Vibration Response of 3-D Space Accessible Sandwich Composite

Vibration Response of 3-D SpaceAccessible Sandwich Composite

A. S. VAIDYA* AND N. UDDIN

Department of Civil and Environmental EngineeringUniversity of Alabama at Birmingham, Birmingham, AL 35294, USA

U. K. VAIDYA

Department of Materials Science and EngineeringUniversity of Alabama at Birmingham, Birmingham, AL 35294, USA

ABSTRACT: A 3-D sandwich composite comprising of E-glass core piles which are woven to thefacesheets is considered in this work. This arrangement creates interstitial spaces in the core whichcan be used for foam infusion for sound/vibration damping, fluid storage, or for routing wires orinserts, in addition to providing strength. The vibroacoustic response of such multi-functionalmaterials has received little attention and is an important issue when the structure witnessesmechanical vibrations. This article presents the vibration related studies carried out on the 3-Dsandwich composite, infused with SC-15 resin. The frequency response function (FRF) and thedamping ratios are the parameters of interest for this study. In this study the experimental data ispresented for the unfoamed (as received) core configuration and the core filled with the polyurethane(PUR) foam. The average damping ratio of the unfoamed sandwich panel was found to be0.55%. An increase of 150% in the damping ratio was observed for the PUR foam filled panels fora 77% increase in weight when compared to an unfoamed sandwich panel. Use of vibration as anon-destructive damage detection technique is demonstrated for beam specimens damaged byflexural loading. A reduction of 35% in the resonant frequency and 193% increase in the dampingratio was observed for approximately 6% core damage of the sandwich composite.

KEY WORDS: multifunctional sandwich composite, vibration damping, damping ratio.

INTRODUCTION

THE MECHANICAL VIBRATION of structures is the dynamic response to the stressesthey undergo. When a structure is excited, it oscillates in all its modes of vibrations.

The number of modes depends on the position of the exciter [1]. The response ofa structure to an excitation is a function of its stiffness and damping. Usually as the extentof defect increases there is a change in the stiffness which in turn changes the dampingratio of the structure. Amongst various materials used for vibration control, sandwichcomposites are ranked much higher as compared with the traditional single layerstructures [1]. Sandwich composite essentially consists of three or more layers in whicha low density core is sandwiched between stiff faces. By adding a lightweight core layer

*Author to whom correspondence should be addressed. E-mail: [email protected] 1 and 3 appear in color online: http://jrp.sagepub.com

Journal of REINFORCED PLASTICS AND COMPOSITES, Vol. 00, No. 00/2008 1

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between the facesheets, the bending stiffness and strength can be substantially increasedwithout adding much weight. The viscoelastic cores such as polymeric foams have a highinherent damping capacity.

The multifunctional sandwich composite presented here offers superior structuralstrength, light weight benefits, excellent thermal insulation, and high sound and vibrationdamping. Damping can be defined as the transformation of vibration energy in some otherform of irrecoverable energy. There are two kinds of damping namelymaterial damping andstructural damping. In composites, the main source of material damping arise from relativeslipping at the fiber-matrix interface, fiber diameter, orientation of the fibers, and thesequence of lay-up. Apart from these, cracks and debonds also contribute to damping [2].When a beam or plate undergoes flexural vibrations, the damped core is constrained in shearwhich causes the flexural motion to be damped and vibration energy to be dissipated [3].

The vibration response of a structure is determined on the basis of its natural frequency,mode shape, and damping factor. There are several experimental techniques to estimatethe dynamic properties of a structure including: time domain methods, peak amplitudemethods, frequency domain methods, and modal testing methods [4]. In the frequencydomain and modal testing methods, vibration response can be measured in terms ofdisplacement, velocity, and acceleration. In the peak amplitude method, the structure isexited by a random noise source and the FRF is measured. The peaks in FRFs correspondto the resonance to the natural frequencies of the structure. These frequencies are used tocalculate damping in a particular mode of excitation. The present study uses frequency anddamping ratio evaluation as a means for determining the vibration characteristics ofmultifunctional 3-D sandwich composite. The half power bandwidth method is then usedto determine the damping ratio [4]. All the specimens are subjected to the random noiseunder flexural vibrations. The FRF of the unfoamed beam specimens is considered as thebaseline result in this article. The use of PUR foam to enhance the damping characteristicsof the sandwich is covered in the subsequent parts of the article. The use of vibrationdamping as a NDE tool is covered in the final section.

