of acoustic response for undamaged and impact-damaged panel. 77 Hz modal excitation (1.0 m/s2); 17.63 kHz acoustical excitation.
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Fig. 8. Power spectra of acoustic response for undamaged and impact-damaged panel. 262 Hz modal excitation (1.1 m/s2); 17.63 kHz acoustical excitation.
Fig. 9. Power spectra of acoustic response for undamaged and impact-damaged panel. 2934 Hz modal excitation (3.9 m/s2); 17.63 kHz acoustical excitation.
excitation, respectively (Fig. 10). The amplitude increase of the first sidebands after 10.1 J impact is quite significant and reaches the approximate level of 15 dB and 7 dB for the 262 and 2934 Hz modal excitation in Figs. 8c and 9c, respectively. A marked decrease of the amplitude of the fundamental carrier frequency may also be observed after the 10.1 J impact for all modal excitation frequencies investigated, as seen in the spectra of Figs. 7–9. The results for the 98.04 kHz ultrasonic excitation and different frequencies of modal excitation are presented in Figs. 11–13. A pattern of sidebands corresponding to multiples of the modal frequencies are now visible in the response of the undamaged panel for all three vibration frequencies examined, as shown in Figs. 10a, 11a and 12a. Similarly to the results previously discussed for the 17.63 kHz excitation, the amplitude of the sidebands always increases with the entity of impact damage (Fig. 14), with the only exception of the spectrum recorded after the 2.04 J impact for the 2934 Hz modal excitation, where an 1.5 dB decrease in the
average amplitude of the first sidebands was measured. A strong reduction of the amplitude of the carrier acoustic frequency is also observed on the response of the laminate damaged by the highest energy impact. 4.4. Effect of clamping on nonlinear acoustic results The presence of sidebands in the response of the undamaged panel (Figs. 7a–9a, 11a–13a) can probably be explained by the existence of inherent nonlinearity, as discussed at the end of Section 2. It is very likely that clamping produces additional nonlinear contact effects results in modulation sidebands and the effect of clamping has been thus investigated further in additional experimental tests. The nonlinear damage detection procedure has been performed for the 17.63 kHz ultrasonic excitation, 77 Hz modal excitation (using an excitation level corresponding to the acceleration of 2 m/s2 peak-to peak) and different clamping force levels. Fig. 15 shows examples of acoustical power
Fig. 10. Increase in sidebands amplitude as a function of impact energy in tests with 17.63 kHz acoustical excitation.
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Fig. 11. Power spectra of acoustic response for undamaged and impact-damaged panel. 77 Hz modal excitation (2.8 m/s2); 98.04 kHz acoustical excitation.
Fig. 12. Power spectra of acoustic response for undamaged and impact-damaged panel. 262 Hz modal excitation (1.1 m/s2); 98.04 kHz acoustical excitation.
Fig. 13. Power spectra of acoustic response for undamaged and impact-damaged panel. 2934 Hz modal excitation (5.0 m/s2); 98.04 kHz acoustical excitation.
Fig. 14. Increase in sidebands amplitude as a function of impact energy in tests with 98.04 kHz acoustical excitation.
spectra for 0.7, 3.7 and 4.7 kN clamping force for the undamaged plate. The results demonstrate that the amplitude of sidebands decreases with the increased clamping force level. The amplitude
levels of the fundamental acoustical frequency and of the first pair of sidebands measured at various levels of clamping force for both the undamaged and damaged (after 10.1 J impact) plate
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are presented in Figs. 16. The plots indicate that the amplitude of the carrier frequency increases and the amplitude of the first sidebands decreases with the clamping force, until a force level higher than about 4200 N is reached and both amplitudes remain relatively constant. In contrast, once the specimen is damaged, increasing the value of the clamping force reduces the amplitude of the fundamental frequency while appears to increase, at least above a certain applied force level, the amplitude of first sidebands. These results indicate that nonlinear mechanisms introduced by boundary effects may differ from those induced by damage phenomena in the material, and may thus suggest possible ways to discriminate between damage and non damage-related nonlinearities.
