diseño de un equipo para la medición de la frecuencia natural en sistemas materiales multicapa

8/18/2019 Diseño de un equipo para la medición de la frecuencia natural en sistemas materiales multicapa

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Title: A vibrating reed apparatus to measure the natural frequency of multilayered thin films

Article Type: Review Article

Keywords: Vibration measurement; natural frequency; thin films

Corresponding Author: Dr. Fidel Fernando Gamboa Perera, Ph. D.

Corresponding Author's Institution: CINVESTAV UNIDAD MERIDA

First Author: Fidel Fernando Gamboa Perera, Ph. D.

Order of Authors: Fidel Fernando Gamboa Perera, Ph. D.; Alejandro López Puerto; Francis AvilésCetina; José Emilio Corona; Andrés Iván Oliva Arias

Abstract: An apparatus for measuring the natural frequency of sub-micrometric layered films in

cantilever beam configuration is presented. The instrument provides a very low uncertainty (∼ 1

mHz) when the sample under test is not removed from the grip, and ∼ 0.2 Hz if the sample is removed

from the grip and placed back. This high sensitivity renders the capability of measuring very small

frequency shifts upon deposition of sub-micrometric films over thicker substrates. In order to assess

the reliability of the apparatus, cantilever beams of 125 μm thick neat Kapton (substrate) and thin

layered films of Au/Kapton and Al/Au/Kapton of 200-250 nm film thickness were fabricated and their

natural frequency and damping factor were measured. Calculations of the natural frequency of such

beams by finite element analysis further support the accuracy of the experimental measurements.

Suggested Reviewers: Jon García BarruetabeñaIndustrial Technologies, Universidad de Deusto

[email protected]

Artur Chrobak

Institute of Physics , Silesia University

[email protected]

Stefano Amadori

Interdepartmental Center for Industrial Research, University of Bologna

[email protected]



Cover LetterSeptember 19, 2014

Dear Dr. K.T.V. Grattan

Editor-in-Chief

I am delivering to you the manuscript of my research work for submission to the

Journal Measurement.

The work is original and it is presented with the title: A vibrating reed

apparatus to measure the natural frequency of multilayered thin films

This work was made in LATEX, with the elsarticle.cls format. Please consider

that the bibliography is kept in separate file (biblio.bib). I have uploaded for

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I would really appreciate your attention to this letter. Any inquiries please feel free

to contact me.

Sincerely Yours

Corresponding Author

Fidel F. Gamboa Perera

CINVESTAV-MERIDA

Km 6 Antigua Carretera a Progreso

Apdo. Postal: 73, Cordemex

Mérida. Yucatán, C.P.: 97310

Tel: +52 01 999 942 94 00 Ext: 2265

Fax: +52 01 999 9812917

Email:[email protected]

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A vibrating reed apparatus to measure the natural frequency of

multilayered thin films

F. Gamboaa,∗, A. Lopezb,c, F. Avilesb, J. E. Coronaa, A. I. Olivaa

a Centro de Investigaci´ on y de Estudios Avanzados del IPN, Unidad Merida, Depto. de Fısica Aplicada, km

6 Antigua Carretera a Progreso, 97310 Merida, Yucat´ an, MexicobCentro de Investigaci´ on Cientıfica de Yucat´ an, A.C., Unidad de Materiales, Calle 43 #130, Col.

Chuburn´ a de Hidalgo, 97200 Merida, Yucat´ an, MexicocFacultad de Ingenierıa, Universidad Aut´ oma de Yucat´ an, Av. Industrias no contaminantes por Periferico

Norte, 97310 Merida, Yucat´ an, Mexico.

Abstract

An apparatus for measuring the natural frequency of sub-micrometric layered films in can-tilever beam configuration is presented. The instrument comprises a specially designed testrig with a sample holder, an electronic excitation source, a vibration sensor and an auto-mated software for the excitation and data recollection. The beam is excited by means of an air pulse and the oscillation amplitude of its free end is measured through a laser diode-photosensor arrangement. The instrument provides a very low uncertainty (∼ 1 mHz) whenthe sample under test is not removed from the grip, and ∼ 0.2 Hz if the sample is removedfrom the grip and placed back. This high sensitivity renders the capability of measuringvery small frequency shifts upon deposition of sub-micrometric films over thicker substrates.In order to assess the reliability of the apparatus, cantilever beams of 125 µm thick neat

Kapton (substrate) and thin layered films of Au/Kapton and Al/Au/Kapton of 200-250 nmfilm thickness were fabricated and their natural frequency and damping factor were mea-sured. Calculations of the natural frequency of such beams by finite element analysis furthersupport the accuracy of the experimental measurements.