LITERATURE REVIEW

Sandwiching a flexible barrier with acoustical foam, for instance, creates a decoupledbarrier absorber, which both blocks and absorbs sound and vibration energy [5]. Rao [6]described the application of viscoelastic damping in automotive and aircraft applications.The researcher also described the use of sandwich glass for windows to reduce the noise.Nakra [7] published a series of reviews on vibration control with viscoelastic materials.Schultz et al. [8] pointed out the importance of vibration testing as applied to composites.The authors measured the elastic moduli and damping ratio for glass fiber-reinforcedunidirectional composite beams in the frequency range of 5–10,000Hz. Vaidya [1]described the use of the vibration techniques for nondestructive (NDE) evaluation ongraphite fiber composites. It was also shown that damage can be correlated to reduction inresonant frequency and increase in damping ratio. Gibson et al. [9] investigated dynamicproperties of composite materials from a theoretical and experimental viewpoint. Theeffects of nonlinear elastic behavior due to large displacement or matrix governednonlinearity are pointed out in their study.

Vibration characteristics of sandwich composites have been studied by a number ofresearchers [10–14]. The Ross–Ungar–Kerwin model is one of the first theories developedfor explaining damping in composite sandwich structures [10]. Li and Crocker in 2005 [11]

2 A.S. VAIDYA ET AL.

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presented a review on vibration damping in sandwich composite structures. The authorsincluded a number of analytical theories related to the damping of sandwich beamsand plates. Li and Crocker [12] also studied the frequency dependence of damping insandwich beams with combined honeycomb-foam cores. It was shown that the viscoelasticproperties of the foam impart greater damping in the core than in the facesheets. Thehoneycomb structure also enhanced the stiffness of the entire structure. Mead and Markus[13] proved that the maximum values of the damping in a sandwich composite are not verysensitive to the boundary conditions. Nilsson [14] studied the vibration response in termsof sound reduction index of honeycomb and solid viscoelastic cores.

MULTIFUNCTIONAL 3-D SANDWICH COMPOSITE

A sandwich composite consists of three or more layers. In this study the focus is ona three-layered multifunctional sandwich composite. The origin of the 3-D sandwichcomposite is in velvet weaving [15]. The facesheets and the core of this sandwich compositeare made up of E-glass fibers. The core is in the form of series of core piles which aremechanically connected (woven) to the facesheets. This arrangement increases the shearresisting properties of the sandwich in longitudinal as well as lateral directions. Thisarrangement also creates interstitial spaces in the core which can then be used for a varietyof applications such as wire routing, conduit routing, fluid storage, and foam filling andhence the 3-D sandwich composites are referred to as ‘multifunctional’.

The processing of the sandwich panels was conducted by the hand lay-up process as aninitial step; which was followed by vacuum bagging. This combination produces highquality specimens with a very little resin pooling on the tool surface. The details ofprocessing can be found in Vaidya’s study [16]. The specimens were then infused with rigidPUR foam (provided by Coosa Composites, Alabama) with a density of 6.40E�05–9.61E�05 g/mm3 (4–6 lb/ft3) to fill the interstitial spaces of the sandwich. In order toachieve uniform compaction of the foam, the foam was infused under controlled vacuum.Figure 1 shows the details of unfoamed and the foamed sandwich composite specimens.

