I

oaSctfdtuoisat

tastscuprea

BicwasBnwt

p2E

7

Downlo

Steven E. OlsonSenior Research Engineer

University of Dayton Research Institute,Dayton, OH 45469

Martin P. DeSimioSenior Research Engineer

ATK Space Systems and Sensors,Dayton, OH 45430

Mark M. DerrisoSHM Team Lead

Air Vehicles Directorate,Air Force Research Laboratory,

WPAFB, OH 45433

Beam Forming of Lamb Wavesfor Structural Health MonitoringStructural health monitoring techniques are being developed to reduce operations andsupport costs, increase availability, and maintain safety of current and future air vehiclesystems. The use of Lamb waves, guided elastic waves in a plate, has shown promise indetecting localized damage, such as cracking or corrosion, due to the short wavelengthsof the propagating waves. Lamb wave techniques have been utilized for structural healthmonitoring of simple plate and shell structures. However, most aerospace structures aresignificantly more complex and advanced techniques may be required. One advancedtechnique involves using an array of piezoelectric transducers to generate or sense elas-tic waves in the structure under inspection. By adjusting the spacing and/or phasingbetween the piezoelectric transducers, transmitted or received waves can be focused in aspecific direction. This paper presents beam forming details based on analytical model-ing, using the finite element method, and experimental testing, using an array of piezo-electric transducers on an aluminum panel. Results are shown to compare well to theo-retical predictions. �DOI: 10.1115/1.2731404�

ntroductionStructural health monitoring �SHM� techniques are being devel-

ped to reduce operations and support costs, increase availability,nd maintain safety of current and future air vehicle systems.HM refers to automated methods for determining adversehanges in the integrity of mechanical systems �1�. In the litera-ure, the capability of SHM systems is typically organized into theollowing levels of increasing difficulty: �i� damage detection, �ii�amage localization, �iii� damage assessment, and �iv� life predic-ion. In general, SHM is accomplished as follows. The structurender investigation is excited using actuators �active SHM� orperational loading �passive SHM�. The response to the excitations sensed at various locations throughout the structure. The re-ponse signals, and possibly the excitation signal, are collectednd processed. Based on the processed data, the state of the struc-ure is diagnosed.

Various SHM techniques have been investigated depending onhe scale of the damage to be detected �2–4�. For example, dam-ge, such as fastener failure, may have a global effect on thetructural dynamics and, therefore, modal-based damage detectionechniques may be suitable �5,6�. This paper focuses on detectingmaller-scale damage, such as cracking or corrosion, which typi-ally has a highly localized effect on the system dynamics. These of Lamb waves, guided elastic waves in a plate, has shownromise in detecting such highly localized damage due to theelatively short wavelengths of the propagating waves �4,6�. How-ver, Lamb wave behavior is fairly complex because the wavesre dispersive and various modes may coexist �7,8�.

Lamb waves are guided elastic waves that occur in a free plate.ecause of their behavior, Lamb waves are particularly useful for

nvestigating damage in plate and shell structures. Lamb wavesan exhibit symmetric and anti-symmetric waveforms, based onhether the out-of-plane displacements on either side of the plate

re in or out of phase. As guided waves, Lamb waves are disper-ive, meaning that the wave speed is a function of frequency.ecause of its finite time duration, any practical excitation signalecessarily contains a range of frequencies. As a result, variousaves with slightly different wavelengths are excited in a struc-

ure. These waves interact, and the resulting wave propagates at a

Contributed by the Technical Committee on Vibration and Sound of ASME forublication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 8,006; final manuscript received January 5, 2007. Review conducted by Bogdan I.

pureanu.

30 / Vol. 129, DECEMBER 2007 Copyright ©

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

group velocity that may differ from the phase velocities of indi-vidual waves. For damage detection purposes, the group velocitycan be thought of as the signal velocity, or the velocity at whichenergy is conveyed through a structure.

As frequency increases, the number of simultaneously existingwaveforms also increases. To limit the number of coexistingwaveforms, the excitation frequency may be kept relatively lowsuch that only the S0 and A0 waveforms will exist �8�. S0 and A0are referred to as the fundamental modes and are typically usedfor Lamb wave damage detection �6,9,10�. For damage detectionpurposes, it is also simpler to analyze only a single waveform. Asa general rule, elastic waves can be used to detect damage on theorder of the wavelength. The A0 mode has a lower wave speedthan the S0 mode. The A0 mode therefore has a smaller wave-length and is more sensitive to smaller levels of damage. Con-versely, the symmetric waveform has a substantially greater groupvelocity and would therefore arrive at a sensor well before theantisymmetric waveform. As a result, reflections of the S0 wavemay arrive at a sensor simultaneously with the initial A0 wave,corrupting the measured signal. Giurgiutiu �11� has shown that, byadjusting the excitation frequency, it is possible to tune certaintransducers to dominantly excite a single mode �either S0 or A0�.