5. Conclusions The application of the nonlinear acoustic technique for impact damage detection in composite materials has been presented. The method was based on frequency modulation of the ultrasonic wave propagating in the plate by a low-frequency modal excitation signal.
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The study demonstrates that damage and delaminations resulting from low-velocity impacts produce sidebands around the fundamental ultrasonic component in the power spectra from acoustical responses. The frequencies of sidebands correspond to multiples of modal excitation and their amplitudes increase with the entity of impact damage (as measured by the delamination area). Significant increase in sidebands amplitude (i.e. by more than 10 dB for the first sidebands) can be observed for the highest-energy impact (10.1 J) data. The pattern of small modulation sidebands could be seen in the acoustical spectrum when delamination was not present in the plate. This phenomenon has been observed before when crack detection in metallic structures has been investigated. Therefore, a template result for undamaged condition is necessary for comparison to avoid false-positive damage detection. The study shows that the level of clamping force (i.e. boundary conditions) affects the amplitudes of both the fundamental acoustical frequency and sidebands. However, different responses to varying boundary conditions were observed in undamaged and damaged panel. Further analyses are required to identify and characterize possible sources of intrinsic (non damage-related) nonlinearities. Any future work should also investigate: the sensitivity of the method to small
Fig. 15. Examples of power spectra of acoustic response of the undamaged panel for different clamping forces. 77 Hz modal excitation (2 m/s2); 17.63 kHz acoustical excitation.
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Fig. 16. Effect of clamping force on the amplitude of fundamental frequency and first sidebands for undamaged and damaged (10.1 J impact energy) panel. 77 Hz modal excitation (2 m/s2); 17.63 kHz acoustical excitation.
damage severities, the results for different types and severities of impact damage, the problem of optimal transducer positions (for both low- and high-frequency excitation). References [1] Abrate S. Impact on composite structures. Cambridge (UK): Cambridge University Press; 1998. [2] Morris WL, Buck O, Inman RV. Acoustic harmonic generation due to fatigue damage in high-strength aluminium. J Appl Phys 1979;50(11):6737–41. [3] Nazarov VE, Sutin AM. Nonlinear elastic constants of solids with cracks. J Acoust Soc Am 1997;102(6):3349–54. [4] Nagy PB, McGowan P, Adler L. Acoustic nonlinearities in adhesive joints. Rev Prog QNDE 1990;10B:1685–92. [5] Antonets VA, Donskoy DM, Sutin AM. Nonlinear-vibro diagnostics of flaw in multilayered structures. Compos Mater 1986;15:934–7. [6] Van Den Abeele K, Johnson PA, Sutin AM. Nonlinear elastic wave spectroscopy (NEWS) technique to discern material damage. Part I: nonlinear wave modulation spectroscopy. Rev Prog QNDE 2000;12(1):17–30. [7] Van Den Abeele K, Carmeliet T, TenCate JA, Johnson PA. Nonlinear elastic wave spectroscopy (NEWS) technique to discern material damage. Part II: single mode nonlinear acoustic spectroscopy. Rev Prog QNDE 2000;12(1):31–42. [8] Van Den Abeele K, De Visscher J. Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques. Cement Concrete Res. 2000;30(9):1453–64. [9] Donskoy DM, Sutin AM. Vibro-acoustic modulation nondestructive evaluation technique. J Intell Mater Syst Struct 1998;9:765–71. [10] Zaitsev VY, Gusev V, Castagnede B. Observation of the ‘‘Luxemburg–Gorki effect” for elastic waves. Ultrasonics 2002;40:627–31. [11] Parsons Z, Staszewski WJ. Nonlinear acoustics with low-profile piezoceramic excitation for crack detection in metallic structures. Smart Mater Struct 2006;15:1110–8. [12] Duffour P, Morbidini M, Cawley P. A study of the vibro-acoustic modulation technique for the detection of cracks in metals. J Acoust Soc Am 2006;119(3):1463–75.