(c)

22 mm

22 mm 22 mm

(a) (b)

Figure 1. Multifunctional sandwich composite: (a) weft direction view, (b) warp direction view, and (c) PURfoam filled 3-D sandwich composite.

Vibration Response of 3-D Space Accessible Sandwich Composite 3



VIBRATION TESTING

A vibration test involves the quantitative measure of the various parameters such asdamping ratio, resonant frequency and mode shapes. The vibration response of thespecimen for the applied excitation force can be obtained over a range of frequencies.The ratio of motion to the force as a function of frequency is referred to as frequencyresponse function (FRF) [1]. The test method used in this study was half power pointbandwidth method [16]. This method assumes a single degree of freedom (SDOF) systemmodel with either a viscous or hysteretic damping [17].

Each beam specimen was excited at its geometric center resulting in bending mode ofvibration. Whenever a sandwich beam is excited, the vibrational energy can propagatethrough the sandwich in the form of bending waves and shear waves. At low frequencyrange such as chosen for this study; the energy is dissipated primarily in bending.All the specimens were tested for their response to random noise using the Bruel andKjaer 2032 dual channel spectrum analyzer in the frequency range of 0–800Hz.A zoom transform was conducted for each resonant frequency peak to measurethe damping ratio. Figure 2 graphically shows the calculation of damping ratio fora typical resonance peak. The damping ratio was calculated using half powerbandwidth method given by:

� ¼ðf2 � f1Þ

2fnð1Þ

where � is damping ratio, fn is resonant frequency, f1 and f2 are locations at which responseis 3 decibels (dB) down with respect to the resonant frequency (Figure 2) [17].

Resonant frequency (Hz)

3 dB

f1 fn f2

Am

plitu

de (

dB)

Figure 2. Half power point method.




VIBRATION TESTING EQUIPMENT

An impedance head Bruel & Kjaer (B & K) Type 8000 mounted on a trunnion andoriented horizontally was used. The impedance head was connected to a B & K type 4809electrodynamic shaker using a stringer rod. The input force and output acceleration signalsfrom the impedance head were fed to a dual channel frequency analyzer B & K 2032through two Kistler-Type 5004 dual mode preamplifiers. The experimental set-up forvibration testing of a sandwich composite specimen is shown in Figure 3(b). The FRF wasmeasured in baseline and zoom modes. Random noise excitation was adopted andamplified by B & K Type 2706 power amplifier. The FRF was measured by mounting thesample at its geometric center. The damping ratio values were measured using the halfpower bandwidth method [17].

VIBRATION TESTING PROCEDURE

Beam specimens of 609� 101� 22mm were prepared for random noise excitation.A hole was drilled at the geometric center of each specimen to lightly fasten a screwto connect the specimen to the impedance head. A small quantity of beeswax was usedto further consolidate the specimen–impedance head interface. The sandwich specimenwas hung from the ceiling using fine nylon wire to ensure near free–free boundarycondition (Figure 3(a)).

Amplitude versus resonant frequency data was collected from the frequency analyzer.

VIBRATION TESTING RESULTS

Vibration Response of Unfoamed Beam Specimens

Representative FRF plots for three sandwich specimens are shown in Figure 4. As seenfrom the figure, the resonant frequency peaks were observed approximately at the samelocations for all the specimens tested. The dominant flexural modes were observed at 108,225, 340, 470, and 580Hz, respectively. The FRF of beam specimens showed high degreeof repeatability, the minor differences in frequencies were attributed to the variationsin core pile concentrations and orientation in local areas. In addition to the dominantflexural modes, minor modes associated with torsional vibrations were noted around the

Pre- amplifierComputer for data

collection

Analyzer

Impedance head

Stinger rod

Beam specimen

(a) (b)

Figure 3. (a) Near free–free boundary condition, (b) Test set-up.




108, 225, and 580Hz peaks. The damping ratios were calculated at the correspondingresonant frequencies. The typical frequencies and damping ratios for individual peaks aretabulated in Table 1.

