Dynamics-based Structural Health Monitoring Using Laser Vibrometry

Transcription

1 Dynamics-based Structural Health Monitoring Using Laser Vibrometry Massimo Ruzzene Atlanta, GA - USA Politecnico di Millano 05/23/

2 Outline Introduction to dynamics-based SHM Laser Vibrometry Our approach to SHM Strain energy damage index Wave filtering approach Research opportunities -2-

3 Introduction -3-

4 Dynamics-based SHM Analysis of the dynamic response of the structure for: Damage detection (presence of damage) Damage identification (type of damage) Damage quantification (extent of damage) Estimation of remaining life -4-

5 Dynamics-based SHM Focus/ State-of-the-art -5-

6 Dynamics-based SHM Damage Size Macroscopic damage (visible through visual inspection) Modal analysis Cracks local disbonds Guided waves Small cracks Dislocations pile-ups Damage precursors Ultrasonics Nonlinear acoustics Frequency [Hz] -6-

7 Modal Testing Estimation of damage through monitoring of modal parameters: Natural frequencies (early approach) Low sensitivity Influence of many parameters other than damage No information about damage location Damping values Very hard to measure No direct physical interpretation No information about damage location -7-

8 -8-

9 Modal Testing Estimation of damage through monitoring of modal parameters: Frequency response functions Dynamic impedances Mode shapes, modal curvatures, modal strain energy distributions: Sensitive Provide location of damage Require large number of sensors -9-

10 Guided Waves Elastic waves guided by the structure Rods, beams (longitudinal waves) Plates, panels (Lamb waves) Lamb waves propagate along the surface of the plate, guided by the plate thickness Damage interferes with propagating waves and it is detected by estimating corresponding reflections -10-

11 Lamb Waves Symmetric mode Antisymmetric mode Plate thickness -11-

12 Guided waves F(t) -12-

13 Ultrasonics Established technique High frequency of interrogation Waves propagating through the thickness High sensitivity Local inspection only Labor intensive -13-

14 Guided waves vs. ultrasonics Piezo discs excitation: Piezo disc Structure Anti-symmetric Lamb mode Symmetric Lamb mode Waves are guided by the structure to travel along the surface: Propagation at long distances (large area inspection); Traditional ultrasonics propagate through the thickness (local inspection only) Guided waves Ultrasonics -14-

15 SHM Using Laser Vibrometry -15-

16 Our approach Damage Size Modal analysis Guided waves Integrated application of modal analysis & guided waves inspection Ultrasonics Nonlinear acoustics Frequency [Hz] -16-

17 Overview Our approach to SHM is based on: Vibration inspection, and Wave propagation inspection; Detection technology: Evaluation of strain energy distribution associated with dynamic response; Dynamic response may be: Operational Deflection Shape (ODS) Transient response Vibration Wave propagation Formulation of a damage index (DI); Formulation does not require baseline data on undamaged structure. Application of wave filtering techniques. -17-

18 Laser Doppler Vibrometer LDVs are vibration sensors measuring VELOCITIES and DISPLACEMENTS; Measurement principle is based on the Doppler effect on Laser light emitted by a source and reflected by the moving object; General classification: Single point LDVs: point sensors; Scanning LDVs (SLDV): single point LDVs equipped with a scanning mechanism which delivers Laser beam on a grid of points on the structure SHM approach is enabled by the application of a SCANNING LASER DOPPLER VIBROMETER. -18-

19 Laser Doppler Vibrometer Enabling characteristics: Non-contact Spatially dense measurements High frequency bandwidth: Potentially infinite bandwidth; Limitations are dictated by AD conversion device of equipment; Typical values: 0-20 khz low end equipment; 0-1 MHz medium end equipment; 200 Hz-20 MHz high end equipment; SCANNING LASER HEAD -19-

20 Damage Index based on analysis of Strain Energy distribution -20-

21 Damage Index Formulation Formulation for a beam Beam is divided into N segments: Strain energy of segment i for kth mode of Euler-Bernoulli beam: Total strain energy for kth mode: Fractional strain energy: -21-

22 Damage Index Formulation Damage Index based on strain energy density Considering damage localized to a single region i=p, Indication of change in flexural rigidity(*): Damaged Damage Index Undamaged This concept can be extended to plate structures with appropriate second derivative and plate rigidity terms, or generalized to any plane surface. (*) Cornwell P., Doebling S.W., Farrar C., Application of the Strain Energy Damage Detection Method to Plate-Like Structures, Journal of Sound and Vibration (1999), 224 (2), pp