Lamb wave techniques have been utilized for structural healthmonitoring of simple plate and shell structures. However, mostaerospace structures are significantly more complex and advancedtechniques may be required. One advanced technique involvesusing an array of spatially distributed piezoelectric transducers togenerate or sense elastic waves in the structure under inspection.By adjusting the spacing between the piezoelectric transducers orthe timing of the signals at each transducer, the transmitted orreceived waves can be focused in a specific direction. This focus-ing can increase the signal-to-noise ratio and therefore improvethe ability to locate damage �12,13�.

Beam forming is the process of adjusting the phasing of signalsin an array of transducers to provide desired directionality prop-erties. Beam forming has been applied in sonar since the 1940s�14�. The same principles have been applied for phased array ra-dars since the 1950s �15�. Phased arrays also have been used forultrasound imaging since the 1960s �16�.

This paper describes beam forming techniques using transmit-ting and receiving arrays applied to Lamb waves. In the followingsections, experimental testing and analytical modeling of Lambwave propagation are discussed. Subsequent sections address the

use of receiving and transmitting arrays, compare experimental

2007 by ASME Transactions of the ASME

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

mtt

E

eassm2

aeptnpfifiq

pccTcdeMaaesams

Fe

J

Downlo

easurements and analytical predictions with theoretical calcula-ions, and introduce adaptive arrays. Finally, conclusions fromhese studies are provided.

xperimental TestingTo demonstrate the utility of Lamb waves for damage detection,

xperimental studies have been performed on an aluminum platend measured results compared to theoretical values as well asimulated results from finite element modeling. Figure 1 shows achematic of the aluminum plate specimen used for the experi-ental Lamb wave studies. The specimen consists of a sheet of

024 aluminum with a thickness of 1.0 mm.A collinear array of eight piezoelectric transducers is located at

pproximately one-third of the plate height. Four individual piezo-lectric transducers are located at approximately two-thirds of thelate height. Positioning the transducers at these heights preventshe direct path and reflected path signals from arriving simulta-eously at a transducer. One short edge of the aluminum plate islaced on a piece of foam, and the other short edge rests against aoam covered vertical support. Both faces of the plate are free tonteract with the surrounding air. These boundary conditions suf-ciently approximate the traction free surfaces theoretically re-uired to provide Lamb wave propagation �7�.

The four upper piezoelectric transducers are at angles of ap-roximately 63 deg, 91 deg, 100 deg, and 110 deg relative to theenter of the array. All of the individual piezoelectric transducersan be used to either excite the structure or sense the response.he piezoelectric transducers used for these studies are lead zir-onate titanate �PZT� disks from APC International and have aiameter of 6.35 mm and a thickness of 0.254 mm. The transduc-rs have been bonded to the surface of the aluminum plate using-Bond 200 adhesive. The piezoelectric disks are thickness poled

nd operate in a radial extension mode, such that an applied volt-ge across the thickness of the ceramic disk results in a radialxpansion or contraction of the disk. Conversely, a radial expan-ion or contraction of the disk �i.e., a radial strain� creates a volt-ge potential across the thickness of the disk. Preliminary experi-ents have verified the generation and reception of Lamb wave

ig. 1 Aluminum plate test article showing locations of piezo-lectric transducers „drawing not to scale…

ignals.

ournal of Vibration and Acoustics

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

The excitation signals sent to the piezoelectric transducers toexcite Lamb waves are commonly Hanning-windowed sine bursts�6,9,10,17,18�. The Hanning window limits the excitation timeand reduces the amount of energy at frequencies other than theexcitation frequency. Rather than continuous signals, pulses ofthree to seven cycles are typically used to allow time of flightcalculations and prevent unwanted interference between waves. Apulse with more cycles has higher energy than a pulse with fewercycles. However, pulses with more cycles increase the likelihoodthat reflections may occur and interfere with the measured re-sponse. Often an additional half cycle is added to an integer num-ber of cycles to provide a peak at the center of the signal. Figure2 shows an example of a five-cycle Hanning-windowed sine burstat 300 kHz, along with the frequency content of the signal.