The minor variation in the damping ratios was due to the local characteristics of the corepiles in the area under excitation. The orientation of the core piles and the resin rich areasformed as shown in Figure 5, dictate the minor variations in the damping ratios aparticular peaks.

The resin rich core piles (Figure 5(b)) tend to vibrate less for the applied random noise.The resin rich areas act like rigid supports which hinder the ability of the core piles tovibrate freely, thus increasing the damping in that particular zone. Also local variations inthe orientation of the core piles imparted due to processing, contribute in changingthe damping properties in a particular mode. In the case as shown in Figure 5(a) inwhich the core pile is already buckled to some extent, absorbs the vibrations, and increasethe damping by microbuckling to a greater extent.

−40

−30

−20

−10

0

10

20

30

40

50

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800

Am

plitu

de (

dB)


Specimen 1

Specimen 3 Specimen 2

Figure 4. Typical FRF of beam specimens.

Table 1. A typical FRF for beam specimens.

Peak f1 (Hz) fn (Hz) f2 (Hz) Damping ratio

1 102.37 102.62 103.12 3.65E�032 227.00 228.25 230.75 8.21E�033 344.00 347.00 349.50 7.93E�034 459.75 464.25 467.50 8.35E�035 565.25 569.75 574.00 7.68E�03

Average damping ratio 7.16E�03




Vibration Response of Foam Filled Beam Specimens

The 3-D sandwich specimens were infused with PUR foam in order to assess the changein the vibration damping behavior of the sandwich composite after filling the interstitialspaces of the core. The change in the weight and the density after infusing the specimenswith PUR foam is summarized in Table 2. The increase in weight after filling with foamwas an average of 77.6% in comparison to the unfilled sandwich composite.

The resonant peaks were significantly damped in the case of foamed specimens.Two prominent peaks were observed (Figure 6) around 200 and 750Hz of frequencyrange. A minor peak was also observed at a frequency of 425Hz. The peaks were seen tobe shifted to lower frequencies for the foamed specimens because of their higher mass.

In the case of the unfoamed specimens, large interstitial spaces were presentwhich allowed free vibrations of the individual core piles. The vibrational energy strainedthe core piles which acted as free vibrating bodies dissipating the energy, thus providingdamping. In contrast to this in the case of the foamed specimens the foam constrainedthe core piles and the core piles were not free to vibrate. Friction between the core pilesand the foam provided a shear damping mechanism. This in turn increased the dampingof the specimen. In addition to this, foam filling increased the weight of specimenas a whole, providing inertial damping. Figure 7 shows the comparison betweenthe damping ratios for the unfoamed and foamed specimens. It was observed thatthe numbers of peaks were suppressed in the case of foamed specimens. The number ofpeaks corresponds to the flexural modes that are excited. In the case of unfilled specimens,

Resin rich areas atthe contact point ofthe facesheet and the core pile and also atthe mid-height of the core pile

Mid-axis Change in the orientation of the core piles

Figure 5. Local variations in the core piles: (a) change in orientation, and (b) resin rich area formation(adapted from Ref. [18]).

Table 2. Weight and density change before and after foam insertion.

Samplesize (mm)

Weight beforefoam filling (g)

Weight afterfoam filling (g)

Density ofsandwich before

foam filling (g/mm3)

Density ofsandwich after

foam filling (g/mm3)

609� 50.8�22 210.00 373.00 1.55E�04 2.75E�04




the damping ratios were found to be in range of 0 (zero) to 0.01, while for foam filledspecimens, the damping ratios were in the range of 0.01–0.025. There was an overallincrease of 150% in damping ratio observed in foamed specimens as compared tounfoamed specimens for a 77% weight increase.

−70

−60

−50

−40

−30

−20

−10

0

10

20

30

40

0 100 200 300 400 500 600 700 800


Am

plitu

de (

dB)

Foam filled specimen

Unfoamed specimen

Figure 6. Comparison of the FRF of unfoamed and foam filled specimens.

