dynamic holographic modal analysis for ndt

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Oprics and L.asers in Engineering 24 (1996) 129-144 Copyright 0 1995 Elsevier Science Limited

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Dynamic Holographic Modal Analysis for NDT

David Rosenthal & James Trolinger

MetroLaser, 18006 Skypark Circle, No. 108, Irvine CA 92714, USA

ABSTRACT

This paper describes crack and defect detection in structures through modification of the vibrational modal patterns and surface responses to stress. Features are made visible with dynamic holographic inter- ferometery combined with parameter estimation. The procedure involves an unconventional, optimized, laser-illumination method. The methods are especially applicable to large structures and could prove pivotal to improved designs, monitoring and maintenance. Components and structures could be designed to better withstand operating stresses, and existing structures could be analysed to predict their response to stress. Since the modal characterization of a structure can act as a type of fingerprint, holographic interferometry can also be used to monitor structural degradation due to operating and aging. Modal characterization includes identification of resonant frequencies and also the corres- ponding mode shapes. Holographic interferometry provides for direct modal characterization of a structure as well as measuring its small loading dynamic response. The project demonstrated that a wide variety of defects can be located in structural components, vessels and pipes. An analytical exercise also demonstrates the ability to use global modal characteristics to determine the presence of local corrosion and erosion.

1 BACKGROUND

Monitoring the integrity of large structures such as buildings, bridges, piping, liquid storage tanks and dams as a consequence of operational, geological and meteorological forces is an important part of the development of building techniques and risk identification for

129

130 David Rosenthal, James Trolinger

structures that must survive earthquakes, harsh weather, and other extreme forces.’ Existing experimental diagnostic instruments include strain gauges, accelerometers, sensitive range finders and interfero- meters. The difficulty and expense of using these instruments on large structures have severely limited the incorporation of advanced structural design technology into civil engineering practices. Previous research* has successfully demonstrated holography, using a double pulsed ruby laser, as a viable, non-intrusive tool that can remove some of these limitations in civil and earthquake engineering. In an effort to expand upon this research and to seize an opportunity for exploring an extremely powerful tool for structural engineers, Global Modal Analy- sis is being investigated.

The present-day, intrusive, structural-diagnostic methods are used in various design stages starting with small-scale models and continuing on to full-size structures. The difficulty and expense of such measurements escalates with the size of the structure. Measurements of interest include displacement, velocity, acceleration, modal structure and inters- tory drift as a response to an input forcing function. Technologies currently addressing the requirements of earthquake engineering include base isolation, shock absorbers and structural modal analysis.

Using current, present-day methods, full yield measurements on these large-sized structures can be extremely difficult to make as well as to interpret, mainly due to the lack of accessibility and the required number of sensors. An added difliculty is the substantial excitation levels needed to produce meaningful response measurements in large scale constructed facilities. A significant step in the design technology could be made by using a full field interferometric method to collect the required measurements without the installation of instruments into the structure. Furthermore, the interferometric sensitivity of an instrument like this could permit one to use very low excitation levels on these structures.

Holographic interferometry of diffuse surfaces makes modal analysis possible, therefore leading to a potential solution. Displacement con- tours and vibrational mode structure can be observed with resolutions of the order of O-03 pm. Experimental structural modal analysis is achieving expanded use in the aerospace and mechanical engineering fields to produce highly refined designs of machinery; however, this powerful design tool has seen almost no application in civil engineering structural design. Civil engineering design is largely limited to use of design tools such as ASME Boilerplate Codes, American Waterworks Codes, American Petroleum Institute and Uniform Building Codes, which have seen only minor refinements in the past years.

Dynamic holographic modal analysis for NDT 131

A major factor in the limited use of structural modal analysis in civil engineering design is the very size of the structures, which makes the generation of a useful database and its experimental application difficult, expensive, and time consuming. To produce a database for structures requires a controlled input forcing function combined with a measurement of the structural response with sufficient temporal and spatial resolution. Therefore, large civil engineering structures require shakers large enough to produce a measurable response and then enough sensors to measure that response. The size of such structures can render this impractical with existing instrumentation.