The array of piezoelectric transducers can be used to receive ortransmit Lamb waves. When a receiving array is utilized, aHanning-windowed sine wave excitation signal is generated usingan Agilent 33250A Function Generator. This signal is sent directlyto one of the four upper piezoelectric transducers. Responses fromthe array of piezoelectric transducers are captured using a Na-tional Instruments PXI 6133 data acquisition card. MATLAB rou-tines are used to process the measured responses.

A similar setup is used for a transmitting array, where eightseparate signals of different phases are required. To reduce thecost of the equipment necessary to create such signals, a NationalInstruments PXI 6542 digital waveform-generating card has beenutilized. However, the card is only capable of generating squarewave signals, which results in greater spread of the frequencycontent in the excitation signal. Figure 3 shows a five-cycle squarewave burst at 300 kHz and the frequency content of the signal.Note that the square wave burst contains a much larger spread infrequencies than the Hanning-windowed sine wave burst shown inFig. 2�b�. In addition to the main peak centered at 300 kHz, thethird and fifth harmonics are clearly visible in the spectrum shownin Fig. 3�b�. However, the energy from these harmonics is morethan 20 dB below the main peak energy. Therefore, reasonableLamb wave signals can be generated from the square wave exci-tation. The Agilent 33250A Function Generator is used to provideclocking for the digital waveform-generating card. Signals fromthe card are sent through an eight-channel amplifier to increase thesignal voltage and then to appropriate piezoelectric transducers in

Fig. 2 Five-cycle Hanning-windowed sine burst: „a… time sig-nal and „b… frequency content of the signal

the array. The eight-channel amplifier has been fabricated in-

DECEMBER 2007, Vol. 129 / 731

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

hee6t

atbtcefleetuos

twaotsa

mmefpegrl

aFnt

Ff

7

Downlo

ouse to provide up to 75 V peak-to-peak amplification of thexcitation signals. Responses at each of the four individual piezo-lectric transducers are captured using a National Instruments PXI133 data acquisition card. MATLAB routines are used to processhe measured responses.

For all of the studies discussed in this paper, excitation signalst 300 kHz have been utilized. Prior to performing beam forming,he group velocity of 300 kHz Lamb waves in the specimen muste determined. The group velocity of the Lamb waves determineshe time of arrival of signal energy at each element in the array. Toalculate the velocity, Lamb waves are generated independently atach of the four upper piezoelectric transducers and the time ofight for the waves to arrive at each transducer in the eight-lement receiving array is measured. Dividing the distance trav-led by the time of flight provides the group velocity. Since fourransmitting and eight receiving piezoelectric transducers aresed, 32 group velocity measurements are obtained. The averagef the 32 measurements is used as the nominal group velocity inubsequent calculations.

Since experiments are conducted at a relatively low frequency–hickness product �0.3 MHz-mm� only the fundamental S0 and A0aves are generated. Because the group velocity of the S0 mode is

pproximately twice that of the A0 mode, attention can be focusedn solely the S0 mode by time gating the response signals. Theime gate is determined by examining the signal responses andelecting the interval corresponding to the S0 pulse. Subsequentnalysis is performed using the gated signals.

The time of flight is found as the time difference between theidenergy points of the received and transmitted pulse bursts. Theidenergy point is the time at which 50% of the cumulative en-

rgy of a signal occurs. In practice, the cumulative distributionunction �CDF� of the pulse energy is calculated and linear inter-olation is used to find the time corresponding to 0.50 on thenergy CDF. Since the excitation signal is identical for all of theroup velocity experiments, a single excitation signal has beenecorded and its midenergy point used for all time of flight calcu-ations. The average group velocity is 5.47 mm/�s.

Beam forming can be accomplished by adjusting the spacingnd/or phasing between the piezoelectric transducers in an array.or these experiments, the piezoelectric disks have been perma-ently adhered to the surface of the aluminum plate. As a result,

ig. 3 Five-cycle square wave burst: „a… time signal and „b…requency content of the signal

he spacing is not easily changed; thus, the phasing will be modi-

32 / Vol. 129, DECEMBER 2007

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

fied to focus the transmitted or received waves. However, it is stillimportant to know the spacing between the various transducerswith respect to the wavelength of the propagating waves. Thewavelength � can be found as

� =c

f�1�

where c is the propagation speed of the waves and f is the fre-quency of the waves. Based on the measured propagation speed of5.47 mm/�s and the excitation frequency of 300 kHz, the wave-length can be calculated to be 18.2 mm. Because our laboratorymethods did not allow for submillimeter precision in positioningthe piezoelectric transducers, they are nominally spaced at9.0 mm. This spacing provides approximately a half wavelengthbetween adjacent elements in the array. For the theoretical calcu-lations discussed in following sections, the spacing between ele-ments is assumed to be a half wavelength.