1 2 3

Mode number

Unfoamed beam specimen

Foamed beam specimen

Dam

agin

g ra

tio

0

0.005

0.01

0.015

0.02

0.025

0.03

4 5

Figure 7. Comparison of damping ratios for unfoamed and foamed beam specimens.




Plate Test Results

The dependency of the vibration response on the geometry of the specimen wasestimated by testing plate specimens of the sandwich composite for the thickness of 22mm.The plate dimension was chosen to be 572� 299� 22mm. The frequency range wasmaintained at 0–800Hz and the specimens were excited at the geometric center as done inthe case of beam specimens. In order to validate the results, each specimen was tested twiceand the typical results are tabulated in Table 3.

As seen from Table 4, higher number (33 peaks) were observed in case of thesandwich plate specimen as compared to a beam specimen (9 peaks) for the same coreheight of 22mm, and in the same frequency range of 0–800Hz. Though the flexuralvibrations were induced in the specimens, there was a prominence of torsional modesin addition to the flexural modes in the case of plate specimens. The plate, because ofits large dimensions, underwent torsion in addition to flexure when excited at thegeometric center. These torsional deflections gave rise to additional modes in theFRFs (Figure 8).

Damping ratio was higher for the first peak for the plate (7.06E�03) as compared to thebeam (3.65E�03), which can be attributed to inertial mass effects. For the fourth and fifthpeak, the damping ratio for a plate (4th peak: 8.80E�03, 5th peak: 7.66E�03) was less ascompared to the beam (4th peak: 8.83E�03, 5th peak: 7.68E�03). Thus, there was nosignificant difference in the damping ratio of the 3-D sandwich for different specimendimensions. The average damping ratios for beam and plate were found to be 7.16E�03,and 7.51E�03, respectively.

Table 4. Modal density comparison for beam and plate specimens.

Frequencyrange

Modal density forbeam specimen

Modal density forplate specimen

0–100 1 4100–200 1 4200–300 1 4300–400 1 4400–500 1 4500–600 2 5600–700 1 4700–800 1 4

Table 3. A typical FRF for plate specimens.

Peak f1 (Hz) fn Hz) f2 (Hz) Damping ratio

1 105.25 106.25 106.75 7.06E-032 229.75 232.20 233.2 7.43E-033 263.75 265.00 267.25 6.60E-034 338.00 341.00 344.00 8.80E-035 387.75 391.50 393.75 7.66E-03

Average damping ratio 7.51E-03




USE OF VIBRATION RESPONSE AS NON-DESTRUCTIVE

EVALUATION (NDE) TOOL

The basic premise of vibration testing for NDE is that a local change in the stiffness dueto a defect or damage changes the vibration characteristics of the structure. The 3-Dsandwich composite was subjected to damage in this study and the FRF of the damagedspecimens were compared with the undamaged specimens. Two sets of damaged specimenswere chosen so as to directly correlate the extent of damage with change in the damping.The damage was caused by testing the beam specimens in flexure. The beam specimens of

−40

−30

−20

−10

0

10

20

30

40

50

0 100 200 300 400 500 600 700 800


Am

plitu

de (

dB)

(572 mm x 299 mm)

22 mm thick plate specimen

22 mm thick beam specimen(609 mm x 101 mm)

Figure 8. Comparison of FRF of a beam and plate specimen.

Table 5. Resonant frequencies before and after the flexural loading.

Modenumber

Resonantfrequency(Hz) of anundamaged

beam

Resonantfrequency

(Hz) of a partiallydamagedbeama

Resonantfrequency(Hz) of a

completelydamaged beamb

% Reductionin resonantfrequency

for a partiallydamaged beam

% Reduction inresonant

frequency for acompletely

damaged beam

1 102.75 95.50 90.00 7.06 12.412 219.75 207.00 146.00 5.80 33.563 334.00 309.25 201.00 7.41 39.824 455.00 413.75 255.25 9.07 43.905 534.00 490.00 311.00 8.24 41.76

Average% drop 7.51 34.29

aA partially damaged beam was loaded to 80% of the ultimate failure load.bA completely damaged beam was loaded to ultimate failure.