Nevertheless, structural modal analysis may offer even more potential to civil engineering than to mechanical engineering. The very size and relative simplicity of many civil engineering structures could make structural modal analysis simple to use in design if sufficient empirical design data become available. Also, in some cases, modal characteristics of civil engineering structures are more relevant to the design. of goals and may actually be easier to apply in design work once the database is generated.

Previous research has enhanced this opportunity by successfully producing and demonstrating holographic concepts as viable tools for earthquake engineering. Also, this research has provided a clear definition of required future work. In an effort to expand upon this work, theoretical and laboratory analysis of large piping was performed to determine if global modal properties could be used to determine the presence and severity of corrosion and erosion.

2 GLOBAL MODAL ANALYSIS

The Stilwell plot estimates the buckling characteristics of a structure. If a load is applied to a column and its frequency of vibration is plotted for several modes, a set of curves similar to Fig. 1 is observed. The mode whose frequency goes to zero first will be the prediction of the buckling load. The shape of the buckling will be that of the envelope of the peak-to-peak motion of the vibrational mode. From this phenome- non it was hypothesized that the vibrational modes of a structure will change as that structure deteriorates or becomes weaker from such external stresses as earthquakes, aging or the environment. Computer models of eroding and corroding pipes were constructed to investigate the possibility of using holographic modal analysis to predict the extent


STILWELL PLOT

\ MODE R ODE 13

:::;-;.:

ODE Xl

BUCKLING LO LOAD -

Fig. 1. Stilwell plot showing buckling load and shape.

of damage. The models were also used to determine which modes would have frequency changes significant enough to measure for reasonable amounts of deterioration. Pipe specimens were constructed and tested using holography to measure these frequencies and confirm the mode shape.

3 THEORETICAL ANALYSIS

For this study, a model pipe was selected as one that might be readily used in a large plant such as a power generation, chemical or petroleum plant. The model pipe was a 12” nominal diameter, Schedule 120, ferrous pipe, 5 ft in length and clamped at both ends. This pipe had an outside diameter of 12.75” and a wall thickness of l$lO”. Material properties used for the ferrous pipe are Young’s modulus of 30 million psi, Poisson’s ratio of 0.3 and a mass density of O-2864 pounds per cubic inch.

Since corrosion growth is non-predictable, it was decided to study growth of several different types. The three growth patterns concentr- ated on a uniform radial growth throughout the interior of the pipe, a longitudinal band along the total pipe length with the corrosion growing in the radial direction and a 360” circumferential band also growing in


la1 lb)

Fig. 2. Corrosion patterns for the model include uniform radial growth (a), a longitudinal strip (b) and a 360“ circumferential band (c).

the radial direction (see Fig. 2). A fourth growth pattern, essentially a point corrosion growing in the radial direction, was studied briefly and found to have no effect on the modal analysis. Material properties of the corrosion were unavailable and had to be approximated. Young’s modulus was set to 1% of steel, i.e. 0.3 million psi, Poisson’s ratio was unaltered (0.3) and the mass density was halved to O-1432 pounds per cubic inch. These properties became the input data to the commercial finite element analysis computer program which was used to perform the frequency analysis.

3.1 Computer model

The finite element code study was COSMOS/M

used for the modal analysis in this corrosion release 1.65386, which is produced by the

Structural Research and Analysis Corporation. This package consists of several modules, with the Geostar module being used here. Geostar is a geometry-based input module. It is designed to be used with pull-down menus for simple model generation. A frequency analysis module is called from within Geostar to produce the actual frequency data once the model is completed in the Geostar module.

Using the material properties given above, models were constructed for the various corrosion growth patterns. The first and simplest model used was for the uncorroded pipe which was to serve as a basis for further comparisons. This model consisted of 200 solid elements, joined


Fig. 3. The pipe and it five mode shapes. (a) Unexcited; (b) first bending; (c) second bending; (d) first breathing; (e) second breathing; (f) third breathing modes.

by 440 nodes. The cylinder had 20 elements in the circumferential direction and 10 elements in the longitudinal direction for a total of 200. In this model all elements were assumed to be of steel and all top and bottom nodes, 80 in total, were fully fixed (in all six degrees of freedom, DOF). This resulted in 1080 DOF for the remaining nodes, 360 nodes by 3 DOF per node. For the frequency analysis, the 10 lowest frequencies were requested from the computer program to a tolerance of 0.01 Hz. This usually, but not always, resulted in five frequency pairs; therefore, five frequencies were tracked in the corrosion studies.