Analytical ModelingTo design accurate and efficient SHM systems, physics-based

models are useful to provide a detailed understanding of the struc-tural dynamics. Major advantages of analytical modeling over ex-perimental testing include the ability to investigate different wavepropagation cases relatively quickly, to examine the wave behav-ior through the entire thickness of the material �rather than solelybased on surface measurements�, and to examine wave behaviorin locations not easily accessible for testing. One approach tomodel Lamb wave propagation is to numerically solve the gov-erning wave equations with the appropriate boundary conditions.This approach can be taken for simple geometries but becomesdifficult for more complicated geometries or when damage is in-cluded. In such cases, different computational techniques can beused to analyze wave propagation. Explicit finite element meth-ods, which step through the solution in time, are one of the morepopular techniques, since numerous finite element codes exist andit is not necessary to develop specialized code �19�.

For these studies, finite element simulations have been per-formed using ABAQUS/EXPLICIT �20�, an explicit time integrationfinite element code based on the central difference method. Analy-ses have been performed using models containing four-node, bi-linear shell elements �S4R elements in ABAQUS�. In the laboratory,Lamb waves are excited and sensed using surface-mounted piezo-electric transducers that are bonded to the plate at the locationsshown in Fig. 1. In the models, excitation is accomplished usingpoint forces and moments at nodes that correspond to locationsaround the perimeter of the piezoelectric discs. Moments are re-quired since the midplane of the aluminum plate is modeled, butthe disks are attached to the outer surface of the structure. Thepiezoelectric disks are not explicitly modeled, and any contribu-tion to the mass or stiffness of the structure due to the disks isassumed to be negligible. Other researchers have used similarmethods with good results �19,21,22�. In the models, the radialstrain experienced by a disk is taken to be proportional to themeasured output voltage of a piezoelectric transducer. Scaled volt-age versus time data is extracted from the analytical results andcan be processed using the same methods used to process theexperimental data. Earlier studies provide additional detail andhave demonstrated the utility of these modeling techniques �23�.

Receiving ArrayFundamental operation of an array is now described based on

receiving sinusoidal energy in the form of plane waves. For designpurposes, arrays are typically assumed to consist of omnidirec-tional elements that, by definition, receive energy equally wellfrom all directions. Figure 4 shows an array of two identical om-nidirectional elements separated by a half wavelength. The outputof the array, r�t�, is obtained by adding the signals received at

each element, r1�t� and r2�t�. Waves arriving from 90 deg will

Transactions of the ASME

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

rtswfasd

T

w

tpmrto

e

watp

bpbadTts

J

Downlo

each both elements simultaneously; thus, the array output will bewice the signal received at either element. Since the elements arepaced a half wavelength apart, the responses, r1�t� and r2�t�, toaves arriving from 0 deg will be 180 deg out of phase. There-

ore, the array output signal will be zero. In general, for a waverriving at an angle �, there will be a time delay between theignals at each element proportional to the additional propagationistance l, where

l = ��

2�cos��� �2�

he time delay � can be found as

� =l

c�3�

here c is the propagation speed of the waves.To illustrate the directional properties of arrays, polar plots of

he received signal amplitude versus angle of arrival—called gainatterns—are created. The lobe of a gain pattern with the largestagnitude is referred to as the main lobe, and the look angle

efers to the angular orientation of the main lobe. Any lobes otherhan the main lobe are referred to as side lobes, and null anglesccur in the directions where the gain pattern equals zero.

It can be shown that the gain pattern for a linear array of Nlements with half wavelength spacing is

G��� =

sin�N�

2cos����

sin��

2cos����

�4�

here � is the angle of arrival �6�. The gain patterns for linearrrays with two and eight elements are shown in Fig. 5. To facili-ate comparisons in this paper, the maximum value in each gainattern has been normalized to unity.

The main lobe of the linear arrays described above will alwayse perpendicular to the axis of the elements. However, by addinghase shifts to the signals from each element, the main lobe cane pointed in any direction. A diagram of an eight-element linearrray with a half wavelength spacing between elements and withelays to enable reorientation of the main lobe is shown in Fig. 6.he fundamental delay time is shown as �. Arbitrarily assigning

he rightmost element in the array to receive zero delay, eachuccessive element to the left receives an additional delay of �.

