Role of Shock Response Spectrum in Electronic Product ... · Role of Shock Response Spectrum in Electronic Product Suspension Design The International Journal of Microcircuits and

© International Microelectronics And Packaging Society

The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number2, Second Quarter 2000 (ISSN 1063-1674)

Intl. Journal of Microcircuits and Electronic Packaging

182

Role of Shock Response Spectrum in ElectronicProduct Suspension Design*Suresh Goyal Gary W. ElkoLucent Technologies Bell Laboratories Lucent Technologies Bell Laboratories600 Mountain Avenue, Rm. 1B-212 600 Mountain Avenue, Rm 2D-553Murray Hill, New Jersey 07974 Murray Hill, New Jersey 07974Phone: 908-582-5959 Phone: 908-582-3373Fax: 908-582-6228 Fax: 908-582-7308e-mail: [email protected] e-mail: [email protected]

Edward K. BuratynskiLucent Technologies Bell LaboratoriesP.O. Box 900, Rm. 2-2031Princeton, New Jersey 08542Phone: 609-639-2313Fax: 609-639-3197e-mail: [email protected]

*Outstanding paper of the International Conference and Exhibition on High DensityInterconnect and Systems Packaging

Abstract

The Shock Response Spectrum (SRS) analysis provides general guidelines for the design of suspensions and cushions for shock-protection of fragile components. This paper presents the central results of the SRS approach in the context of designing a compliantsuspension for a Printed Circuit Board (PCB) in a wireless telephone handset, for shock amelioration. The dynamic response of thePCB, to a spectrum of shock pulses, is measured for a rigid suspension and for three versions of a grommeted compliant suspension.The resulting SRS plot shows clearly the resonant response of the PCB, and the effectiveness of the compliant suspensions in reducingshock pulse amplification during resonance. The results also illustrate the usefulness of high damping of the suspension material inreducing peak accelerations. The guidelines generated through this study are applicable for packaging design for a wide array ofelectronic products, especially those pertaining to communications/computing.

Key words:Drop-Testing, Velocity Shocks, Portable Electronics, FragileComponents, Printed Circuit Board, Shock Protection, ImpactTolerance, and Elastomeric Grommets.

1. Introduction

Impact-tolerance, or the ability to safely withstand accidentaldrops and bangs, is becoming an increasingly important aspect

of the reliability of telecommunication network components andenablers1,2,3,4,5. This includes, for example, fragile componentslike ceramic substrates in high-frequency packaged modules,optical sub-systems like Dense-Wave-Division-Multiplexingmodules, end-terminals like wireless phones, notebook comput-ers, Personal Digital Assistants, among other products. Theshock-tolerance of a product, or electronic equipment, is gener-ally determined by the fragility of its ‘weakest’ components. In-variably, impact-induced forces and deformations are not uni-form throughout a product and depend strongly on the locationwithin the object and the ‘connections’ leading to that location.Hence, one of the challenges for the product designer is finding/creating ‘safe’ locations6 within the object for the placement offragile components.

Role of Shock Response Spectrum in Electronic Product Suspension Design


© International Microelectronics And Packaging Society 183

Frequently, during the design of rugged products, a decisionhas to be made whether a component like a Printed Circuit Board(PCB) or a disk drive be mounted rigidly inside an outer chassisor be connected compliantly through elastomeric-grommets. Inthis paper, the authors highlight the importance of accountingfor the Shock Response Spectrum (SRS) in making the abovedecision. The work is presented through the example of design-ing an elastomeric suspension for the PCB inside the housing ofa mobile (wireless) telephone.

For completeness, the authors first review the theory underly-ing the SRS approach, considering the response of suspendedfragile systems to uni-modal shock pulses of different shapes anddurations, for suspension and cushioning design is first reviewed.The central message of the SRS, that shock pulse duration andthe time response of the suspended fragile system be separated toavoid shock-pulse amplification, is highlighted. The design ofthe PCB suspension tackled in this paper is then presented. Theinitial experimental results, and the full shock response spec-trum evaluation of the PCB that followed using various suspen-sion configurations and a range of elastomeric-grommet materi-als are presented. The experimental procedure is described indetail along with the results. The results are also verified ana-lytically. The results clearly indicate the resonant response of thePCB, the role played by the grommets in altering this response,and the effect of high damping of the grommet materials in re-ducing the accelerations on the PCB.

