(Open Access) Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals. (2017) | Marco Miniaci

Q: What are the contributions mentioned in the paper "Proof of concept for an ultrasensitive technique to detect and localize sources of elastic nonlinearity using phononic crystals" ?

In this paper, Miniaci, A.M. Gliozzi, B.S. Morvan, Krushynska, F. Bosia, M. Scalerandi, and N.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic

Nonlinearity Using Phononic Crystals

M. Miniaci,

A. S. Gliozzi,

2,*

B. Morvan,

A. Krushynska,

F. Bosia,

M. Scalerandi,

and N. M. Pugno

4,5,6

University of Le Havre, Laboratoire Ondes et Milieux Complexes, UMR CNRS 6294, 75 Rue Bellot, 76600 Le Havre, France

Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Department of Physics and Nanostructured Interfarces and Surfaces Centre, University of Torino,

Via Pietro Giuria 1, 10125 Torino, Italy

Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering,

University of Trento, Via Mesiano 77, 38123 Trento, Italy

School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom

Ket Lab, Edoardo Amaldi Foudation, Italian Space Agency, Via del Politecnico snc, 00133 Rome, Italy

(Received 23 December 2016; published 26 May 2017)

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive

indicators of the onset of material damage. However, these effects are usually very small and can be

detected only using cumbersome digital signal processing techniques. Here, we propose and exper-

imentally validate an alternative approach, using the filtering and focusing properties of phononic crystals

to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization

of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its

potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and

damage detection.

DOI: 10.1103/PhysRevLett.118.214301

In recent years, phononic crystals (PCs) have attracted

great attention due to their unconventional dynamic behav-

ior, with effects such as negative refraction [1], frequency

band gaps [2,3], wave filtering or focusing [4–6], acoustic

cloaking [7–9], subwavelength sensing [10,11], etc. Their

periodic structure, rather than single material constituents,

is responsible for their behavior, which exploits Bragg

scattering [12,13]. Their attractive properties to act as stop-

band filters [12] or to concentrate energy in selected

frequency ranges [14] makes them potentially interesting

for nonlinear elastic source detection and to reveal the

presence of defects, e.g. cracks, in a sample. This is

because, in general, a nonlinear response is generated at

the defect location and several possible features may

appear, including the generation of higher order harmonics

[15–17] or subharmonics [18,19], the nonlinear depend-

ence of the elastic modulus and of attenuation coefficients

on strain [20–22], and, as a consequence, the shift of the

resonance frequency with increasing excitation amplitude

[23,24] and the failure of the superposition principle

[25,26]. All of these possible signatures can be used to

detect and monitor the presence and evolution of damage,

exploiting the greater sensitivity of nonlinear detection

techniques compared to conventional linear ones [27].

In the past years, nonlinear imaging techniques such as b

scan, c scan, and tomography [28] have attracted much

interest. A particularly robust and efficient approach is the

combination of time reversal (TR) and nonlinear elastic

wave spectroscopy (NEWS). This technique (TR-NEWS)

exploits space-time focusing of the wave field achieved in

TR [29] and applies it to a defect acting as a source of

nonlinear elastic waves [30–33]. The scattered signal is

recorded, the frequency generated by the primary source is

filtered out using a bandpass filter, and the resulting signal

is time reversed and reinjected by the receiver: due to the

(t → −t) symmetry, the wave field back propagates to its

original (nonlinear) source, focusing energy at the defect

location at a specific time. Many studies have proved the

efficiency and robustness of TR-NEWS in various con-

figurations, for different types of nonlinear sources [34–36]

and in assorted experimental conditions [31]. However,

TR-NEWS relies—as do most of the techniques for both

the detection and the location of damage—on extensive

signal manipulation (normally, digital filtering), which

might be critical in the case of short signals and/or when

continuous signal acquisition is required (such as in

acoustic emissions). Furthermore, the nonlinear compo-

nents of the wave field are often very small, if not

submerged by the noise level, making it difficult to detect

and estimate them. The concept adopted in this Letter

overcomes these limitations, combining TR-NEWS and

phononic crystals in order to introduce a technique capable

of filtering out and concentrating energy in target frequency

ranges. We experimentally demonstrate the feasibility and

the efficiency of this technique, providing the proof of

concept for an ultrasensitive phononic crystal device to

detect and localize nonlinear elastic sources such as cracks

or delaminations.