Fig. 4 Array of two identical omnidirectional elements

The look angle, �, as a function of the delay � is �6�

ournal of Vibration and Acoustics

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

� = cos−1� c�

d� �5�

where c is the wavespeed and d is the spacing between arrayelements. By definition, c=�f and f =1/T0, where T0 is the periodof the wave energy. For a half wavelength spacing �i.e., d=� /2�the look angle becomes

Fig. 5 Theoretical gain patterns for „a… two- and „b… eight-element arrays

Fig. 6 Functional diagram of a receiving array

DECEMBER 2007, Vol. 129 / 733

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Atpdafipt

atm

7

Downlo

� = cos−1�2�

T0� �6�

s shown in Eq. �6�, the look angle is controlled by the ratio ofhe time delay to the period of the signal. The main lobe can beointed in a desired direction by computing the array output forelay values ranging from 0 to T0 /2. Figure 7 shows a plot of lookngle versus normalized delay ratio �� /T0�. In practice, beamorming with a receiving array is done with digital signal process-ng of sampled signals. A MATLAB function has been developed torovide arbitrary, noninteger sample period delays according tohe digital filter method of Oppenheim and Schafer �24�.

The experimental test article uses an eight-element collinearrray with half wavelength spaced elements. Theoretical gain pat-erns for an eight-element array with � set to obtain look anglesatching the angles to the four individual piezoelectric transduc-

Fig. 7 Look angle versus normalized delay

Fig. 8 Theoretical gain patterns using e

of „a… 63 deg, „b… 91 deg, „c… 100 deg, and „d

34 / Vol. 129, DECEMBER 2007

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

ers are shown in Fig. 8. The tick mark on the outer circle of eachgain pattern indicates the angle to an individual piezoelectrictransducer.

Gain patterns of the array used in the experiment have beenmeasured as follows. One of the four upper piezoelectric trans-ducers transmits a pulse. The receiving array is operated with theappropriate delays to provide look angles from 0 deg to 359 degin 1 deg increments. The energy of the array output signal is com-puted over the time interval corresponding to the arrival of the S0

wave. The theoretical gain pattern relates the beam former outputsignal amplitude to angle. Because energy corresponds to squaredamplitude, the square root of the energy is computed to obtain theexperimental gain pattern. An experimental gain pattern is ob-tained by plotting the square root of the received pulse energy asa function of look angle. Figure 9 shows gain patterns correspond-ing to transmission from individual piezoelectric disk sources at63 deg, 91 deg, 100 deg, and 110 deg. The measured look anglesfor the sources are 61 deg, 91 deg, 99 deg, and 109 deg; the re-sultant root-mean-square �rms� error in look angle is 1.2 deg.

Similar to the experimental testing, finite element simulationshave been performed where each of the four individual piezoelec-tric transducers transmits a pulse. The response of each element inthe array, due to excitation from an individual piezoelectric disk,has been calculated. Appropriate delays have been added to eachchannel of simulated data to provide specific look angles. Gainpatterns corresponding to transmission from individual piezoelec-tric disks at 63 deg, 91 deg, 100 deg, and 110 deg are shown in

t-element receiving array for look angles

igh … 110 deg

Transactions of the ASME

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

F9a

T

dtFFaifsafo

wcwtsp0

ppe

J

Downlo

ig. 10. The measured look angles for the sources are now 57 deg,1 deg, 104 deg, and 115 deg, the resultant rms error in lookngle is 4.1 deg.

ransmitting ArrayBeam forming can also be used in transmitting arrays. Time

elays are applied to the excitation signal sent to each element inhe array to focus the transmitted energy in a specific direction.igure 11 shows an example of a transmitting array. As shown inig. 11, delayed versions of the excitation signal are applied todjacent elements in the array. The gain pattern for an array isdentical whether used for transmitting or receiving �12�. There-ore, the look angle of the transmitted energy is determined by theame relationship used to calculate the look angle of the receivingrrays discussed above. Furthermore, the theoretical gain patternsor the transmitting arrays will be identical to those shown previ-usly in Fig. 8 for the receiving arrays.