Keywords: Vibration measurement; natural frequency; thin filmsPACS: 07.10.-h, 06.30.Ft, 68.60.Bs

1. Introduction

The natural frequency of an object is its vibrational fingerprint which depends on itsgeometry and the material conforming it, and its determination is of vital importance forpredicting resonant damages, amplifying electrical signals, or optimizing acoustical cavitiesand resonators [1]. Determination of the natural frequency plays a very important role in a

∗Corresponding author.Email address: [email protected] (F. Gamboa)

Preprint submitted to Measurement September 19, 2014

nuscript

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http://ees.elsevier.com/meas/viewRCResults.aspx?pdf=1&docID=8106&rev=0&fileID=264970&msid=035CBAAB-896B-4F7A-9644-6905B88EF322

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variety of fields such as mechanical resonators, sensors, instrumentation, and determination of elastic properties of materials [1–4]. The study of mechanical, acoustic, and sensing of prop-erties of solid materials has promoted the development of new methods and devices for thepurpose of vibration measurement. These devices span from torsion apparatuses to devicesfor measuring longitudinal or transverse vibrations, with a variety of excitation and detectionmethods [1, 5]. One of the applications of vibration measurements consist in correlating thechange in the measured natural frequency to an elastic property (such as Young’s modulus)or existent damage [3–6]. When the transverse vibrations of the a slender cantilever beam isused to this aim, the method is known as the vibrating reed method, which has the advantageof being non-invasive, allowing both frequency and damping analyses. Several vibrating reedapparatuses have been used in order to determine the material properties in a wide range of geometries and thicknesses, ranging from samples in bulk geometry [6, 7], thin films [8, 9]and nanostructured films [10, 11]. However, given their small thickness, the measurementsfor films at the micrometer thickness and bellow can be very challenging. Thin films are fre-

quently part of micro- and nano-electromechanical systems, and to know their fundamentalvibratory frequency is useful for a correct design, operation and reliability [ 12–14]. Applica-tions of thin films as electronic conductors and in nanosensors and actuators are extensive.For example, curved beams used in atomic force microcopy are used for measuring frequencyshifts and damping factors [11]. Thin films can also be used as bilayers cantilevers for remotetemperature sensors [15]. A doubly supported metallic beam configuration can be used forstudying the influence of overlapping length and adhesive joints, to obtain the variation of the resonance frequency, peak amplitudes and loss factor which is useful for vibration controlapplications [16]. However, accurate measurement of mechanical properties of materials inthin film geometry is known to be a challenging task [8, 17, 18]. The instrument designed forsuch an aim must provide high accuracy and low experimental uncertainty, and a vibratory

device seems to be excellent candidate for such a task. Therefore, details of a precise appa-ratus specifically designed and constructed for determining the natural frequency of layeredthin (sub-micrometer) films in cantilever beam configuration is presented herein. In order toevaluate the operation of the apparatus for the intended application, thin films comprisingone, two or three layers were fabricated and their natural frequency and damping factor weremeasured. To further support the reliability of the apparatus, finite element analysis wasused to predict the natural frequency of such layered systems and their results were comparedto the measurements conducted with the constructed apparatus.

