DAMAGE DETECTIN OF STEEL STRUCTURES WITH PIEZOELECTRIC TRANSDUCERS AND LAMB WAVES

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1 IV INTERNATIONAL SYMPOSIUM FOR STUDENTS OF DOCTORAL STUDIES IN THE FIELDS OF CIVIL ENGINEERING, ARCHITECTURE AND ENVIRONMENTAL PROTECTION Nemanja Marković 1 Dragoslav Stojić 2 Tamara Nestorović 3 DAMAGE DETECTIN OF STEEL STRUCTURES WITH PIEZOELECTRIC TRANSDUCERS AND LAMB WAVES Abstract: Piezoelectric sensors/actuators are widely used to detect different types of damage in various types of steel structures and showed great potential in Civil engineering applications. Lamb waves are highly suitable for damage detection in thin plates because they have property of propagation through a relatively long distance with a very small amplitude decrease. In this paper we report various types of methods (Pitch-Catch method, Pulse-Echo method and Time Reversal method) for damage (vertical notches with different orientation, holes and corrosion) detection. By analyzing the signal output we can quantify damage by defining damage index. Among other, in this paper we report various signal processing methods (Wavelet Analysis (WA) and Fast Fourier Transformation (FFT)). Key words: piezoelectric, Lamb waves, signal processing, damage detection, damage index DETEKCIJA OŠTEĆENJA KONSTRUKCIJA OD ĈELIKA POMOĆU PIEZOELEKTRIĈNIH SENZORA I LAMB TALASA Rezime: Piezoelektrični senzori/aktuatori se dosta primenjuju za detekciju različitih tipova oštećenja kod velikog broja različitih čeličnih konstrukcija i pokazuju veliki potencijal u primeni kod graďevinskih objekata. Lamb talasi su naročito pogodni za detekciju oštećenja kod pločastih elemenata zbog svoje osobine da se prostiru kroz relativno veliku duţinu sa malom promenom amplitude. U ovom radu su prestavljene tri metode (Pitch-Catch metoda, Pulse-Echo metoda i Time Reversal metoda)za detekciju oštećenja (vertikalni zarezi različite orjentacije, rupa i korozije). Analizom dolaznog signala moţemo da kvantitativno odredimo veličinu oštećenja pomoću indeksa oštećenja. IzmeĎu ostalog, u ovom radu su prikazane i metode analize signala (Wavelet Analysis (WA) i Fast Fourier Transformation (FFT)). Ključne reči: piezoelektrično, Lamb talas, analiza signala, detekcija oštećenja, indeks oštećenja 1. INTRODUCTION Lamb waves have been widely used for damage detection of steel structures in recent years. Ultrasonic guided waves, like Lamb waves, are suitable for damage detection in large civil engineering structures. Tree methods for damage detection are specifically imposed in the practical implementation and in this paper we presented them (Pitch-Catch method, Pulse-Echo method and Time Reversal method). P. S. Tua [4] used piezo-actuated Lamb waves for detection cracks in metalic plates. In paper [5] Jeong-Beom Ihn and Fu-Kuo Chang used Pitch-Catch method for damage detection in plate like aircraft structures. Victor Giurgiutiu [2] in his book present all tree damage detection methods and practical apllications with 1 PhD student, University of Niš, The Faculty of Civil Engineering and Architecture in Niš, Aleksandra Medvedeva 14, Niš, Serbia, 2 PhD, full professor, University of Niš, The Faculty of Civil Engineering and Architecture in Niš, Aleksandra Medvedeva 14, Niš, Serbia, 3 PhD, professor, University of Bochum, The Faculty of Civil Engineering, Germany -353-