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Contents lists available at ScienceDirect
Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Impact damage detection in composite laminates using nonlinear acoustics F. Aymerich a,*, W.J. Staszewski b a b
Department of Mechanical Engineering, University of Cagliari, Piazza d0 Armi, 09123 Cagliari, Italy Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
a r t i c l e
i n f o
Article history: Received 29 May 2009 Received in revised form 27 August 2009 Accepted 8 September 2009
Keywords: A. Carbon fibre B. Delamination B. Impact behaviour D. Ultrasonics
a b s t r a c t The paper demonstrates the application of nonlinear acoustics for impact damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is instrumented with bonded low-profile piezoceramic transducers. A high-frequency acoustic wave is introduced to one transducer and picked up by a different transducer. A low-frequency flexural modal excitation is introduced to the plate at the same time using an electromagnetic shaker. The damage induced by impact is exhibited in a power spectrum of the acoustic response by a pattern of sidebands around the main acoustic harmonic. The results show that the amplitude of sidebands is related to the severity of damage. The study investigates also the effect of boundary conditions on the results. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Composite materials have been widely used in many advanced engineering structures. High specific strength, light weight, resistance to fatigue/corrosion and flexibility in design displayed by these materials have benefited many industries especially in the transportation area. Despite of these benefits the susceptibility of composite materials to incur impact damage is well-known and creates a major concern related to structural integrity [1]. In aerospace structures, low-velocity impacts are often caused for example by tool drops during manufacturing and servicing or runway stones during landing or take off. Such impacts may result in various forms of damage such as indentation, matrix cracking, delamination or fibre fracture, leading to severe reduction in strength and integrity of composite structures. Although structures designed with fail-safe principles can withstand in theory partial system failures, impact damage detection is an important issue in maintenance of aircraft and space structures. While visible damage can be easily detected and remedial action taken to maintain structural integrity, a major concern to end-users is the growth of undetected, hidden damage caused by low-velocity impacts and fatigue. This internal damage is also known in aerospace applications as Barely Visible Impact Damage (BVID), and failure to detect BVIDs may result in a catastrophic collapse of the structure. Many techniques have been developed for impact damage detection in composite structures over the last few decades. These * Corresponding author. Tel.: +39 70 6755727; fax: +39 70 6755717. E-mail addresses: [email protected] (F. Aymerich), w.j.staszewski@sheffield. ac.uk (W.J. Staszewski). 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.09.004
include various Non-Destructive Testing (NDT) methods based on visual inspection, ultrasonic waves, acousto-ultrasonics, acoustic emission or X-rays. Although various research activities are ongoing in order to automate inspection effort (e.g. robot-assisted scanning systems), current NDT techniques used for damage detection are labour-intensive, time-consuming and often expensive. Recent years have shown a range of different Structural Health Monitoring (SHM) techniques developed for damage detection in composite structures. Guided ultrasonic waves and nonlinear acoustic techniques are particularly attractive because of their ability of inspecting large structures with a small number of transducers. Nonlinear vibration and acoustic effects have been also used for damage detection for many years. Application examples include methods based on second harmonic frequency generation [2,3], quasi-static time-of-flight measurements [4], frequency mixing [5,6], resonance spectra [7,8], reverberation analysis [8], modulation analysis [9–12] and investigations of slow dynamic behaviour [13]. The majority of these investigations are related to fatigue crack detection in metallic structures. Applications to composite structures are very limited and include [14–17]. In particular, damage detection techniques based on nonlinear elastic wave spectroscopy were successfully used to detect the damage introduced in the laminated skin of a sandwich panel by penetration with a sharp object [14], and for comparing the responses of a set of composite panels, each characterized by a different impact-induced delamination area [16]. The objective of the paper is to demonstrate the application of nonlinear acoustics for detecting impact damage in composite structures and monitoring its progression under multiple impacts. For the sake of completeness, Section 2 introduces briefly
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nonlinear acoustic principles used for damage detection. Section 3 describes the experimental work performed to impact composite plate and the experimental tests undertaken to detect structural impact damage. Damage detection results are presented in Section 4 and the paper is concluded in Section 5.