For experimental studies using transmitting arrays, a digitalaveform-generating card has been utilized to avoid using the

ostly equipment necessary to generate multiple channel sinusoidsith precise phase control. A National Instruments PXI 6542 digi-

al waveform-generator card provides eight replicas of a five-cyclequare wave. The digital waveforms are created with 60 sampleser cycle. Delays of +30 to −30 samples steer the mainlobe fromdeg to 180 deg.To assess the effectiveness of experimental beam forming, gain

atterns of the array have been computed. Five-cycle square waveulses at the 300 kHz fundamental frequency are used to excite

Fig. 9 Measured gain patterns using eigpiezoelectrics at angles of „a… 63 deg, „b…

ach element in the array. Experiments have been performed using

ournal of Vibration and Acoustics

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

arrays with each of the possible 60 delay values to steer the main-lobe from 0 deg to 180 deg. For each delay value, responses ateach of the four upper piezoelectric transducers are recorded. Aswith the receiving arrays, the time interval corresponding to thearrival of the S0 mode has been identified, and the energy of eachrecorded signal is computed over this interval. Gain patterns areapproximated from the signals received at each individual trans-ducer by plotting the square root of the computed energy versusthe transmitting array look angle. Figure 12 shows the measuredgain patterns found by this method. The tick marks indicate theangular position of the receiving transducer. The measured lookangles for the transmitter array are 62 deg, 90 deg, 100 deg, and110 deg; the resultant rms error in look angle is 1.4 deg.

Adaptive ArraysSHM systems may benefit from the capability of adaptive beam

forming arrays to perform automatic, online adaptation to chang-ing environmental conditions. For example, such arrays could re-duce the effects of noise from time-varying locations. Adaptivebeam forming uses adjustable weights to modify the gain patternof an array. Algorithms have been designed such that the arrayresponse converges to a statistically optimum solution �13�. Ingeneral, the algorithms compute adjustments to the magnitudesand phases of the responses of each element in the array such thatthe total array response maintains gain in the direction of a desiredsignal, but minimizes contributions from other directions.

A functional block diagram of an adaptive receiving array isshown in Fig. 13. Signals are received at each sensor and then

element receiving array for transmittingdeg, „c… 100 deg, and „d… 110 deg

ht-91

split into in-phase and quadrature paths. The in-phase path is the

DECEMBER 2007, Vol. 129 / 735

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

spalaabrpSa

7

Downlo

ignal from the sensor, and the quadrature path adds a 90 deghase shift to the received signal. The array shown in Fig. 13ssumes narrowband received signals, such that a single time de-ay corresponding to a 90 deg phase shift is used. The in-phasend quadrature signals are multiplied by adjustable weight valuesnd then added to obtain the output of the array. The weights cane computed using the least-mean-squares �LMS� or other algo-ithms. A complete discussion of the LMS algorithm and its ap-lication to adaptive beam forming is given by Widrow andtearns �25�. Although the LMS algorithm is simple to computend works well in many applications, convergence can be slow.

Fig. 10 Simulated gain patterns using eipiezoelectrics at angles of „a… 63 deg, „b…

Fig. 11 Functional diagram of a transmitting array

36 / Vol. 129, DECEMBER 2007

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

Alternative algorithms that have better convergence properties,but greater computational requirements, have been based on leastsquares and Kalman filtering �13�.

Adaptive arrays are useful for generating customized array pat-terns. For example, an array with seven uniformly spaced ele-ments will have a main lobe at 90 deg and significant side lobes at45 deg and 135 deg. Assuming a noise source appears at 45 deg,using an adaptive array it is possible to compute weight valuessuch that a desired signal at 90 deg is received at full strengthwhile simultaneously reducing gain of the noise by more than20 dB. Array patterns for a uniform array with and without thenoise-canceling notch are shown in Fig. 14. The Cartesian plotbetter illustrates the noise-canceling notch at 45 deg.

DiscussionFor receiving arrays, good agreement is generally seen between

the theoretical, experimental, and simulated gain patterns shownin Figs. 8–10, respectively. The overall structures of the gain pat-terns compare well across the three methods; however, the experi-mental and simulated look angles differ slightly from the theoret-ical look angle. A small difference is seen between theexperimental and theoretical results, as the RMS error in the lookangle is only 1.2 deg. Considerably more variation is seen in theanalytical results, although the rms error in the look angle is stillonly 4.1 deg. These differences are due, in part, to inaccuracy inthe piezoelectric transducer spacing. Recall that the theoreticalcalculations assume a half-wavelength spacing, whereas the actual

-element receiving array for transmittingdeg, „c… 100 deg, and „d… 110 deg

ght91

experimental spacing is nominally slightly greater and will have

Transactions of the ASME

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

sssmhd

J

Downlo

ome placement variation because the piezoelectric disks are po-itioned by hand. In addition, the group velocity in the analyticalimulations may differ somewhat from the theoretical or experi-ental group velocities due to potential differences between the

andbook values used for the aluminum properties �modulus andensity� and the actual properties of our test article. Regardless,

Fig. 12 Measured gain patterns of eighangles of „a… 63 deg, „b… 91 deg, „c… 100angle varies from 0 deg to 180 deg

Fig. 13 Functional diagram of an adaptive array

ournal of Vibration and Acoustics

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

the theoretical and analytical results generally provide a good firstapproximation of the actual beam forming behavior and illustratethe potential benefits of receiving arrays.