A schematic representation of the experimental setup is

given in Fig. 1. The sample is a pristine 300 × 300 × 3 mm

aluminum plate (the density ρ ¼ 2700 kg=m

, the Young’s

modulus E ¼ 70 GPa, and the Poisson’s ratio ν ¼ 0.33),

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attached to which is a device, consisting of two phononic

crystal regions (referred to as PC1 and PC2, respectively).

PC1 consists of a 1D array of eight crosslike cavities cut in a

narrow rectangular waveguide and PC2 of a C-shaped array

of smaller unit cells. The cavities are fabricated using water-

jet cutting, with different lattice parameters depending on the

filtering [Fig. 1(b)] or reflecting [Fig. 1(c)] function that they

are designed for. Specifically, the lattice parameters are

¼ 8 mm, L

¼ 0.9L

, and L

¼ 2R ¼ 0.3L

for PC1

and l

¼ 4 mm, l

¼ 0.9l

, and l

¼ 2r ¼ 0.3l

for PC2,

respectively. A crosslike geometry is chosen because it

allows large band gap (BG) nucleation [38].

In order to investigate the BG structure of the PC1

region, its transmission spectrum is first investigated in a

pitch-catch experiment [38] according to the schematic

representation of Fig. 1(a) (see Ref. [39] for details). An

ultrasonic pulse with a frequency content between 50 and

450 kHz is launched by a transducer attached to the top

surface of the plate [point E in Fig. 1(a)] and received at

points A and B using 5-mm-diameter piezoelectric disk

sensors. Figure 2(a) shows the fast Fourier transform (FFT)

of the input signal in E (the green line) and those recorded

in A and B (the blue and red lines, respectively). A large BG

appears between 172 and 244 kHz, highlighted by a

considerable frequency drop at the corresponding frequen-

cies (up to 100 dB). Three smaller BGs are visible around

153, 285, and 380 kHz. On the contrary, the spectral

content of the signal recorded in the plate [the blue line in

Fig. 2(a)], which is not subject to any filtering, shows the

same frequency content as the excitation. These results are

in agreement with numerically computed dispersion dia-

grams using Bloch-Floquet theory [41] in full 3D FEM

simulations [Fig. 2(b)]. Here, the band structure is shown in

terms of the reduced wave vector k



¼½k

=π; k

=π,

varying along the first irreducible Brillouin zone boundary

Γ − X, with colors indicating mode polarization [39]. The

BGs are highlighted in grey.

Further information on the dynamical properties of the

PC1 region is obtained by injecting a short pulse at point E

and using a scanning laser Doppler vibrometer (SLDV) to

measure the out-of-plane component of the velocity at the

surface along the dotted path highlighted in Fig. 1(a)

(a) (c)

(b)

FIG. 1. (a) Schematic representation of the specimen composed

of an aluminum plate connected to a filtering phononic crystal

region (PC1) and a chaotic cavity [37] with an additional focusing

phononic crystal–based structure (PC2). Three-dimensional view

of the unit cells for (b) the PC1 region and (c) the PC2 region.

Frequency (kHz)

0 1

100

200

300

400

500

0.2

0.4

0.6

0.8

0.05 1 50

100

200

300

400

500

Norm. FFT

Frequency (kHz)

(a)

(b)

FIG. 2. (a) Experimental normalized transmission frequency

spectrum and (b) the corresponding numerically predicted

dispersion band structure for the PC1 region. Mode polarization

is indicated by color, ranging from pure in plane (blue) to pure out

of plane (red).

(a)

(b)

Norm. ampl.

FIG. 3. (a) Out-of-plane displacement as a function of time t and

position d along the dotted line in Fig. 1(a). White areas correspond

to the crosslike cavities of the PC1 region. (b) Frequency f vs wave

number k representation of the measured signals. Theoretical

dispersion curves (in white) are superimposed.

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(details are provided in the Supplemental Material [39]).