2. Nonlinear acoustics It is well-known that NDT applications based on ultrasonic techniques use linear amplitude and/or phase variations of reflected, transmitted or scattered ultrasonic waves to reveal material damage. In contrast, nonlinear acoustics uses different nonlinear phenomena to detect damage. These phenomena can be related to either various imperfections of atomic lattices or non-symmetric thermo-elastic behaviour of interfaces such as opening–closing cracks, rubbing surfaces or other contacts. The first type of nonlinearity is well-known [18,19] and often called material (or intrinsic) nonlinearity. Various techniques have been developed since the early 1960s to detect material imperfections and application examples include work on micro-cracks in materials [20–22]. The second type of nonlinearity is a local phenomenon arising from the interaction of ultrasonic waves with contact-type interfaces [23,24]. This phenomenon has demonstrated a great interest of theoretical and applied research for the last 15 years. The majority of theoretical investigations are related to various models of nonlinear elastic, thermal and acoustic interactions, as reported in [22]. The exploitation of this nonlinear effect for damage detection has resulted in numerous inspection techniques based on generation of higherharmonics, frequency mixing, analysis of slow dynamics, reverberation analysis and signal modulations [2–13]. It is the latter effect which is of interest in the current investigations. The focal point of the nonlinear acoustic technique when used for damage detection is the combined vibro-acoustic interaction of a high-frequency ultrasonic wave and a low-frequency vibration excitation. The entire technique can be illustrated using Fig. 1. An ultrasonic wave (high-frequency range) is introduced to a structure using actuator A, while the structure is simultaneously excited modally at position B. One of the modal frequencies – for example the frequency f1 of the first bending mode – can be used as the lowfrequency excitation, in order to generate a flexural vibration wave in the structure. The intact or undamaged structure acts as a ‘‘linear carrier” for the ultrasonic propagating wave. In other words the
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spectrum around the high-frequency response captured in position C displays only the major frequency component f0 of the propagating acoustic wave. When the structure is cracked, the high-frequency ‘‘weak” ultrasonic wave is modulated by the low-frequency ‘‘strong” vibration wave. As a result, frequency sidebands f0 ± nf1 (where n = 1, 2, 3, . . .) can be observed around the main acoustic harmonic in the spectrum of the ultrasonic signal acquired in position C. The intensity of modulation strongly relates to the crack size. Often additional effects – such as frequency shift, amplitude reduction and/or generation of higher-harmonics – can also be observed. However, these effects are not used in the current investigations. It is important to note that the theoretical understanding of the modulation mechanism is still not clear and various models are available, as reported in [22]. Nevertheless, it is widely accepted that the modulation of the acoustic wave relates to the nonlinear contact dynamics. Using this approach, different nonlinear models of modulation mechanisms are possible following the nonlinear relationship between the stress r and strain e as:
r¼
Z
gðe; e_ Þde
ð1Þ
where g is a nonlinear function. The normal stiffness of the interface formed by two crack surfaces which are in contact can be modeled using a nonlinear elasticity, as demonstrated in [23]. An acoustically-driven clapping between crack interfaces can be modeled using a nonlinear piece-wise stress–strain function [23]. A different nonlinear mechanism can be used to model energy dissipation due to friction or adhesion between crack interfaces, as also shown in [23]. Delaminated and damaged regions in composite materials are in fact weak areas where all the above nonlinear effects, i.e. local nonlinear elasticity, clapping, energy dissipation between internal fractured surfaces or delaminated interfaces, are possible, leading to modulations of the acoustic wave. It is important to note that non damage-related contact effects, such as those occurring at boundaries (due to the support between the monitored structure and external bodies) and lose elements (joints, rivets), or those inherently related to material deformation (e.g. molecular or fibre/matrix internal friction in composites) are likely to produce similar nonlinear phenomena, as pointed out in [12] and observed experimentally for example in [10,25].