Good agreement also is seen between the theoretical and ex-perimental gain patterns for transmitting arrays. As with the re-ceiving arrays, the overall structures of the experimental gain pat-terns shown in Fig. 12 compare well to the theoretical gainpatterns from Fig. 8. However, the experimental look angles againdiffer slightly from the theoretical look angles. These differencesresult, at least in part, to the inaccuracy of the piezoelectric trans-

ement transmitting array for sensors atg, and „d… 110 deg as transmitting look

Fig. 14 Gain patterns for seven-element, uniformly spacedcollinear arrays, with „heavy line… and without „thin line…

t-elde

weights corresponding to a noise canceling notch at 45 deg

DECEMBER 2007, Vol. 129 / 737

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

dndams

wbapwfsi

C

aLhfsrpn

A

DOCetTtt

R

7

Downlo

ucer spacing assumed for the theoretical calculations. Prelimi-ary analytical simulations using square wave excitation have pro-uced poor results, likely due to the stepped forces and momentspplied in the model. Analytical studies are continuing to deter-ine if better results can be produced using sine burst excitation

ignals.Lastly, a brief introduction has been given to adaptive arrays

here adjustable weights are used to modify the gain for narrow-and signals. Adaptive arrays are useful for generating customizedrray patterns and may prove extremely beneficial for SHM ap-lications to cancel out noise from known sources or unwantedave reflections �e.g., off the free edges of a plate rather than

rom damage�. It is anticipated that adaptive arrays will enhancetandard beam forming arrays by allowing additional tuning formproved performance.

onclusionsThese experiments demonstrate successful beam forming, using

n array of piezoelectric transducers to either receive or transmitamb wave signals, in an aluminum plate. Finite element analysisas been shown to provide a good first approximation of the beamorming behavior. Results from the experiments and analyticalimulations compare well to theoretical calculations. Adaptive ar-ays, using adjustable weights, may further improve SHM systemerformance by providing a degree of robustness to operationaloise sources.

cknowledgmentThese investigations have been performed at the Air Vehicles

irectorate of the Air Force Research Laboratory. The efforts of S.lson and M. DeSimio have been performed under Air Forceontract No. FA8650-04-D-3446. The authors wish to acknowl-dge the support of Todd Bussey, for setting up the instrumenta-ion and collecting experimental measurements, and Lt. Dustinhomas, for designing the beam forming hardware layout to con-

rol the phasing of signals sent to the array. Their assistance withhe experiments discussed in this paper is greatly appreciated.

eferences�1� Sohn, H., Farrar, C., Hemez, F., Shunk, D., Stinemates, D., and Nadler, B.,

2003, “A Review of Structural Health Monitoring Literature: 1996-2001,” LosAlamos National Laboratory Report No. LA-13976-MS, available online at:http://www.lanl.gov/projects/damage_id/reports/LA-13976-MS-Final.pdf.

�2� Worden, K., Farrar, C., Manson, G., and Park, G., 2005, “Fundamental Axiomsof Structural Health Monitoring,” Structural Health Monitoring 2005: Ad-vancements and Challenges for Implementation, F. Chang, ed., DEStech Pub-lications, Lancaster, PA, pp. 26–41.

�3� Fritzen, C., 2005, “Recent Developments in Vibration-Based Structural HealthMonitoring,” Structural Health Monitoring 2005: Advancements and Chal-lenges for Implementation, F. Chang, ed., DEStech Publications, Lancaster,

38 / Vol. 129, DECEMBER 2007

aded 08 Sep 2011 to 115.248.179.1. Redistribution subject to ASME

PA, pp. 42–60.�4� Rose, J., 2002, “A Baseline and Vision of Ultrasonic Guided Wave Inspection

Potential,” ASME J. Pressure Vessel Technol., 124, pp. 273–282.�5� Derriso, M., Braisted, W., Rosenstengel, J., and DeSimio, M., 2004, “The

Structural Health Monitoring of a Mechanically Attached Thermal ProtectionSystem,” JOM, 56�3�, pp. 36–39.