2. Apparatus design and automation

2.1. Mechanical design

The mechanical components of the vibrational apparatus are identified in Fig. 1. Theapparatus comprises a 100 mm x 100 mm aluminum base-plate (#1) for the mechanicalsupport of all components. It is made of solid aluminum contributing to the mechanicalstability. This base-plate rests on a rubber pad (#2) which acts as a vibration isolator forreducing external perturbations. Four vertical screws (#3) join the base plate with an upper

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Figure 1: Mechanical components of the vibrating apparatus. 1- Base metallic plate; 2- Rubber pad; 3- Joinscrews; 4- Auxiliary plate; 5- C-shape arm; 6- Sample holder; 7- Straightedge mechanism; 8- Thin rubberstrip; 9- Flexible steel sheet; 10- Fixing screws for the steel sheet; 11- Adjustment screw; 12- Vibration sensor;13- Air valve; 14- Adjustable height crossbar; 15- Height adjustment screws for the air valve; 16- Supportcolumns; 17- Fixed crossbar; 18- Crossbar fixing screws.

auxiliary plate (#4), which supports the main elements of apparatus. A C-shaped arm (#5)is fixed in its center. The ends of the C-shaped arm contain both the sample holder (#6) andthe straightedge mechanism (#7) for adjusting the sample to similar conditions at each testfor reproducibility. Since an imperfect clamping is one of the most significant error sources[4, 19], the designed straightedge plays an important role on the measurements, especiallywhen the cantilever beam needs to be take out of the rig and measured different times. Aclose-up of one end of the C-shaped arm is detailed at the right side of Fig. 1. The sampleis clamped between a thin rubber strip (#8) and the top surface of an end of the C-shaped

arm (#5) by means of a flexible steel sheet (#9). Two screws (#10) fasten the steel sheetin one end while a screw at the mid-section (#11) is used to adjust the applied pressure tothe sample. The block with the vibration sensor (#12) is located under the sample edge.The block contains a laser diode and a photo-sensor to detect the oscillation amplitudesof the sample. The block height can be changed in order to adjust the best zone of thesample optical reflection. An air valve (#13) is positioned above the free-end of the samplewhich is fixed through an adjustable support system (#14 to #19). For sample oscillation,

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a controlled short pulse of air of a few milliseconds of duration is applied at the free-end of the sample.

2.2. Excitation and sensing arrangement

Figure 2 shows a schematic of the excitation and sensing arrangement that comprisesthe sample holder, an air valve and a vibration sensor arrangement. The sample is clampedby the holder at one of its ends comprising a cantilever beam configuration. A miniatureair valve [20] is gated during 20 ms to produce a short air pulse which is concentrated ona small area (∼ 1 mm2) at the free end of the sample. The air supplied to the valve ispreviously filtered and its pressure is controlled to 1 psi by means of a pressure regulator.The oscillation amplitude at the free end of the sample is measured through a laser diode-photosensor arrangement (see bottom part of Fig. 2). This design was chosen because itpermits an easy sample handling with high accuracy. A light beam emitted by an OPV332laser diode [21] is reflected by the bottom surface of the sample and detected by an UDT-455

photosensor [22]. For better pick up, both sensor components are positioned at an angle of 30 with respect to the perpendicular axis of the incidence plane. The laser beam spot is0.4 mm2 while the photosensor has an active area of 5.1 mm2. The photo-voltage registeredis a function of the displacement of the reflection surface with respect to the position of the photosensor [23]. This arrangement requires a sample surface with enough reflectanceto detect the vibration frequency. The reflectance of the Kapton foil used in this work assubstrate beam was enough for an adequate operation of the apparatus. However if thesample surface has not enough reflectance, a small area (∼ 6 mm2) can be covered with athin reflective coating to fulfill this purpose.

Figure 2: Excitation and sensing arrangement.

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2.3. Control and data acquisition

A schematic of the control and data acquisition system of the vibration apparatus is shownin Fig. 3. A data acquisition board NI USB-6216 [24] carries out the tasks of controlling

and acquiring the different signals used. A dedicated program developed in LabVIEW [25]controls and acquires the measurements. The air pulse is executed by means of a digitaloutput of the board and a conditioning circuit connected to the air valve by sending a 20 msprogrammed voltage pulse. A conditioning circuit increases the voltage in order to drive theair valve. The laser diode is powered by means of the board and a constant current circuit isapplied in order to maintain a constant light intensity. The oscillatory signal produced by theair pulse is sensed by the photosensor and registered by an analog input of the board. Theprogram developed in LabVIEW synchronizes the air pulse and the data acquisition of thevibration signal. For better definition of the natural frequency of the samples a fast Fouriertransform (FFT) is applied to the registered amplitude vs. time data.