The five mode shapes that were tracked during this study are shown in Fig. 3. The undeformed cylinder, ‘a’, is shown for comparison to the deformed shapes. The first and second bending, ‘b’ and ‘c’, modes are given and are similar to bending modes that one might encounter for an ideal beam. The first bending mode is similar to a sine curve from 0 to n, while the second bending mode is similar to a sine curve from 0 to 21~. The breathing modes shown as ‘d’, ‘e’ and ‘f’, however, are more complex than the bending modes. Each of the three breathing modes is symmetric about the origin of a perpendicular coordinate system that has the z-axis running the length of the cylinder. For the first breathing mode shown, ‘d’, the cylinder first expands along the &x-axis and contracts along the *y-axis, and then expands along the *y-axis and contracts along the *x-axis. For the second breathing mode shown, ‘e’, both the upper and lower halves of the cylinder behave as the first breathing mode, except that the two halves are perfectly out-of-phase with each other. Hence, while the top half is expanding along the *-x-axis and contracting along the *y-axis, the bottom half is


expanding along the *y-axis and contracting along the *x-axis. This motion then repeats, alternating the axis as in the first breathing modes. Here, the cylinder is divided into thirds along its length, with each third behaving similarly to the first breathing mode. Further, each end two-thirds behaves similar to the second breathing mode. Therefore, the top and bottom thirds are expanding and contracting orthogonally in-phase, while the middle third is expanding and contracting orthogonally to the two end thirds, but exactly out-of-phase with them. The modes shown are based on two basic deformation patterns (the first bending and first breathing mode) and are repeated along the length of the cylinder multiple times, with phase shifts as necessary, to produce the various higher modes.

The second series of models was based around a corrosion depth of 10%. For these cases, the model was similar to the uncorroded model except that there were two elements in the radial direction, one that was 10% of the wall thickness and one that was 90% of the wall thickness. This produced a model with 400 elements, 660 nodes, 120 fully restrained nodes and 1620 DOF. Five variations were made using this model to account for the three corrosion growth patterns being studied. The first was to use this model with all 400 elements having the material properties of steel. This was necessary to serve as the comparison base for the 10% corrosion case, since the 400 element model was slightly more flexible than the 200 element model and the resulting ‘all steel’ frequencies would be slightly lower. The second variation was to replace the inner 200 elements, the 10% wall thickness elements, with the properties of the corroded material to model the uniformly corroded pipe (see Fig. 2(a)). The third variation was to replace 10 inner elements in a longitudinal band with those of the corroded material to investigate the longitudinally corroded pipe (see Fig. 2(b)). The fourth variation was to replace only 20 inner elements at approximately mid-height with those of the corroded material to model the circumferentially corroded pipe (see Fig. 2(c)). Each corroded element is 6” in height, 0.1” thick and encompassed 18” of arc. Finally, a last variation was studied which removed the 200 inner elements completely. This left a model very similar to the first, uncorroded model, except that the wall thickness was 0.9” thick with the same outer diameter. This variation was used to represent the condition that the corrosion was 100% complete to the specified depth and none of the corroded material remained attached inside the pipe. Ten frequencies with the same tolerance of 0.01 Hz were again requested for each of the five variations. Each frequency analysis run required about lo-15 min of PC computing time.


The same five variations were repeated for corrosion depths of 20%, 30%, 40% and 50% of the wall thickness. The results of all the frequency analysis studies are given in normalized form in Figs 4-7.

0.8

PO8 f 07

f 0.6

‘p 0.5

i :::

* 0.2

0.1

0

Frequency vs. Corrosion Depth of Cylinder

4

0 5 $0 15 20 25 30 35 40 45 50

x of corrosbn

Fig. 4. Frequency versus corrosion depth when corrosion stays attached to the inside wall of the cylinder.