The value of this work lies as an illustration of the tenets ofthe SRS (based primarily on linear systems theory) in a real-world problem, and the applicability of those results to a wide-array of related products that have similar scale and construc-tion.

The layout of the rest of the paper is as follows. The SRSapproach is described and the design problem, suspension de-sign for a PCB, is introduced. The testing scheme is explainedincluding a description of the new test fixture that facilitated it.Results for the shock response of the PCB are shown to be ingood agreement with the predictions of the SRS approach andwith computational results.

2. Shock Response SpectrumApproach

Modeling or measuring impact forces, even in the simplest ofcollisions, is a hard problem due to the multitude of factors in-volved and the extreme nature (high magnitudes, low durations)of the events7,8. The complicated interactions that occur between(and within) the components of an electronic product duringimpact make the task of estimating impact loads and deforma-tions even more difficult. Instead of trying to model impact loadsin their entirety, the SRS approach, explained in detail in refer-ences9,10,11, focuses on the failure of components suspended inter-nally to the main structure of the product. The dynamics of smallinternal parts during an impact is known as shock response.

To fall within the scope of the SRS analysis, a fragile compo-nent must: a) be considerably smaller in mass than the system towhich it is joined; b) not be a load-bearing structural element; c)in combination with its suspension elements, be well approxi-mated by a linear model; d) have its limiting (damaging) condi-tions defined by its peak acceleration or its peak displacementexceeding some critical value acr or xcr, respectively. Commonexamples include a PCB suspended inside a product chassis, ce-ramic substrates or Micro-Electro Mechanical Systems (MEMS)in portable communication/computing terminals, the display ordisk drive of a laptop computer, or a product in its shipping con-tainer (the classical application). The subject of shock modelingfor such systems divides naturally into two parts: impact-inducedmotion of the ‘suspension point’ that supports the fragile ele-ment and the consequent dynamic response of the element. Foreach of these parts, the SRS approach is to classify typical behav-iors; the resulting potential for damage is then either intuitivelyclear or can be assessed easily.

The general shock problem arises from the impact of a mov-ing (falling) object with a floor, desk, or a fixture, generally some-thing more massive by far. The magnitude of the collision isdefined by the velocity of impact (or the drop height). The firststep in shock analysis is to recognize that the suspension point ofa fragile component undergoes a sudden variation in velocitydue to a collision-induced acceleration, or shock pulse ab(t) .Although the exact nature of ab(t) may be very hard to predict,just a few characteristics are important. First, there is a net changeof mean velocity ∆v of the suspension point, given as follows,

(1)

where t is the duration of the shock pulse.The essence of ab(t), frequently a unimodal pulse, can be char-

acterized simply by its magnitude and duration. A particularlyuseful measure of pulse duration is its effective duration, τeff ,defined as follows,

(2)

A more complete pulse specification must include its shape, butit has been found that a broad range of pulse shapes is more orless similar. The key information relates to spectral content: doesthe pulse rise and fall relatively gently? Or do level changesoccur extremely rapidly, and thus contain significant high fre-quency components. Finally, the shock pulse need not beunimodal and the suspension point may continue to oscillate or‘ring’ after the change in mean velocity ∆v.

The consequences of concern to this forcing input at the sus-pension point are the fragile-body peak acceleration and displace-ment. Hence, the most common shock response calculations arethose evaluating peak fragile-element acceleration due to a rangeof acceleration pulse inputs. It turns out that the relationship of




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τeff to the time period of free vibration of the suspended fragilesystem, Tn, is critical for determining this response. The mostuseful facts for shock-protection that emerge from the above cal-culations are the limiting behaviors, that is, fragile-componentresponse to short duration and long duration shock pulses11.