3. Impact tests on composite panel This section reports impact tests performed in the damage detection experiments. In what follows, the composite specimen, experimental set-up and procedure are described in detail. This is complemented by the description of X-ray tests performed to assess the severity of impact damage. 3.1. Composite specimen
Fig. 1. Schematic layout demonstrating the principle of nonlinear acoustics used for damage detection.
The specimen used in the current study, shown graphically in Fig. 2, was a rectangular 420 120 2 mm laminated composite plate with [0/+45/45]2s stacking sequence. The plate was cut from a laminate made up from Seal TexipregÒ HS160/REM carbon/epoxy prepreg layers (0.17 mm nominal thickness) and consolidated in an autoclave at a maximum temperature of 160 °C. The nominal fibre fraction of prepreg layers was 61.5% in weight. The panel was instrumented with two PI Ceramic PIC 151 lowprofile piezoceramic transducers (6.35 mm diameter, 0.25 mm thickness) positioned as shown in Fig. 2. The transducers were surface bonded using a two-component epoxy adhesive and wired using additionally bonded connectors. The composite plate was
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Fig. 3. X-radiographs of impact damage for 2.04 J and 10.1 J impacts.
Fig. 2. Schematic diagram of the composite specimen.
ultrasonically C-scanned prior to testing to assess the quality of the laminate and to exclude the presence of manufacturing defects. 3.2. Impact tests A drop-weight impact testing tower with a 2.2 kg impactor was used in order to introduce damage onto the composite plate. The impactor was provided with a hemispherical indentor of 12.5 mm diameter and instrumented with a semiconductor strain-gauge bridge for dynamic load acquisition. A pneumatic catch mechanism was used to capture the impactor after the rebound in order to prevent multiple impacts on the specimens. The energy dissipated during the impact was evaluated from the impact and rebound velocities, as measured by an infra-red sensor. During testing, the laminate was simply supported on a steel plate with a rectangular opening measuring 87.5 mm (along the 0° direction of the laminate) by 65 mm and subjected to impact on the centre of the 300 mm by 120 mm area (Fig. 2). Impact energies of 2.04 and 10.1 J, obtained by varying the drop height of the impactor, were used to progressively introduce different levels of damage in the laminated panel.
across the thickness of the laminate, together with a dense network of 0° and ±45° matrix cracks. Short fibre fracture paths may also be seen on the impact side of the plate in the proximity of the contact area, while only a shallow indentation (about 0.08 mm in depth) may be noticed at the impact location on the surface of the laminate. Extensive delaminated areas, major fibre fracture (on both the tensile and compressive sides of the panel) and a much larger indentation (0.85 mm) are on the other hand observed for the 10.1 J impact energy. Such an energy level may be therefore approximately assumed as the energy threshold indicating the onset of laminate penetration [26]. A summary of the main indicators of the damage response of the panel to impact energies of 2.04 and 10.1 J is reported in Table 1. 4. Impact damage detection with nonlinear acoustics Damage detection experimental work using nonlinear acoustics is described in this section. The experimental modal analysis was performed initially to estimate the best frequency values for modal and ultrasonic excitation. The undamaged plate was then monitored using nonlinear acoustics. This was followed by a series of damage detection nonlinear acoustic tests performed after each impact in order to reveal possible damage. In what follows, the entire experimental procedure and results are presented.
3.3. Inspection for impact damage 4.1. Experimental modal analysis Non-destructive penetrant-enhanced X-ray inspections were carried out after each impact to identify and characterize internal damage. Radiographic analyses were performed with a HP Faxitron cabinet, using a 20 kV voltage, 3 mA current, and 100 s exposure time to produce X-ray images on an AGFA NDT D4 film. After processing, digital images of the negative were acquired by an optical scanner for direct observation of damage and measurement of projected delaminated areas. Fig. 3 shows X-ray pictures of internal damage after 2.04 J and 10.1 J impacts. Damage induced by the 2.04 J impact mainly consists of multiple delaminations developing along several interfaces
Simple modal analysis experiments were preliminary performed in order to establish frequencies for the modal excitation in nonlinear acoustics. As shown in Fig. 4, the plate was clamped between two steel plates, using a Galdabini SUN 500, 5 kN servoelectric testing machine in order to control the clamping level. The clamped area of the plate is indicated graphically in Fig. 2. The clamping load adopted during the analyses was equal to 5 kN. The composite plate was excited modally using a Bruel & Kjaer 4809 electrodynamic vibration shaker, as visible in Fig. 4. The position of the excitation was selected to avoid possible nodal points of
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Absorbed energy (J)
Peak force (N)
Indentation depth (mm)
Projected delamination area (mm2)
2.04 10.1
0.28 7.73
2010 6790
0.08 0.85
104.4 558.4
Fig. 4. Experimental clamping arrangement for the composite specimen.