2 appropriated experiments. B. Poddar [6] used Time reversal Lamb wave method for damage detection in metalic plate. Also, damage detection is not possible without signal processing methods and definition of damage indexes. Wavelet analysis method and Fast Fourier transformation method are presented in this paper. 2. LAMB WAVES Lamb waves, a.k.a., guided plate waves, are a type of ultrasonic waves that are guided between two parallel free surfaces, such as the upper and lower surfaces of a plate. Lamb waves can exist in two basic types, symmetric and antisymmetric. For each propagation type there exist a number of modes corresponding to the solution of the Rayleigh-Lamb equation. The symmetric Lamb waves resemble the axial waves, whereas the antisymmetric Lamb waves resemble the flexural waves. In fact, it can be proven that, at low frequencies, the symmetric Lamb waves approach the behavior of the axial plate waves, whereas the antisymmetric Lamb waves approach the behavior of the flexural plate waves. Lamb waves are highly dispersive, and their speed depends on the product between frequency and the plate thickness. The waves-speed dispersion curves are obtained from the solution of the Rayleigh-Lamb equation. At a given frequency-thickness product, for each solution of the Rayleigh-Lamb equation, one finds a corresponding Lamb-wave speed and a corresponding Lamb-wave mode. Without a detailed performing, we will present the final forms for symmetric and antisymmetric Lamb wave modes. ( ) Equation (1) is the Rayleigh-Lamb wave equation for symmetric modes. The solution of this transcendental equation is not easy, because p and q also depend on. Numerical solution of equation (1) yield the symmetric (S) eigenvalues,. (1) Figure 1 - Wave speed dispersion curves for symmetric Lamb waves in an aluminum plate (c s -shear wave speed, d-half thickness of the plate) ( ) (2) This is the Rayleigh-Lamb equation for antisymmetric modes. The solution is also not easy, and yields the antisymmetric (A) eigenvalues,

3 Figure 2: Wave speed dispersion curves for antisymmetric Lamb waves in an aluminum plate (c s -shear wave speed, d-half thickness of the plate) 3. FINITE ELEMENT MODELING AND SIMULATION Lee and Staszewski in his paper [3] summarized the major achievements of modeling Lamb waves for the purpose of damage identification. The approach include finite element method, finite difference method, boundary element method (BEM), finite strip element method, spectral element method and local interaction simulation approach. Among the different approaches, finite element method based modeling and simulation is the most cost-effective with commercial software available such as ABAQUS, ANSYS and Patran. Basically, the use of finite element method to simulate the propagation of Lamb waves in a solid medium has two components: activation of Lamb waves, and acquisition of Lamb waves upon travelling a certain distance. For the activation, in accordance with particle motion, S 0, A 0 and SH 0 wave modes can be activated by imposing radial in-plane, out-of-plane and tangential in-plane constraints (e.g., displacement, force or stress), respectively, on the finite element method nodes of the actuator. 4. DAMAGE DETECTION METHODS Victor Giurgiutiu in his book [2] gave a comprehensive overview of damage detection methods in structural health monitoring, and in this paper we were show a short review of these methods Pitch-Catch Method The Pitch-Catch method detects damage from the changes in the Lamb waves traveling through a damage region. The method uses the transducers in pairs, one as transmitter, and the other as receiver. The Pitch-Catch method can be used to detect changes that take place between a transmitter transducer and a receiver transducer. The detection is performed through the examination of the guided wave (Lamb wave) amplitude, phase, dispersion, and TOF in comparison with a pristine situation. Guided wave modes that are strongly influenced by small changes in the material stiffness and thickness (such as the A 0 Lamb wave) are well suited for this method. Typical applications include (a) corrosion detection in metallic structures; (b) diffused damage in composites; (c) disband detection in adhesive joints; (d) delaminating detection in layered composites, etc. Pitch-Catch method can also be used to detect the presence of cracks from the wave signal diffracted by the cracks. Figure 3: Ultrasonic damage-detection techniques with pitch-catch method -355-