23 General DI formulation Structure Actuator SLDV Damage Measurement grid Scanned surface is divided into triangular or quadrilateral elements; Strain Energy is computed over each grid element through interpolation of displacements measured at grid points: i, j Interpolation functions (b-splines) Measured out-of-plane displacement Formulation is general and can accommodate complex grid geometries. -23-

24 General DI formulation Slopes evaluation NOTES: Slopes are obtained through the analytical differentiation of the splines; Procedure minimizes errors due to noise in the data. Interpolation of displacements and slopes in matrix form: where Strain evaluation: -24-

25 General DI formulation Energy functional over region g Assuming that over damaged region (*) : Damage Index: Damaged Undamaged -25-

26 Synthesis of baseline data Baseline information is obtained from test on damaged structure (only one set of data is required); Spatial decimation: data are analyzed and interpolated over a coarser grid, less sensitive to the damage; Baseline response: Subset of measured response Decimation factor quantifies spatial decimation: Number of under-sampled data Number of available measurements -26-

27 Numerical results for beam Influence of Decimation on Damage Index Curvature Mode Shape, w xx Φ 1xx x [m] Decimation Factor=50% Damage Index f 1 Decimation Factor=90% x [m] Φ 1xx 4 3 f x [m] X x [m] w xx = Curvature corresponding to ODS at 1 st natural frequency X -27-

28 Time and frequency domain formulations Modal Damage Index: = i-th natural frequency Cumulative Damage Index: Time domain Damage Index: -28-

29 Experimental set-up for wave propagation analysis Wavefield detection/visualization Low-frequency signal (1 Hz) Function generator 2 Sinusoidal burst Voltage Amplifier LDV Head (4) (3) Plate Function generator 1 Trigger (1) (2) Phase information Plate response Measured Wave-field DAQ & Signal processing Reconstructed wave-form -29-

30 Example of propagating wavefield Propagation of a 7 cycles 50 khz sinusoidal burst in an aluminum plate -30-

31 Experimental results Aluminum plate Cumulative DI (first 5 modes) Damage Index Unexposed Surface of Test Specimen Groove Actuator Damaged area Aluminum plate with artificial damage. Scanning points -31-

32 Wave propagation analysis on aluminum plate Aluminum plate with 1.4 groove Time domain DI Unexposed Surface of Test Specimen Groove Actuator Scanned area -32-

33 F-15 Wing Panel * Courtesy of Warner Robins Air Logistic Command -33-

34 F-15 Wing Panel Identification of damage location Using Damage Index on Modal data (10 modes) Measured region Damage location Actuator -34-

35 F-15 Wing Panel Zoom-in to the region identified during modal test Time domain damage index 2 Piezoceramic Disk 50 KHz Sine Burst -35-

36 F-15 rib Damage Index application to wavefield data Scanned area is affected by hairline crack Damage 35kHz Piezoceramic Actuator * Courtesy of Warner Robins Air Logistic Command -36-

37 Composite lap-joint Contour Plot of Damage Index Laser Beam Lap-Joint Specimen Defects at the Edge Interior Defects DI estimations correlate perfectly with X-Ray analysis of lap joint Non-Interfering Piezoelectric Actuator * Courtesy of Lockheed Martin Co., Marietta GA -37-

38 Honeycomb structure and turbine blade Honeycomb Structure Turbine Blade Disbond region Defect not visible by the naked eye -38-

39 Field Tests in Planning Stage F-16 Vertical Tail Honeycomb/Skin Disbond -39-

40 Frequency-Wavenumber Domain Filtering -40-

41 Introduction Wavefield time-domain data allow the application of Multidimensional Fourier Transforms (2D/3D FFTs): Representation of the response in the frequency/wavenumber domain. 2D/3D FFTs allow: The analysis of multi-mode wave signals and the characterization of the various modes; The identification of dispersion relations; Highlighting all wave components propagating in directions opposite to the direction of the main injected pulse; The detection of presence of reflections and mode conversions caused by damage. -41-

42 Introduction Objective: Application of the frequency/wavenumber representation to devise simple filtering strategies for: Eliminating the applied excitation and corresponding propagating wave from the recorded response, while Highlighting the presence of any reflections along the wave path. -42-

43 Concept 1D waveguide: 1D stress in x<x 0 region: where -43-

44 Concept Letting: Harmonic wave gives: 2D FFT: Incident Reflected -44-

45 Concept Incident Reflected Incident Reflected k x [rad/m] ω [rad/s]

46 Original response 15 k x [rad/m] Incident = window function (2D Hanning) 5 10 Reflected Filtered response ω [rad/s] k x [rad/m] ω [rad/s] -46-