the plate in order to guarantee good signal responses. A sweep sine signal starting at 1 Hz and crossing 3200 Hz in 2 s was used to excite the plate. The excitation signal was generated using a Wavetek FG3B, 2 MHz function generator and amplified using a Bruel & Kjaer 2706 power amplifier. The acoustic response was acquired using a National Instruments NI 5112, 100 MSa/s High-Speed Digitizer operated in a WinXP – LabViewÒ environment. During both the preliminary modal analyses and the subsequent damage detection tests, the level of modal vibration was monitored by acquiring the signal of a Bruel & Kjaer 4393 piezoelectric charge accelerometer, located on the front face of the laminate along the axis of shaker excitation. The accelerometer signal was amplified by a Bruel & Kjaer 2635 charge amplifier and acquired using an HP 54520 digital oscilloscope. Fig. 5 shows the main equipment used in the experimental investigations. The excitation (electromagnetic shaker at position B, as indicated in Fig. 2) and response signals (from transducer C) were used to obtain the vibration Frequency Response Function (FRF). The level of the excitation, as measured by the maximum acceleration in B, was equal to 6 m/s2 peak-to-peak. Twenty sets of data were used
to calculate the average FRF amplitude in order to increase the signal-to-noise ratio. The FRF amplitude, presented in Fig. 6a, reveals a number of vibration modes of the plate. The 77, 262 and 2934 Hz frequencies were selected for modal excitation in damage detection tests. These frequencies correspond to the lowest, strongest and highest analysed vibration mode, respectively. A similar procedure was applied to obtain the best ultrasonic frequencies in nonlinear acoustic tests. This time, bonded piezoceramic transducers were used to introduce the ultrasonic wave (transducer A) and to measure the ultrasonic response (transducer C). Positions for the transducers were selected in line with the impact location following previous investigations (e.g. [11,25]). A sweep sine signal starting at 3 kHz and crossing 210 kHz in 3 s was used to excite the plate acoustically. The excitation signal was generated using a TTI TGA1241 40 MHz function generator. The peak-to-peak amplitude of excitation was equal to 20 V. The excitation and response signals were again acquired using the NI 5112 digitizer and used to obtain the acoustical transfer function as the average spectrum of twenty data-sets. The transfer function amplitude, presented in Fig. 6b, reveals a number of vibration modes of the plate. The 17.63 and 98.04 kHz frequencies were selected for ultrasonic excitation in subsequent nonlinear acoustics tests. These frequencies were selected by trial-and-error from the acoustic transfer function as the best two local acoustical modes exhibiting relatively strong signal-tonoise ratio responses. 4.2. Experimental set-up and procedure for damage detection Nonlinear acoustic tests were then performed, with the experimental equipment described in the previous section, first on the undamaged, intact panel and subsequently on the same panel after damaging the laminate with 2.04 J and 10.1 J low-velocity impacts. The composite panel was loaded between the clamping plates with a 5 kN force applied by the servoelectric testing machine. An ultrasonic sine wave (peak-to-peak amplitude = 20 V) was introduced to the low-profile piezoceramic actuator at location A (Fig. 2) and, at the same time, the plate was vibrated using the electromagnetic shaker at location B. The study was performed for the modal (f1) and ultrasonic (f0) frequencies established in Section 4.1 and applying levels of modal excitation (as measured by acceleration signals recorded at location B) ranging between 1 and 5 m/s2 peak-to-peak. The response signal from the piezoceramic trans-
Fig. 5. Experimental equipment used in modal analysis and nonlinear acoustics tests.