If τeff is considerably shorter than Tn, the peak fragile-elementacceleration will depend only on the velocity change of the baseand not on the time period over which it occurs. This gives riseto the very important notion of ‘velocity shock’ (applicable gen-erally to all well-behaved systems): a base acceleration for a suf-ficiently short time period whose effects depend only on the netvelocity imparted, not on the pulse’s shape, peak magnitude, orprecise duration. A velocity shock just great enough to causedamage defines a critical velocity, vcr .

If τeff is considerably longer than Tn, there are two cases toconsider. If the shock pulse increases and decreases gently (likea very wide half-sine), there will be no suspended object tran-sients and it will respond quasistatically to the imposed accelera-tion. In this case fragile part peak acceleration af

max = abmax and

damage will occur only if the imposed acceleration exceeds acr.The second case is if the shock pulse has a rapid rise time, nomatter how broad it is, its frequency content will excite over-shoot.

The shock-protection implications of the above limiting be-haviors are as follows;

· If the suspended fragile component will be subject to shockpulses that result in an impulsive velocity change of its base ∆v <vcr, no damage will occur irrespective of how great the peak ac-celeration of the shock pulse may be, and no protection is neces-sary.

· If the shock pulse causes a velocity change ∆v ≥ vcr, twocases have to be considered

1) If the shock pulse has magnitude abmax < acr, it will cause no

damage and any Dv is permitted.2) If ab

max ≥ acr, the shock pulse will cause damage. Shock-protection in this case could either involve the usage of cushion-ing to increase the effective duration of the shock pulse so ab

max <acr; modification of the suspension (stiffness decreased and swayspace increased) to make vcr > ∆v; or ruggedization of the fragilecomponent itself to increase its acr > ab

max , Reference11.The concepts of the SRS approach can be reinforced through

the example of the system illustrated schematically in Figure 1.

mf

cfkf

ab(t)

Lighter fragileobject

Heavierchassis

Exteriorcushioning

Suspension-pointof base

Figure 1. Schematic of an electronic product, with a lighterfragile component suspend inside a heavier outer chassis,for Shock Response Spectrum (SRS) analysis. The suspensionis modeled as a combination of a linear spring and damper.

3. Representing Shock Response

Figure 1 shows a fragile component of mass mf connected to aheavier chassis through a suspension modeled by a combinationof a spring (stiffness kf) and damper (stiffness cf). The chassismay be covered by a cushioning material to increase the durationof, or soften, the impact. The net force exerted on the fragile mass,that which may cause damage, is given by its mass times its accel-eration af(t). The forcing input is a suspension point accelerationpulse, ab(t), that is produced when the cushioned chassis hits theground with velocity v0.

Since the system of Figure 1 is linear its dynamic response,when subjected to various shock pulses, is represented through

a so-called ‘base pulse response ratio R’, given as follows,

(3)

To characterize this response ratio analytically for a large varietyof shock pulses (differing in shape, spectral content, and dura-tion), simple, analytic, unimodal acceleration pulses of variousshapes (like rectangular, sinusoidal, versed sine, or triangular)are applied to the suspension point.

The resulting peak fragile component acceleration afmax due to

the above shock pulses, either during or after the pulse, can bedetermined analytically solving the equation of motion for a forcedspring-mass-damper system12,13. For instance, it can be shownthat in response to a velocity shock of magnitude ∆v,

(4)

where fff mkc 2/=ζ is the damping ratio. Similarly, for astep change in acceleration of magnitude ab

max applied to thesuspension point,

(5)

Collating the response ratios of the fragile component to variousshock pulses, the SRS approach plots R as a function of effectiveshock pulse duration (normalized by the time period Tn of freevibration of the fragile system). Figure 2 presents the SRS for an




undamped system, that is, the system of Figure 1 with cf = 0.

Figure 3 presents a close-up of the SRS plots of Figure 2, aroundthe region of resonant response. Although Figure 2 plots theSRS for a few, but representative, pulse shapes, plots for otherwell-behaved pulse are not too different and have an upper-boundrepresented by the response for a rectangular pulse12,11. Observein Figure 3 that for τ

eff /T

n < 1/6, the SRS does not depend on pulse

shape and is approximately a straight line through the origin. Thismeans, for example, that for a given pulse shape, halving shockpulse duration and doubling its amplitude, that is applying thesame ∆v, leaves the internal peak accelerations unchanged. Thisis the short-pulse response discussed earlier.