Figure 3: Schematic of the control system and data acquisition.

3. Samples and material properties

In order to evaluate the performance of the vibration apparatus, several rectangular beamsof 24.0 mm as total length and 4.8 mm width (b) were obtained from a 125 µm thick 500HN KaptonR foil [26]. The free beam length (effective length) of the cantilever is l = 21.0mm, and 3 mm overhang were allowed for edge clamping. First, ten repetitive vibration

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measurements of a baseline Kapton beam were conducted in order to evaluate the uncer-tainty of the apparatus. Afterwards, a group of four rectangular Kapton beams of identicaldimensions were cut as substrates for subsequent metallic film deposit using a thermal evap-oration technique. Before the film deposition, the Kapton substrates were ultrasonicallycleaned with isoprophylic alcohol and distilled water. During the film growth the thicknessof the films were measured in situ with a quartz crystal sensor and monitored with a Max-tek 400 controller with ± 0.1 nm accuracy. Initially, four of the Kapton substrates wereplaced closely inside the thermal deposition chamber in order to deposit a 250 nm thick gold(Au) layer to produce four Au/Kapton identical specimens. After vibration measurementsof the Au/Kapton beams a new 200 nm thick layer of aluminum (Al) was deposited overthem, forming in this way four Al/Au/Kapton three-layered samples, see Fig. 4. New vibra-tion measurements of those three-layered samples were performed. Given that the vibratorymeasurement technique is not destructive, it allows us the use of the same specimens forsequential film deposition. Table 1 shows a summary of the thicknesses, elastic modulus (E )

Sampleholder

Au (250 nm) Al (200 nm)

Kapton (125 m)

l = 21.0 mm3 mm

Figure 4: Schematic of the Al/Au/Kapton multilayered beams fabricated.

and density (ρ) of the Kapton substrate and the deposited metallic layers. The values E andof ρ were taken from references [10] and [27].

Table 1: Thickness, elastic modulus (E ) and density (ρ) of the beam constituents.

Material Thickness (µm) E (GPa) ρ (kg/m3)

Substrate (Kapton) 125 3.64 1420

Film #1 (Au) 0.25 69.1 19320

Film #2 (Al) 0.20 78.0 2699

4. Finite element analysis

The vibratory measurements conducted on single-layered and multilayered thin films werefurther supported by calculations of the natural frequency based on finite element analysis

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(FEA). The model was constructed by a beam of length l, width b and total thicknessh consistent with the experimental conditions and the layer properties given in Table 1.Tridimensional FEA was conducted by using the commercial software ANSYS R 11.0 [28]employing a solid layered element (“SOLID46”) with translational degrees of freedom ateach node. This layered element allows the definition of layer-by-layer properties which issuitable for modeling multi-layered materials. A typical layered beam was constructed with3,930 solid elements using a mesh of 30 elements in the width direction and 131 elementsin the length direction with one element through the thickness. Aspect ratios of 1.0 in thex-y plane and 1.2 in the y-z plane were used for analysis, see Fig. 5. Zero deflection atthe clamped edge was considered and the natural frequency of the beam under transversevibrations (W(x, t)) was numerically found by solving the resulting modal eigenvalue problem.

Figure 5: Finite element model of a vibratory beam.

5. Results and discussions

5.1. Reproducibility and uncertainty

The uncertainty and reproducibility of the apparatus were first evaluated. To this aim,natural frequency measurements of the Kapton beam were conducted. The first experi-ment consisted in conducting ten sequential vibratory measurements, maintaining the beam

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clamped. The ten measurements conducted in this way yielded frequencies with an averageof 74.6 Hz whose maximum difference was only 1 mHz, evidencing the high reproducibilityof the apparatus. One of the key factors governing the uncertainty in this kind of vibrationexperiments is the boundary conditions (clamping force). Therefore a second set of experi-ments conducted consisted in repeating the vibration measurements on a given sample butremoving the sample from the apparatus (clamp) after each measurement. The straightedgedevice shown as #7 in Fig. 1 assisted in positioning the sample back at, in principle, thesame position, after each test. Figure 6 shows the results of the ten replicated experimentsconducted in this way, using the frequency domain. As seen from this figure, a narrow dis-persion of the curves with low experimental uncertainty is achieved in the measurements.The average frequency measured is 74.6 Hz with maximum deviations from this value of ±0.2 Hz and a coefficient of variation of only 0.18 %

Figure 6: Ten measurements of natural frequency of the same Kapton beam, removed from the grip andplaced back.