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Fig. 6. Modal analysis results: (a) vibration Frequency Response Function (FRF) and (b) acoustic transfer function.
ducer at location C was acquired by the NI 5112 digitizer using 125 kpoints and a 125 kSa/s sampling rate for the 17.63 kHz acoustic excitation, and 500 kpoints and 1 MSa/s sampling rate for the 98.04 kHz acoustic excitation. The resulting frequency resolutions of the signal spectra were thus 1 Hz and 2 Hz for the 17.63 kHz and 98.04 kHz acoustic excitation frequencies, respectively. Averaged power spectra were finally calculated from 10 datasets of the response signal using a specifically written LabView code, and then zoomed on the fundamental harmonic of the acoustic wave in order to reveal possible modulations sidebands. 4.3. Damage detection results and discussion Fig. 7–9 show examples of power spectra from acoustical responses for the 17.63 kHz ultrasonic excitation and three different modal excitation frequencies. The acoustical harmonic dominates all analysed spectra. From Fig. 7, which shows the results for the
77 Hz modal excitation, we may see that spectra recorded after 2.04 and 10.1 J impacts (Fig. 7b and c) exhibit a clear pattern of sidebands around the acoustical frequency component. The frequency of these sidebands corresponds to multiple values of the 77 Hz modal frequency and their amplitude increases with the impact energy (Fig. 10) and thus with the entity of laminate damage. In particular, the average amplitude of the first pair of sidebands increases approximately by 2 dB and 8 dB after 2.04 and 10.1 J impacts, respectively. It is worth noting that one small 77 Hz sideband is also present on the left hand side of the acoustical main component for the undamaged plate, as visible in Fig. 7a. Similar features can be observed in Figs. 8 and 9, where the results for the 262 and 2934 Hz modal excitation are presented. However, the patterns of sidebands for the undamaged specimen in Fig. 8a and 9a are relatively strong if compared with those in Fig. 7a. This time the amplitude of sidebands increases by 4 dB and by 0.4 dB after 2.04 J impact for the 262 and 2934 modal
Fig. 7. Power spectra of acoustic response for undamaged and impact-damaged panel. 77 Hz modal excitation (1.0 m/s2); 17.63 kHz acoustical excitation.
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Fig. 8. Power spectra of acoustic response for undamaged and impact-damaged panel. 262 Hz modal excitation (1.1 m/s2); 17.63 kHz acoustical excitation.
Fig. 9. Power spectra of acoustic response for undamaged and impact-damaged panel. 2934 Hz modal excitation (3.9 m/s2); 17.63 kHz acoustical excitation.
excitation, respectively (Fig. 10). The amplitude increase of the first sidebands after 10.1 J impact is quite significant and reaches the approximate level of 15 dB and 7 dB for the 262 and 2934 Hz modal excitation in Figs. 8c and 9c, respectively. A marked decrease of the amplitude of the fundamental carrier frequency may also be observed after the 10.1 J impact for all modal excitation frequencies investigated, as seen in the spectra of Figs. 7–9. The results for the 98.04 kHz ultrasonic excitation and different frequencies of modal excitation are presented in Figs. 11–13. A pattern of sidebands corresponding to multiples of the modal frequencies are now visible in the response of the undamaged panel for all three vibration frequencies examined, as shown in Figs. 10a, 11a and 12a. Similarly to the results previously discussed for the 17.63 kHz excitation, the amplitude of the sidebands always increases with the entity of impact damage (Fig. 14), with the only exception of the spectrum recorded after the 2.04 J impact for the 2934 Hz modal excitation, where an 1.5 dB decrease in the
average amplitude of the first sidebands was measured. A strong reduction of the amplitude of the carrier acoustic frequency is also observed on the response of the laminate damaged by the highest energy impact. 4.4. Effect of clamping on nonlinear acoustic results The presence of sidebands in the response of the undamaged panel (Figs. 7a–9a, 11a–13a) can probably be explained by the existence of inherent nonlinearity, as discussed at the end of Section 2. It is very likely that clamping produces additional nonlinear contact effects results in modulation sidebands and the effect of clamping has been thus investigated further in additional experimental tests. The nonlinear damage detection procedure has been performed for the 17.63 kHz ultrasonic excitation, 77 Hz modal excitation (using an excitation level corresponding to the acceleration of 2 m/s2 peak-to peak) and different clamping force levels. Fig. 15 shows examples of acoustical power
Fig. 10. Increase in sidebands amplitude as a function of impact energy in tests with 17.63 kHz acoustical excitation.