Figure 2. SRS plots for an undamped systems (cf = 0), when

subjected to a spectrum of shock pulses. The chosen pulseshapes, as shown, include rectangular (that is, a very fastrising pulse), half-sine, versed sine and symmetric-triangular.

Figure 3. SRS plots of Figure 2 drawn to higher resolutionon the time axis to highlight the resonant response. Insetshows pulse durations in comparison to system freevibration period for τττττ

eff/T

n = 0.5 and 1.

The highest R for any pulse shape occurs for a pulse durationτ

eff ≈ T

n /2, which is similar to the phenomenon of resonance expe-

rienced with sustained-periodic excitation (vibration). The valueof R at resonance depends on the pulse shape, being highest for arectangular pulse. At long pulse lengths, the SRS approaches ahorizontal line, of a level depending only on pulse rise time. Thisis the long-term response discussed earlier and it clarifies the roleof cushioning: to transform a given velocity change into an accel-eration pulse of longer duration and lower magnitude.

The addition of damping to the suspension, although not illus-trated in Figures 2 and 3, tends to reduce R for a given pulse shapeand amplitude, particularly around resonance. For velocity shocks,moderate damping (that is ζ < 0.5) is beneficial. For reducing thepeak fragile component acceleration to long duration pulses, themore the damping, the lower the R12,11.

The behaviors outlined above and in Figure 2 are applicable tofar more general systems than those of Figure 111. One such sys-tem, a PCB suspended compliantly inside a wireless handset, isdescribed next section.

4. Suspension Design: PrintedCircuit Board

Figure 4 shows a PCB suspended inside a wireless telephoneusing six screws and six half-grommets around the screws. Thehandset was expected to be able to safely withstand 20-30 dropsfrom 1.5m onto vinyl tile and 250 drops from 1m onto vinyl tile.Based on drop testing of a wide range of wireless handsets fromsimilar heights, it was estimated that the telephone chassis wouldbe subjected to shock pulses of durations τ ranging from 0.3 –2.0ms (miliseconds).

PCB

PCB Support

140 mm

56 mm

Grommet R 4.5mm1.34mm

R 2.75mm

Figure 4. Schematic of the suspended Printed Circuit Board(PCB) and an elastomeric grommet to illustrate suspensionconfiguration, approximate shape, and dimensions.

The aim was to design a suspension for the PCB that would




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minimize the resulting peak accelerations on the PCB. The choicesfor the suspension were either to connect the PCB rigidly to theouter chassis using the six screws, or to connect it compliantlywith elastomeric grommets made from commercially availabledamped elastomers14. The additional design challenge, commonin all portable products where small size and low weight are highlydesirable, arose from the fact that the space to accomodate thegrommets was quite limited, as shown in Figure 4.

Initial impact testing with shock pulses of a fixed durationshowed that parts of the PCB experienced acceleration peaks thatwere considerably higher than the applied pulses and no clearresolution was available for the design choices. It was recog-nized, then, that these amplifications were a result of the shockresponse of the dynamic system formed by the compliant PCB,and its suspension had to be tested using a spectrum of shockpulses as detailed in next section.

5. Experimental Procedure

SRS testing was performed using a Dynatup® Impact TestingMachine, Model 825014,15, equipped with a specially designedfixture that allowed it to be used as a drop-table, as shown inFigures 5 and 6. The fixture, allowing rigid and easy attachmentof the suspended PCB, replaced the webs in the dropping cross-head of the machine. The shock pulses were generated throughimpacts between the falling tup (directly beneath the fixture) andvarious elastomeric pads placed on a fixed steel plate, that re-sulted in dead (non-bouncy) impacts. The drop height was set tobe 1m and essentially-unimodal shock pulses of durations rang-ing from 1.5-16ms were obtained. (Finding the right combina-tion of material and size of rubbery pads, to yield a desired pulseduration, is a non-trivial task.) Due to limitations of availablematerials, it was found difficult to get non-noisy unimodal shockpulses of less than 1.5ms duration.