1.2

- 16 Baldng - IsI Brdhing

1 0.4 .- --x-indBr&hing

s 0.2 '- -indBendng

- 3rd8eWmg

03 1

0 5 10 15 20 25 30 35 40 45 50

X R~ductlon of WA Thickness

Fig. 5. Frequency versus corrosion depth when corrosion washes away from the inside wall of the cylinder.


Fmqlwncy vs. Longkudlnal Depth of Cylindm

-2ndBmdng 1 ‘_

-.._

-‘- L

088 1 ,

0 5 IO 15 m 25 w 35 40 45 50

Y (Longludlnal) Conalan Depth

Fig. 6. Frequency versus corrosion depth of longitudinal corrosion segment.

3.2 Results from the computer model

The graphs of normalized frequency versus corrosion depth for each of the four corrosion growth variations are shown in Figs 4-7. It can be seen that the two graphs representing the uniform corrosion growth, with and without corrosion remaining, show substantial reductions in frequency (for the modes tracked) as a result of increasing corrosion, while the longitudinal and circumferential corrosion growths show only a slight decrease in natural frequency versus corrosion depth. The longitudinal growth pattern showed a slightly larger decrease than the

Frequency vs. Annular Corrosion Depth

5 10 15 m 25 30 35 40 45 50

$4 (Armuhr) CO,WSh” hPm

Fig. 7. Frequency versus corrosion depth of circumferential corrosion segment.


circumferential growth pattern. Also, for the most part, the breathing modes were more sensitive to increasing corrosion than the bending modes. Furthermore, the uniform corrosion growth pattern which retained the corroded material showed a slightly higher shift than the growth pattern which retained no corroded material, especially in the two bending modes. Since the elementary formula for natural frequency is stiffness divided by mass, this was to be expected. For the growth pattern which did not retain material, the 100% loss of mass balanced the loss of stiffness, whereas in the other growth pattern, mass was retained at 50% while the stiffness was greatly reduced. Thus, the much greater mass with only slightly greater stiffness accounts for the greater frequency shift in all five modes for the uniformly corroded pipe which retained corroded material. It is required to observe the frequency shift of a particular mode to determine the extent of corrosion. By using holographic interferometry by producing time-averaged holograms, the resonance frequencies and their respective modes can be determined.

4 LABORATORY VERIFICATION

Holographic experiments were conducted in the MetroLaser laboratory to confirm the changes in the modal frequencies as a function of flaw size using sections of pipes. Six pipe sections were characterized using a Holographic Non-destructive Testing system. The specimens were 12-inch-long sections of 3; inch nominal diameter schedule 80 steel pipe. The ends were threaded to mount into the fixturing and aluminum end caps were threaded onto both ends. One end was mounted to the shaker and the other was secured by the fixturing.

The optical system as shown in Fig. 8 was used with the shaker system outlined in Fig. 9 to locate the modes and frequencies.

The light from a 35 mW HeNe laser, with a wavelength of 0.633 pm, was directed into the variable beam splitter BSl via mirror Ml, where it was split into two beams. One of the beams, the object beam, was diverted via mirrors M2-M5 to the spatial filter, SFl, where the beam was expanded and spatially filtered to reduce non-uniformities in the beam. The beam then travelled to and illuminated the pipe section. The light was scattered off of the test specimen in all directions with some of the light striking the thermoplastic film plate. The other beam, the reference beam, was directed via mirrors M6-M8 and beam splitter BS2 through spatial filter SF2. The spatial filter expands the beam, cleans it and directs it onto the film plate. Mirror M7 is adjusted so the path lengths from BSl to the film plate in both the object and reference beams are equal.

Dynamic holographic modal analysis for NDT

Zocin and Ctose

0 I

MT )-_-_---_f______--__-)M6

Fig. 8. Holographic set-up for determining the mode shapes and frequencies of the pipe models.

Function Generator I@ 0 O opl

lmpedence Matching Network

Fig. 9. Outline of the PZT shaker system used to locate the vibrational modes pipe model.

of the


Fig. 10. Photograph of a pipe specimen in its fixturing and mounted to the shaker.

Thermoplastic film was used for the testing instead of the normal silver halide holographic film. The thermoplastic is processed in place and is reusable. The in situ processing allowed for simple determination of the vibrational mode and its frequency, as described later.