47 2D example: Sum of plane and spherical wave 3D FFT: Plane wave Spherical wave -47-

48 Snapshot of original waveform 200 3D ω=ω k y [rad/m] Snapshot of filtered waveform k x [rad/m] Filtered 3D ω=ω k y [rad/m] k x [rad/m]

49 2D example: Sum of two spherical waves 3D FFT: -49-

50 Snapshot of original waveform D ω=ω k y [rad/m] Snapshot of filtered waveform k x [rad/m] Filtered 3D ω=ω k y [rad/m] k x [rad/m]

51 Numerical results: Damaged rod Rod is modeled using FE method (160 bar elements); Excitation is a 5-cycles 50 khz sinusoidal burst; Damage is modeled as a thickness reduction at a selected location. -51-

52 Response at x=3/4 L 2D FFT Filtered Response at x=3/4 L Filtered 2D FFT -52-

53 Numerical results: 2D elastic domains with cracks Wave propagation is simulated according to the Mass Spring Lattice Model (MSLM); Domains have dimensions L x =0.5 m and L y =0.25 m, and they are discretized using a 200*100 lattice; Excitation is a 5-cycles 100 khz sinusoidal burst; Damage is modeled as a 30% stiffness reduction. -53-

54 Single crack Original response 150 3D f=100 khz k y [rad/m] Filtered response k x [rad/m] 150 Filtered 3D f=100 khz k y [rad/m] k x [rad/m]

55 Two cracks Original response 150 3D f=100 khz k y [rad/m] Filtered response k x [rad/m] 150 Filtered 3D f=100 khz k y [rad/m] k x [rad/m]

56 Experimental results Al Plate with 4 slits of controlled dimensions 4 Actuator

57 Experimental results Example of 3D FFT of recorded response Cross section at excitation frequency (90 khz) Original response Filtered response ky [rad/m] 0 ky [rad/m] kx [rad/m] kx [rad/m] -57-

58 Experimental results 90 khz excitation Measured response Filtered response -58-

59 Experimental results RMS of the filtered response: -59-

60 Experimental results 2 Tongue and groove connection Epoxy is used for bonding; Bonding defect is simulated by preventing epoxy to reach middle part of the connection. -60-

61 Experimental results 2 Set up and area of scanning Measured response Piezoceramic Actuator Disc Damage Location Tongue and Grove Joint -61-

62 Experimental results 2 RMS of the filtered response: y [m] Disbond length x [m] -62-

63 Experimental result 3 Honeycomb plate Face sheets are bonded to the core with epoxy; Grease is placed over a small area to prevent bonding (defect simulation). -63-

64 Experimental result 3 Measured response RMS of filtered response Area of damage -64-

65 Vought aircraft sample Section of graphite wing spar Region 4 Actuator not being used for testing Region 3 Region 1 Region 2 Location of actuator used for testing (on back side) -65-

66 Vought aircraft sample Region 1-66-

67 Vought aircraft sample Region 3-67-

68 Vought aircraft sample Region 4-68-

69 Conclusions Simple filtering technique based on spectral representation of a wavefield; Technique is demonstrated on analytical and numerical results; Experimental application is enabled by the use of a Scanning Laser Vibrometer; Results are presented for various types of damage; Technique is model independent. -69-

70 Research opportunities Damage Size Modal analysis Guided waves Ultrasonics Area of interest Nonlinear acoustics Frequency [Hz] -70-

71 Nonlinear acoustics Nonlinear constitutive law : Nonlinear parameter β depends on : density of dislocations plasticity creep β is a damage precursor Nonlinear material -71-

72 Nonlinear acoustics Amplitude of second harmonic can be measured during high frequency tests: A 2 is proportional to β: Relation is valid only assuming 1D plane wave propagation and it is based on a 1965 analytical solution -72-

73 Opportunities Moneti fellowship for Italian students: Fully funded Maters Degree (Tuition + salary) Possibility for extension to a PhD Tesi di Laurea in collaboration: Visiting period at GATech Topic to be coordinated with local relatore -73-

74 Topics of immediate interest SHM: Optimization of current techniques and software implementation Wave filtering techniques for complex structures Actuator design Structural Dynamics: Vibration and noise control through application of shunted piezoelectric materials -74-

75 Contact: Massimo Ruzzene