Figure 5. Photograph of the designed test fixture that isattached to the falling cross-head of the Dynatup ImpactTesting machine model 8250. the PCB is mounted with sixscrews onto a plate that can be attached easily to the fixture.The dark cylindrical tup, whose impact with elastomeric padsproduces the shock pulse, is clearly visible under the testfixture.

Figure 6. Close-up of the area where the PCB is suspended,in the test fixture, to show the locations where theaccelerometers were attached.




The PCB was tested in four configurations: attached rigidly tothe test fixture, and attached compliantly with grommets madefrom three different versions of the elastomer VersaDampTM, sup-plied by E-A-R Speciality Composities® (of Indianapolis, IN).The VersaDampTM family of elastomers is thermoplastic, with aproprietary formulation16. The chosen grades of VersaDampTM

represented a wide range of stiffnesses and damping. They were,V2590 (highly damped, Shore A durometer 57), V2750 (moder-ately damped, Shore A durometer 70), V2325 (lower damping,Shore A durometer 40).

Accelerations were measured at four locations (as shown inFigure 6):

1) At the site where impact first occurs between the tup andthe elastomeric pads (using the load cell inside the tup).

2) At the base of the suspended PCB (using an accelerom-eter), to measure the forcing input, a

b(t), on the suspended PCB.

3) At a point on the PCB which is close to a support. Asexpected, the accelerations recorded at this location were not toodifferent from those recorded at the base of the suspended PCB.

4) In the middle of the lower half of the PCB (that is, the mostflexible point on the PCB) to measure maximal PCB response,a

f(t).

For each pulse duration, and PCB configuration, multiple dropswere done to check repeatability.

6. Results and Data Analysis

Since the PCB is flexible, it has natural vibration modes thatcouple with those introduced from a compliant suspension. Theaccelerometer results showed a clear resonance of the PCB ataround 350 Hz and a resonance of the test fixture itself at around1400 Hz. Keeping this in mind, the accelerometer data was passedthrough a low-pass filter, designed using the softwareMATLABTM, with a high frequency cut-off at 2200 Hz. Thefiltering only smoothed accelerometer data for the very shortduration, 1.5-1.6ms, shock pulses; it left the data for longer du-ration pules unaltered. Figures 7 and 8 shows examples of a

b(t),

and the corresponding af(t), respectively, for a shock pulse that

excites resonant response and for a much longer shock pulse.

Figure 7. Accelerometer data for the applied shock pulse (ab(t))

and the measured acceleration (af(t)) at the center of the bottom

half of the PCB (its most flexible portion), for a pulse durationthat excites resonant response with the PCB suspended withV2590 grommets.

15ms

Figure 8. Accelerometer data (ab(t) and a

f(t)) for a very-long

duration shock pulse, for the PCB when suspended withV2325 grommets.

For each PCB configuration, response ratios R = afmax/a

bmax

were calculated for all the pulse durations they were tested in.The results are displayed in Figures 9 and 10 where the ordinateis R and the abscissa is the actual shock pulse duration, τ, at thebase of the PCB. Figure 10 is a close-up of the SRS plots aroundthe region of resonant response. For a linear, undamped, systemwith a natural frequency of 350 Hz (that is, T

n ≈ 2.8ms), the SRS

approach predicts that sinusoidal shock pulses will yield peakresponses at τ ≈ 2.2ms (τ

eff ≈ 1.4ms). Observe in Figure 6 that for

each PCB configuration, the maximum response occurs around τ ≈2.2ms !




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Figure 9. SRS plots for four configurations of the PCB, onewhen it is rigidly connected and the other three with grommetsmade out of differing elastomers.

Figure 10. SRS plots of Figure 9 drawn to higher resolutionto highlight the resonant response.