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Fig. 11. Power spectra of acoustic response for undamaged and impact-damaged panel. 77 Hz modal excitation (2.8 m/s2); 98.04 kHz acoustical excitation.
Fig. 12. Power spectra of acoustic response for undamaged and impact-damaged panel. 262 Hz modal excitation (1.1 m/s2); 98.04 kHz acoustical excitation.
Fig. 13. Power spectra of acoustic response for undamaged and impact-damaged panel. 2934 Hz modal excitation (5.0 m/s2); 98.04 kHz acoustical excitation.
Fig. 14. Increase in sidebands amplitude as a function of impact energy in tests with 98.04 kHz acoustical excitation.
spectra for 0.7, 3.7 and 4.7 kN clamping force for the undamaged plate. The results demonstrate that the amplitude of sidebands decreases with the increased clamping force level. The amplitude
levels of the fundamental acoustical frequency and of the first pair of sidebands measured at various levels of clamping force for both the undamaged and damaged (after 10.1 J impact) plate
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are presented in Figs. 16. The plots indicate that the amplitude of the carrier frequency increases and the amplitude of the first sidebands decreases with the clamping force, until a force level higher than about 4200 N is reached and both amplitudes remain relatively constant. In contrast, once the specimen is damaged, increasing the value of the clamping force reduces the amplitude of the fundamental frequency while appears to increase, at least above a certain applied force level, the amplitude of first sidebands. These results indicate that nonlinear mechanisms introduced by boundary effects may differ from those induced by damage phenomena in the material, and may thus suggest possible ways to discriminate between damage and non damage-related nonlinearities.
5. Conclusions The application of the nonlinear acoustic technique for impact damage detection in composite materials has been presented. The method was based on frequency modulation of the ultrasonic wave propagating in the plate by a low-frequency modal excitation signal.
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The study demonstrates that damage and delaminations resulting from low-velocity impacts produce sidebands around the fundamental ultrasonic component in the power spectra from acoustical responses. The frequencies of sidebands correspond to multiples of modal excitation and their amplitudes increase with the entity of impact damage (as measured by the delamination area). Significant increase in sidebands amplitude (i.e. by more than 10 dB for the first sidebands) can be observed for the highest-energy impact (10.1 J) data. The pattern of small modulation sidebands could be seen in the acoustical spectrum when delamination was not present in the plate. This phenomenon has been observed before when crack detection in metallic structures has been investigated. Therefore, a template result for undamaged condition is necessary for comparison to avoid false-positive damage detection. The study shows that the level of clamping force (i.e. boundary conditions) affects the amplitudes of both the fundamental acoustical frequency and sidebands. However, different responses to varying boundary conditions were observed in undamaged and damaged panel. Further analyses are required to identify and characterize possible sources of intrinsic (non damage-related) nonlinearities. Any future work should also investigate: the sensitivity of the method to small
Fig. 15. Examples of power spectra of acoustic response of the undamaged panel for different clamping forces. 77 Hz modal excitation (2 m/s2); 17.63 kHz acoustical excitation.
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Fig. 16. Effect of clamping force on the amplitude of fundamental frequency and first sidebands for undamaged and damaged (10.1 J impact energy) panel. 77 Hz modal excitation (2 m/s2); 17.63 kHz acoustical excitation.
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