4 4.2. Pulse-Echo Method The Pulse-Echo method follows the general principles of conventional Lamb wave nondestructive evaluation. A piezoelectric transducer attached to the structure acts as both transmitter and detector of guided Lamb waves traveling in the structure. The wave sent by the piezoelectric transducers is partially reflected at the crack. The echo is captured at the same piezoelectric transducer acting as receiver. For the method to be successful, it is important thet a low-dispersion Lamb wave be used. The selection of such a wave, e.g., the S 0 mode, is achived through the Lamb-wave tuning methods. Figure 4: Ultrasonic damage-detection techniques with pulse-echo method 4.3. Time Reversal Damage Detection Method The Time Reversal method was developed by Fink (1992) in connection with the Pitch-Catch method. The signal sent by the transmitter arrives at the receiver after being modified by the medium in which it travels. If the received signal is time reversed and sent back from the receiver to the transmitter, the effect of the medium is also reversed. This reversal is quite spectacular in the case of dispersive Lamb waves. Lamb-wave time reversal method is a new and tempting baseline-free damage detection technique for structural health monitoring. With this method, certain types of damage could be detected immediately without prior baseline data. However, this method is complicated by the existence of the least two Lamb modes at any given frequency and by the dispersion nature of the Lamb wave modes. The theory of Lamb wave time reversal is still under development. Figure 5: Lamb wave time-reversal procedure block diagram 5. SIGNAL PROCESSING In this part of paper, we will present the basic expressions of direct Fourier Transform, Short-Time Fourier Transform and Wavelet analysis Fourier transform and short-time Fourier transform The classical Fourier transform (FT) determines the frequency contents (spectrum) of a stationary signal by comparing it with an infinite number of sine and cosine functions of different frequencies. The mathematical expressions of the direct Fourier transform (FT) of the inverse Fourier transform (IFT) are, respectively: -356-

5 ( ) ( ) (3) ( ) ( ) (4) Equation (5) is called short-time Fourier transform (STFT) since only the signal around the interest time t 0 is analyzed. ( ) ( ) ( ) ( ) (5) 5.2. Wavelet analysis The presence of short-duration high-frequency signal bursts occur are hard to detect, whereas in our pulse-echo damage detection, burst signals are often used. Time-frequency method, the wavelet transform, are used as an alternative to overcome the disadvantages of the STFT. Wavelets can keep track of time and frequency information, zooming in on short bursts or zooming out to detect long, slow oscillations. The Continuous Wavelet Transform (CWT) of signal x(t) by using mother wavelet ( ) is: Where ( ) ( ) is called the mother wavelet. ( ) ( ) (6) 6. DAMAGE INDEXES The damage index is a scalar quantity that serves as a metric for the damage present in the structure. Sun et al. (1995) used a damage index based on the root mean square deviation (RMSD) change of the E/M impedance real part spectrum. The damage index compares the amplitudes of the two spectra (damaged vs. pristine) and assigns a scalar value based on the formula: [ ( ) ( )] [ ( )] (7) Where N is the number of sample points in the spectrum, and the superscript 0 signifies the pristine state of the structure. 7. CONCLUSION This paper presents new developed damage detection methods, methods for signal analysis and defining the damage using damage indices. Tree active sensing methods were presented for monitoring and crack detection in steel structures: 1) Pitch-Catch method, 2) Pulse-Echo method and 3) Time reversal method, for damage (vertical notches with different orientation, holes and corrosion) detection. Pitch-Catch method can be used when the damage is between the piezoelectric sensor and actuator, so the signal passes through the damaged area of the element. Pulse-Echo method doesnt required the presence of damage between the actuators and sensors, because the one piezoelectric element is actuator and sensor. Disadvantage of this method is the detection of a large number of damages. Time-reversal method doesnt require the existence of the results of the undamaged structure, unlike the first two methods, and this is the main advantage of this method. By analyzing the signal output we can quantify damage by defining damage index and we present a root mean square deviation (RMSD) damage index. The direct Fourier Transform, Short-Time Fourier Transform and Wavelet analysis are shown in this paper. REFERENCES [1] Zhongqing Su, Lin Ye, Identification of Damage Using Lamb Waves, Springer, [2] Victor Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer Active Sensors, Elsevier,

6 [3] Lee B. C., Staszewski W. J., Modelling of Lamb Waves for damage detection in metallic structures: part I wave propagation, Smart Materials and Structures 12, , [4] P. S. Tua, S. T. Quek, Q. Wang, Detection of cracks in plates using piezo-actuated Lamb waves, Smart Materials and Structures 13 (2004), [5] Jeong-Beom Ihn, Fu-Kuo Chang, Pitch-Catch Active Sensing Methods in Structural Health Monitoring for Aircraft Structures, Structural Health Monitoring 7, (2003). [6] B. Poddar, A. Kumar, M. Mitra, P. M. Mujumdar, Time reversal of a Lamb wave for damage detection in a metallic plate, Smart Material and Structures 20 (2011)

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