Figures 9 and 10 show that for pulse durations that exciteresonant response, the acceleration on the PCB can be signifi-cantly higher than the shock pulse, as predicted by the SRS analy-sis. This is true for all configurations of the PCB, with and with-out the elastomeric suspension. The lowest response, near reso-nance, occurs with the V2590 grommets, illustrating the benefitsof using highly damped materials in the suspension. Note thatresonant response occurs at a somewhat longer pulse duration, τ≈ 2.5ms, only for the softest suspension, made of V2325. Also,observe that the SRS plots for all PCB configurations have thesame slope before resonance, highlighting the uniformity of theshort-pulse response.

7. Computational Results

A modal analysis of the PCB, using I-DEAS® software17, com-puted its first mode at 423 Hz. This compares well with the ex-perimentally determined mode of 350 Hz for the PCB, given thatthe mass of the accelerometers was not modeled and an approxi-mate shape of the PCB was used during analysis. In order tounderstand why the elastomeric grommets did not alter the re-sponse of the PCB dramatically, as hoped, from the configura-tion when it was attached rigidly to the test fixture, the followingapproximate analysis can be done.

The flexibilities of the PCB and the grommets are modeled aslinear springs, and the mass of the PCB by a lumped mass, toyield a spring-mass oscillator. Using the natural frequency ofthe first mode of the PCB ϖ

PCB = 350 Hz, and its mass m

PCB = 0.02

kg, the equivalent spring stiffness for the flexible PCB can be esti-mated as:

kPCB

= mPCB

*(ϖPCB

)2= 96.7 N/mmUsing the area of contact A

c = 20 mm2 for each of the six grom-

mets, and l = 1.34 mm as maximal allowable deformation, theequivalent spring stiffness for the six grommets together can beestimated as k

gr = 6*E*A

c/l = 90*E mm, where E is the Young’s

Modulus for the grommet materials. Using the values of EV2590

=4.8 N/mm2, E

V2325 = 2.48 N/mm2, E

V2750 = 7.4 N/mm2 from16, we

get:k

V2590 = 432.0 N/mm,

kV2325

= 223.2 N/mm,k

V2750 = 666.0 N/mm.

Comparing the stiffness of the PCB and the grommets, it canbe seen that all three of the grommet materials are essentially toostiff to have any softening effect on the suspension of the PCB!However, the softest amongst the three, V2325, does decreasethe natural frequency of the suspended PCB somewhat, to about314 Hz, as mentioned earlier.

8. Discussion

The main aim in this paper was to explain the reason for aperplexing situation that electronic packaging engineers encoun-ter, measurement of higher shock pulses on internal componentsof an electronic product than on its outer shell, by describing theresponse of compliant dynamic systems to a spectrum of shockpulses (called shock response spectrum, or SRS). The work waspresented through the example of a suspension design for thePCB of a wireless handset for shock amelioration.

Through measurement of the peak acceleration of the sus-pended PCB in response to slow-rising shock pulses of differentdurations, the central message of the SRS, that shock pulse dura-tion, in comparison with suspended fragile component naturalresponse time, is critical in determining suspended componentresponse, was illustrated. It was shown that parts of the PCB




experienced peak accelerations that were considerably higher(sometimes almost double) than the magnitude of the applied shockpulse, for pulse durations of around 2.2ms, corresponding to the‘resonant response’ predicted by the SRS analysis. It was alsoshown that the resonant response occurred for all configurationsof the PCB, whether it was suspended through grommets or con-nected rigidly to the outer chassis. However, the peak accelera-tions at resonance were always lower for the PCB with grommets,than with the rigidly connected PCB, being least severe for thegrommets made from the highly damped elastomer V2590. Thedesign implications of this are several.

Amongst the available choices, a compliant suspension withgrommets made from V2590 is the most effective in reducingpeak accelerations on the PCB near resonance. Additionally, thehigh damping is useful in combating vibratory loads. The effec-tiveness of the V2590 grommets can be increased further if thePCB was made a little stiffer (for instance, by adding more sup-port points) so more of the deformation occurs in the grommets.For a given drop height, conservation principles imply that ashorter pulse duration results in a higher amplitude. It can beseen from Figure 10 that for pulses with duration less than 1.5ms,the preferred PCB configuration does not show any amplifica-tion; the amplification above that duration may not be damagingbecause of the lower amplitudes of the applied shock pulses asso-ciated with them. If further separation is desired between theresonant response and expected shock pulses, the height of thegrommets (that is, available sway space) would have to be in-creased in conjunction with a much softer and damped materialfor the grommets. This is illustrated, to some extent, by the re-sults for the V2325 grommets. Finally, fragile components thatare susceptible to higher accelerations should be located close toa support point, the grommets (see also References18,19).