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5.2. Measurement of the natural frequency in multilayers

The natural frequency of cantilever beams comprising one (Kapton), two, (Au/Kapton)and three (Al/Au/Kapton) layers was measured by means of the constructed apparatus.

Figure 7 shows typical vibratory measurements of the three beam architectures investigated.The left side of Fig. 7 shows the normalized amplitude of vibration as a function of elapsedtime, indicating the period (T) for the Kapton (a), Au/Kapton (b) and Al/Au/Kapton (c)beams. The right side of Fig. 7 shows the FFT of each corresponding signal, in the frequencydomain. Periods of T = 13.4 ms, 12.9 ms and 12.3 ms corresponding to f n = 74.6 Hz, 77.5Hz and 81.1 Hz are identified for Kapton (a), Au/Kapton (b) and Al/Au/Kapton (c) beams,respectively. As seen from this figure an important frequency shift, at least an order of

Figure 7: Representative vibratory measurements conducted on multilayered beams using the constructedapparatus. a) Kapton, b) Au/Kapton, c) Al/Au/Kapton beams. Left side shows a period (T) in the timedomain while right side shows the FFT in the frequency domain.

magnitude larger than the determined experimental uncertainty of the apparatus (∼ 0.2 Hz)is detected when additional thin metallic layers (200-250 nm thick) are added to the Kapton

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beam. Table 2 lists a summary of the fundamental frequencies measured (average valueand standard deviation), considering the four tested replicates for each layered system. Anincrease in f n is observed when each layer is added, which corresponds to the added massand stiffness upon film deposition. An important issue to point out is that such changes inf n are due to the deposit of very thin (200 and 250 nm thick) metallic films and the proposedapparatus has enough resolution to detect such small changes in natural frequency. Thesechanges in frequency can be associated to the change in effective stiffness of the beam, and,if a proper data reduction model is used, the elastic modulus of each layer could be obtainedby this technique, see e.g. [29].

Table 2: Measured natural frequency of the four layered beams with dimensions of l = 21 mm and b = 4.8mm. The thickness of each layer is indicated in Table 1.

Beam

No.

f n (Hz)

Kapton Au/Kapton Al/Au/Kapton

1 74.6 ± 0.1 77.5 ± 0.2 81.1 ± 0.2

2 74.6 ± 0.2 77.5 ± 0.3 80.9 ± 0.2

3 74.5 ± 0.2 77.6 ± 0.2 81.1 ± 0.2

4 74.6 ± 0.3 77.5 ± 0.3 81.2 ± 0.3

5.3. Damping analysis

In vibration experiments, the amplitude of oscillation decreases with the elapsed timebecause of friction with the air and the test rig. This damping can be characterized by thedamping factor (ζ ), which is a function of the logarithmic decrement (δ ). This decrement δ

is defined as the ratio of two consecutive amplitudes W 1 and W 2 (see Fig. 8), i. e.,

δ = ln

W1

W2

. (1)

The damping factor ζ can be determined from δ by means of the relationship [1],

ζ = δ (2π)2 + δ 2

. (2)

For the case of the investigated beams, Fig. 9 shows two consecutive amplitudes (normalized)

considering that W 1 = 1, which facilities the calculations of the damping factor. For thecases presented in Fig. 9, W 2 = 0.9880, 0.9815 and 0.9800 for the Kapton, Au/Kaptonand Al/Au/Kapton layered systems, respectively. The inset in Fig. 9 shows the completevibratory oscillation for 1 second, indicating a slow decay in the vibrating amplitude. Thevibratory parameters (ζ and δ ) extracted from the vibratory curves measured are listed inTable 3. Very small damping factors ranging between 0.0019 and 0.0034 were obtained forall the investigated multilayer system, given their low mass.