609� 101� 22mm were tested under three-point bend flexure using a span of 558mm.A Tinius–Olsen Universal Testing Machine (capacity 27,215N (60,000 lb)) was used forflexural testing. The maximum load was attained in 5min and the loading rate of 0.08N/swas used. Completely damaged specimens were loaded to failure while the partiallydamaged specimens were loaded to 80% of the failure load.

Comparison of Damaged and Undamaged Beam Specimens

Table 5 shows the resonant frequency values for the undamaged, partially damaged andthe undamaged specimens. There was a 7.5% drop in the resonant frequency of the partiallydamaged beam specimens and a 34.2% drop for the fully damaged beam specimens.

As the beam was loaded in flexure, whitening of the core piles was observed at theinterface of the core and face sheets. The stresses developed at the interface of the core andfacesheets resulted in fracture of the core piles. Loss of contact between the core members

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

1 2 3 4 5

Dam

ping

rat

io

Undamaged beam

Mode number

Partially damaged beam

Completely damaged beam

Figure 9. Plot of mode number versus damping ratio for undamaged, partially damaged, and fully damagebeams.

Table 6. Comparison of damping ratios for undamaged, partially damagedand fully damaged beams.

Mode number

Dampingratio for

undamaged beam

Damping ratiofor partially

damaged beam

Damping ratio forcompletely

damaged beam

1 6.54E�03 1.27E�02 3.33E�022 7.25E�03 6.89E�03 1.37E�023 5.66E�03 6.80E�03 9.33E�034 4.23E�03 6.20E�03 1.18E�025 4.08E�03 6.79E�03 1.29E�02Average damping ratio 5.55E�03 7.87E�03 1.62E�02




and the facesheets increased the friction and thereby free vibrations of facesheets inrelation to the core. This initiated loss of stiffness of the sandwich panel. Resonantfrequency and damping coefficient are sensitive to the variation in damage state ofcomposite in response to either fatigue or impact loading [1]. The damping ratio of asystem is a function of its stiffness. As damage developed within the material, the stiffnessreduced in accordance with the damage, thereby increasing the damping ratio.Comparison of damping ratio for different sets of specimens is presented in Table 6.

The average damping ratio for the undamaged, partially damaged, and fully damagedspecimens was noted to be 0.55, 0.78, and 1.62%, respectively. The damping ratio for fullydamaged beams was found to be 193% higher than the baseline beams. The increase indamping is attributed to the friction between the damaged surfaces and the core piles, andthe increased free vibration due to loss of integrity in the local area of the damage. Figure 9plots the comparison of damping ratio for the first 5 modes of vibration for differentdamage states of the sandwich beam.

SUMMARY

The space accessible 3-D sandwich composite beam specimens were tested for vibrationresponse in this study. The findings from this study are summarized as follows.. When the 3-D sandwich beam specimens were tested for the flexural vibrations, the

average damping ratio was found to be 0.75%. The flexural mode of vibrations wasdominant as the specimen was excited at its geometric center.

. PUR foam in the interstitial spaces of the sandwich increased the damping ratio by 150%for 77% increase in weight. The number of modes of vibration were seen to have reducedto 2 as against 5 over the 0–800Hz frequency range for the foamed when compared to theunfoamed specimens. The increased friction between the foam and the core pilesprovided additional damping, thus increasing damping ratio by an average of 150%.

. Plates of 3-D sandwich composites having dimensions of 572� 299� 22mm were testedin the frequency range of 0–800Hz. In addition to the flexural modes, there was aprominence of torsional modes for the plate specimens. The average damping ratio forthe plate specimens was 0.76%.