Then, there are aspects of the PCB suspension design thathave not been presented in the paper. This includes double inte-gration of the accelerometer data to estimate peak deflections onthe PCB (or estimating deflections from the accelerations usingspring-mass system formulae), and testing of the PCB in a verti-cal orientation resulting in shock pulses being applied in the planeof the PCB. Note that the results presented here only consideredthe first vibrational mode corresponding to the largest PCB de-flection. Depending on the duration of the shock pulse and thelocation of the fragile component, a higher mode may need to beanalyzed to assess damage potential.

The results of the SRS analysis are very versatile and appli-cable for almost all well-behaved systems11. Even the results de-scribed above are fairly general, being directly useful for a wide-array of products that have similar scale and construction, forexample, most hand-held portable electronic products20,21, andoptical network component packages.

Acknowledgments

The authors wish to thank Peter Hewett, Rodger Andrew, andIan Armstrong for their work on the design of the grommets andwith initial experimentation; Jeff Bream and David John-Lugofor fixture design; E-A-R Speciality Composites for supplyingthe grommets and material data; Jonathan Rush for help withthe I-DEAS analysis; and Mike Pye, Lou Manzione, and UrmiRay for support.

References

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About the authors

Suresh Goyal received his B.S. Degree from the Indian Insti-tute of Technology, Kharagpur, his M.S. Degree from the Uni-versity of Iowa, and his Ph.D. Degree from Cornell University,all in Mechanical Engineering. After a year of postdoctoral workin computer Science at Cornell University, he joined Bell Labo-ratories at Murray Hill, New Jersey, in 1989. Currently, he isinvolved in research related to wireless packaging. In particular,his research is focused on developing the science and technologyto engineer rugged, reliable network components, and equipment.His research interests are fairly broad, encompassing dynamics,solid mechanics, structural mechanics, modeling and simulation,experimental techniques, software development, wireless com-munication, and data networking.

Edward K. Buratynski received his B. Math from the Universityof Waterloo in Ontario, Canada in 1978. He specialized in AppliedMathematics, Computer Science, and Physics. He then proceededto earn a Ph.D. from Cornell University in Theoretical and AppliedMechanics in 1983. Following his education, he joined the AT&TEngineering Research Center in Princeton, New Jersey which even-tually became part of Bell Laboratories. , Lucent Technologies.During his 17 year career in AT&T, he has worked in a number ofareas related to electronics manufacturing. The responsibilitiesincluded the development of scientific computational codes forheat transfer and stress analyses, statistical studies of part toler-ances, analytical modeling of thermal stress response of trilayerstructures and experimental studies in shock and vibration test-ing. He is currently working in the area of product reliability.

Gary W. Elko was born in Philadelphia in 1955. He receivedthe B.S.E.E. from Cornell University in 1977, and a M.S. andPh.D. from Penn State University in 1980, and 1984, respec-tively. He is presently a Distinguished Member of the TechnicalStaff at Bell Labs, Lucent Technologies where he is supervisinga group working on signal processing and electroacoustics re-lated to the hands-free acoustic telecommunication problem. Hiscurrent interests are in adaptive beamforming, acoustic echo can-cellation, 3D audio, and room acoustics. He is a past AssociateEditor of the IEEE Transactions of Acoustics, Speech and Signalprocessing, a member of the IEEE Audio and ElectroacousticsTechnical Committee, and a fellow or the Acoustical Society ofAmerica.

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Role of Shock Response Spectrum in Electronic Product ... · Role of Shock Response Spectrum in Electronic Product Suspension Design The International Journal of Microcircuits and