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Figure 8: Schematic representation of the oscillatory response of a beam under damped transverse vibrations.

Table 3: Logarithmic decrement (δ ) and damping factor (ζ ) corresponding to vibration experiments of Kapton, Au/Kapton and Al/Au/Kapton beams.

Beam δ ζ

Kapton 0.0121 0.0019

Au/Kapton 0.0192 0.0030

Al/Au/Kapton 0.0219 0.0034

5.4. Comparison with finite element analysis

FEA was used to predict the fundamental frequency of the tested beams in order tofurther support the reliability of our apparatus. Table 4 shows the FEA predictions of thenatural frequency along with the average and standard deviation of the measured frequency.An excellent agreement is observed between the measured data and the FEA predictions. Theslight differences observed are practically within the experimental scattering, which providesfurther reliability to the constructed apparatus for measuring natural frequencies of thinmultilayer beams.

Table 4: Measured natural frequency and FEA predictions of the layered beams.

Beam f n (Hz)

Measured FEA

Kapton 74.6 ± 0.3 74.6

Au/Kapton 77.5 ± 0.3 77.7

Al/Au/Kapton 81.2 ± 0.3 80.8

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Figure 9: Close-up of the first oscillation amplitude used to determine the damping factor of the layeredbeams. a) Kapton, b) Au/Kapton, c) Al/Au/Kapton. Insets show the full oscillatory signal for 1 s.

6. Conclusions

A vibratory apparatus was introduced for measuring the natural frequency of thin (mi-crometric or sub-micrometric) layered beams. The apparatus consists of an aluminum framewith a C-shaped arm holding the sample in cantilever configuration. The excitation-sensingarrangement uses a controlled air pulse applied at the free-end of the cantilever beam and anoptical system for sensing the vibratory amplitude. A commercial data acquisition board andan in-house software were used for the control and data acquisition. A high reproducibilitywas found in the constructed apparatus with a maximum uncertainty of 1 mHz if the sampleis not removed from the clamp. When the sample is removed from the apparatus and placedback, the coefficient of variation of ten measurements is only ∼ 0.2 %. Kapton, Au/Kaptonand Al/Au/Kapton layered beams were fabricated and their natural frequency was measuredusing this apparatus. The average measured frequency for the three layered system was 74.6

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Hz (Kapton), 77.5 Hz (Au/Kapton) and 81.2 Hz (Al/Au/Kapton) and the shifting uponthin film deposition is at least an order of magnitude larger than the detected experimentaluncertainty of the apparatus. The measured frequencies for the multilayered beams agreewell with finite element analysis computations, which provide further confidence to the ap-paratus. With an appropriate data reduction model, this shift could used, for example, fordetermination of elastic modulus or assessing delimitation or damage in multilayered beamsand others thin film structures.

Acknowledgements

The authors wish to thank O. Gomez (CINVESTAV), Alejandro May (CICY) and CesarVillanueva (FI-UADY) for their technical support.

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http://optekinc.com/















http://www.osioptoelectronics.com/




















http://sine.ni.com/ds/app/doc/p/id/ds-9/lang/es




























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http://www.ni.com/labview








http://www2.dupont.com/Kapton















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ampleholder

Au (250 nm) Al (200 nm)

Kapton (125 m)

l = 21.0 mm3 mm

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eX Source manuscript

k here to download LaTeX Source Files: newarticle_fgamboa.tex

http://ees.elsevier.com/meas/download.aspx?id=264925&guid=132f3c23-a7b5-45ac-b735-932af00fc9ce&scheme=1

http://ees.elsevier.com/meas/download.aspx?id=264925&guid=132f3c23-a7b5-45ac-b735-932af00fc9ce&scheme=1



eX bibliography

k here to download LaTeX Source Files: biblio.bib

http://ees.elsevier.com/meas/download.aspx?id=264926&guid=33aa0c47-ec84-400a-a47d-6d30de709e79&scheme=1

http://ees.elsevier.com/meas/download.aspx?id=264926&guid=33aa0c47-ec84-400a-a47d-6d30de709e79&scheme=1

diseño de un equipo para la medición de la frecuencia natural en sistemas materiales multicapa

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