The specimen was mounted onto a fixture with a piezoelectric transducer shaker. The shaker was driven by a function generator whose signal was amplified by a 500 W power amplifier. The output characteristics of the amplifier were matched to the shaker through the use of an impedance matching network. The conditioned signal was then fed to the shaker. A counter was attached to the function generator to accurately measure the frequency. Figure 9 is a schematic of the shaking system and Fig. 10 shows the pipe section and shaker mounted in the fixturing.

The test consisted of first producing a hologram of the pipe section at rest, the shaker turned off. This is done by erasing and sensitizing the thermoplastic plate and is accomplished by a push of a button on the controller. An exposure is then made by opening and closing the shutters. The plate is processed, again automatically. It takes about 1 min for the whole process. This hologram serves as a reference image and is reconstructed by opening the reference beam shutter. The object beam shutter is also opened. The TV camera now simultaneously sees both the reconstructed image of the pipe and the actual pipe and, initially, these two images exactly overlay each other. The shaker is turned on and the frequency is manually swept. When a resonance frequency is encountered during the sweep, a low contrast fringe pattern is seen overlaying the pipe. The fringe pattern is observed because a resonance mode causes a standing displacement wave in the

Dynamic holographic modal analysis for NDT

Fig. 11. Time average hologram of mode 2DlT.

pipe. The contrast is low but very adequate to identify the resonance mode and to accurately tune the frequency. To confirm the mode, a time average hologram was produced by making an exposure while the pipe was vibrating at resonance. This time average hologram is reconstructed by using just the reference beam. Figures 11-15 show time average holograms of the modes used. These time average holograms were not necessary to identify these relatively low order modes or to determine their frequencies. The identification and determination could have been accomplished by using just the real-time holographic interferogram.

The first three of these modes correspond to breathing modes d, e, and f, respectively, as shown in Fig. 3. The nomenclature used is

fig. l2. Time average hologram of mode 2D2T.


Fig. 13. Time average hologram of mode 2D3T.

nDmT, where II refers to the number of the diametrical axis and m refers to the mode order number. In the 2D modes, the pipe is breathing on about two orthogonal axes. The pipe collapses about one axis as it expands about the other, or one axis of deformation is 180” out-of-phase from the other. The 3D modes have three axes of deformation acting 120” out-of-phase from each other. Figure 3 shows that only the breathing modes and not the bending modes were able to detect the erosion; therefore, they and higher order ones were used for this test.

Figure 16 shows the normalized frequency versus the depth of uniform corrosion. Notice, at these higher modes, the effect of the erosion appears to be almost linear with resonance frequency. Figure 17

Fig. 14. Time average hologram of mode 3DlT.


Fig. 15. Time average hologram of mode 3D2T.

is a plot for the annular erosion. Notice the slope is but a 10% change in the wall thickness will produce a frequency. This small change can readily be observed.

5 CONCLUSIONS

not as steep, 2% change in

We have shown that global modal analysis can be used to identify the vibrational modes of piping with sufficient accuracy not only to determine the presence of corrosion or erosion, but also the extent. This was accomplished through the use of finite element analysis

Simulated Uniform Erosion

---t 2D3T

.JDlT

. px- 3021

0.00 0 10 020 030

Ems&n Depth

040 050

Fig. 16. Normalized frequency versus uniform erosion depth for sample pipes.


Simulated Annubr Erosbn

0.92 4 4

030 0.10 0.20 0.m 0.40 0.50

ErosIon Dap(h

Fig. 17. Normalized frequency versus annular erosion depth for sample pipes.

models with laboratory verification. This technique could be extended to determine the integrity of other structures such as bridges, buildings and liquid storage tanks. Through the use of models we can determine if the modal frequency shift in a structure caused by the degradation is sufficient to observe with holographic interferometry.

1.

2.

REFERENCES

Timoshenko, L. & Krieger, S. W., Theory of Plates and Shells. McGraw- Hill, New York, 1970. Trolinger, J. D. et al., Application of long range holography in earthquake engineering. SPIE paper 1162-17, Proc.-Laser Znterferometry: Quantitative Analysis of Znterferograms, third in the series, 7-9 August 1989.

dynamic holographic modal analysis for ndt

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