. For a specimen size of 609� 101� 22mm which was tested to failure, approximately100–150 core piles were fractured as a combination of damage due to flexural failureand shear failure. This resulted in reduction in resonant frequency by an average of35% and increase in the damping ratio by 193%, respectively.

. In terms of vibration correlation to damage; approximately 6% core damage resulted in35% reduction in resonant frequency and 193% increase in damping ratio.

REFERENCES

1. Vaidya, U. K. (1993). Nondestructive Evaluation of Graphite Fiber Based Composites Using Acoustic andVibration Techniques, PhD dissertation, Auburn University.

2. Adams, R. D. (1987). Damping Properties Analysis of Composites, Engineering Materials Handbook, 206–217.

3. Li, Z. and Crocker, M. J. (2005). A Review on Vibration Damping in Sandwich Composite Structures,International Journal of Acoustics and Vibrations, 10(4): 159–169.

4. Chopra, A. (2000). Dynamics of Structures, Theory and Application to Earthquake Engineering, 2nd edn,Vol. 48, Prentice Hall, New Jersey.

5. Company Literature: www.earcomposites.com (Visited: April 22, 2005).




6. Rao, M. D. (2003). Recent Applications of Viscoelastic Damping for Noise Control in Automobiles andCommercial Airplanes, Journal of Sound and Vibration, 262(3): 457–474.

7. Nakra, B. C. (1976). Vibration Control With Viscoelastic Materials, Shock and Vibration Digest, 8(6): 3–12.

8. Schultz, A. B. and Warwick. D. N. (1971). Vibration Rresponse: A Non-destructive Test for Fatigue CrackDamage in Filament Reinforced Composites, Journal of Composite Materials, 5: 394–404.

9. Gibson, R. F. and Wilson, D. G. (1983). Dynamic Mechanical Properties of Fiber Reinforced CompositeMaterials and Structures, Shock and Vibration Digest, 15(2): 3–15.

10. Ross, D., Ungar, E. E. and Kerwin, E. M. (1959). Damping of Plate Flexural Vibrations by Means ofViscoelastic Laminate, Structural Damping, ASME, 49–88.

11. Li, Z. and Crocker, M. J. (2005). A Review on Vibration Damping in Sandwich Composite Structures,International Journal of Acoustics and Vibrations, 10(4): 159–169.

12. Li, Z. and Crocker, M. J. (2003). A Study of Damping in Sandwich Structures, In: Proceedings of the TenthInternational Congress on Sound and Vibrations, pp. 2301–2308, Stockholm, Sweden.

13. Mead, D. and Markus, J. S. (1969). The Forced Vibrations of a Three Layer, Damped Sandwich Beam WithArbitrary Boundary Conditions, Journal of Sound and Vibrations, 10(2): 163–175.

14. Nilsson, E. and Nilsson, A. C. (2002). Prediction and Mmeasurement of Some Dynamic Properties ofSandwich Structures with Honeycomb and Foam Cores, Journal of Sound and Vibration, 251(3): 409–430.

15. Company Literature: www.parabeam.nl (Visited: September 7, 2007)

16. Vaidya, A. S., Vaidya, U. K. and Uddin, N. (2005). Vibration Response of MultifunctionalSandwich Composites Applicable in Commercial Motor Vehicle Applications, SAMPE Conference,Long Beach, CA, USA.

17. Vaidya, U. K., Shriram, R. and Ricks, H. (2003). Vibration Damping Studies in Metal Foam CompositeSandwich Plates Subjected to Impact. In: Proceedings of the 10th International Congress on Sound andVibration, pp. 2375–2382, Stockholm, Sweden.

18. van Vuure, A. W., Pflung, J., Ivens, J. A. and Verpost, I. (2000). Modeling the Core Propertiesof Composite Panels Based on Woven Sandwich-fabric Preforms, Composites Science and Technology,60: 1263–1276.






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Vibration Response of 3-D Space Accessible Sandwich Composite