�6� Kessler, S., 2002, “Piezoelectric-Based In-Situ Damage Detection of Compos-ite Materials for Structural Health Monitoring Systems,” Ph.D. dissertation,Massachusetts Institute of Technology.

�7� Rose, J., 1999, Ultrasonic Waves in Solid Media, Cambridge University Press,Cambridge, England.

�8� Alleyne, D., and Cawley, P., 1992, “The Interaction of Lamb Waves WithDefects,” IEEE Trans. Sonics Ultrason., 39�3�, pp. 381–397.

�9� Wilcox, P., Lowe, M., and Cawley, P., 2000, “Lamb and SH Wave TransducerArrays for the Inspection of Large Areas of Thick Plates,” Review of Quanti-tative Nondestructive Evaluation, D. Thompson, and Chimenti, D., ed., Ameri-can Institute of Physics, Melville, NY, pp. 1049–1056.

�10� Lee, B., and Staszewski, W., 2003, “Modeling of Lamb Waves for DamageDetection in Metallic Structures: Part II. Wave Interactions With Damage,”Smart Mater. Struct., 12, pp. 815–824.

�11� Giurgiutiu, V., 2005, “Tuned Lamb Wave Excitation and Detection with Piezo-electric Wafer Active Sensors for Structural Health Monitoring,” J. Intell.Mater. Syst. Struct., 16�4�, pp. 291–305.

�12� Orfanidi, S., 2006, Electromagnetic Waves and Antennas, draft book availableonline at http://www.ece.rutgers.edu/�orfanidi/ewa/

�13� Van Veen, B., and Buckley, K., 1988, “Beamforming: A Versatile Approach toSpatial Filtering,” IEEE ASSP Mag. 5�2�, pp. 4–24.

�14� Knipfer, R., 1992, “Sonar Beamforming—An Overview of Its History andStatus,” Naval Undersea Warfare Center Detachment, New London, CT, Tech-nical Report No. 10,003.

�15� Fenn, A., Temme, D., Delaney, W., and Courtney, W., 2000, “The Develop-ment of Phased-Array Radar Technology,” Lincoln Lab. J., 12�2�, pp. 321–338.

�16� Wells, P., 1999, “Ultrasonic Imaging of the Human Body,” Rep. Prog. Phys.,62, pp. 671–722.

�17� Liu, W., and Giurgiutiu, V., 2006, “Finite Element Modeling and Simulation ofPiezoelectric Wafer Active Sensors Interaction With the Host Structure forStructural Health Monitoring,” Proc. of SPIE’s 13th International Symposiumon Smart Structures and Materials, San Diego, CA Paper No. 6174-107.

�18� Sundararaman, S., Adams, D., and Rigas, E., 2005, “Structural Damage Iden-tification in Homogeneous and Heterogeneous Structures Using Beamform-ing,” Struct. Health Monit., 4�2�, pp. 171–189.

�19� Moser, F., Jacobs, L., and Qu, J., 1999, “Modeling Elastic Wave Propagationin Waveguides with the Finite Element Method,” NDT&E Int., 32, pp. 225–234.

�20� ABAQUS, 2005, Analysis User’s Manual, Version 6.5, ABAQUS, Inc., Provi-dence, RI.

�21� Diamanti, K., Hodgkinson, J., and Soutis, C., 2004, “Detection of Low-velocity Impact Damage in Composite Plates Using Lamb Waves,” Struct.Health Monit., 3�1�, pp. 33–41.

�22� Giurgiutiu, V., Bao, J., and Zhao, W., 2003, “Piezoelectric Wafer Active SensorEmbedded Ultrasonics in Beams and Plates,” Exp. Mech., 43�4�, pp. 428–449.

�23� Derriso, M., Olson, S., DeSimio, M., and Sanders, B., 2005, “Development ofAutomated Damage Detection Techniques,” Materials Damage Prognosis,J. M. Larsen, L. Christodoulou, J. R. Calcaterra, M. L. Dent, M. M. Derriso,W. J. Hardman, J. W. Jones, and S. M. Russ, eds., TMS, Warrendale, PA.

�24� Oppenheim, A., and Schafer, R., 1989, Discrete-Time Signal Processing,Prentice-Hall, Englewood Cliffs, NJ.

�25� Widrow, B., and Stearns, S., 1985, Adaptive Signal Processing, Prentice-Hall,Englewood Cliffs, NJ.

Transactions of the ASME

license or copyright; see http://www.asme.org/terms/Terms_Use.cfm