Results for the space-time evolution of the measured

amplitudes are shown in Fig. 3(a). Because of the excita-

tion, mainly antisymmetric A0 Lamb waves are generated.

However, Fig. 3(a) also clearly shows the presence of the

S0 mode (i.e., the faster waves visible in the t ¼ 40 μs

region), derived from direct generation by the transducer.

Strong reflections of the incident waves are clearly visible

at a distance d ¼ 50 mm (corresponding to the first cavity

in the PC1 waveguide) due to Bragg scattering from PC1.

Finally, Fig. 3(a) highlights a slight variation of the slope

for the modes crossing the PC1 region, corresponding to

a gradual decrease of the wave speed with the distance

traveled in PC1.

The signals detected at various positions along the path are

processed by applying a two-dimensional (2D) FFT and

determining the energy values for each processed point. This

enables us to obtain a frequency wave number representation

[Fig. 3(b)]. Data are shown for the d1 acquisition region of

the plate (i.e., from d ¼ 0 up to the first cavity), with negative

and positive values of the wave number k

corresponding to

reflected and incident waves, respectively. This representa-

tion clearly identifies the energy distribution among the

excited modes. The energy maxima of the reflected waves

[Fig. 3(b), left panel] occur near the predicted BG frequency

range, i.e. around 200 and 380 kHz, associated with the

incident A0 mode [Fig. 3(b), right panel]. The excited

S0-mode frequencies are greater than 450 kHz [see

Fig. 3(b)], i.e., outside the PC1 BG. In this frequency range,

the polarization of the propagating waves in PC1 is pre-

dominantly in plane [see Fig. 2(b)]. Therefore, most of the S0

wave field appears to be reflected since the SLDV setup is

mainly sensitive to out-of-plane components (see also the

Supplemental Material [39]). Numerically predicted

dispersion curves (the white lines) are superimposed onto

the experimental data, showing excellent agreement (see also

the Supplemental Material [39]).

The PC1 region thus acts as a natural filter for frequencies

in the 172–244 kHz range. The excitation of a nonlinear

elastic material with a monochromatic wave of frequency

falling inside the BG of PC1 (e.g., 200 kHz) produces higher

harmonics in the plate that can cross the PC1 barrier and

enter the circular “chaotic cavity” [37]. Owing to its ergodic

properties and negligible absorption, the latter is widely used

in TR experiments to generate multiple reflections and a

reverberant acoustic field, making a single transducer

sufficient for signal acquisition [37,42,43]. The additional

C-shaped phononic crystal structure (PC2) is designed to

reflect the higher harmonics of the signal falling within the

BG and to concentrate them in the geometric center of the

mirror, thus enhancing their signal-to-noise ratio. Analysis

of SLDV-measured signals filtered at the frequencies of

interest shows that there is good energy concentration at the

center of the mirror structure compared to peripheral regions

in the chaotic cavity [39].

Additional FEM transmission simulations using the

ABAQUS

software are performed. The incoming wave is

the superposition of two quasimonocromatic waves cen-

tered around f

¼ 200 kHz and f

¼ 400 kHz, respec-

tively, with an imposed out-of-plane displacement of

1 × 10

−6

mm at point E. Two models are compared:

one comprising both the filtering and focusing regions

and another consisting of only the filtering region (i.e., with

a homogeneous aluminum chaotic cavity). Figures 4(a) and

4(b) provide snapshots of the von Mises stress maps at

t ¼ 160 μs for the two configurations. In the case of the

chaotic cavity with the C-shaped structure, the formation of

stationary waves occurs between the vertical portion of the

mirror and the beginning of the waveguide. This allows the

focusing of the energy of the wave at the frequency f

(i.e.,

the signature of the nonlinearity) to be enhanced.

The possibility of combining both the filtering and

focusing functionalities of the device for TR-NEWS is

now demonstrated. As discussed, the higher harmonics

generated by the nonlinear source are transmitted through

the PC1 region without the need for any postprocessing

procedure (e.g., FFT). This allows the signal recorded by

the sensor in the C-shaped mirror to be readily inverted and

retransmitted into the sample. On the other hand, the PC2

region allows us to focus energy of the second harmonic in

order to enhance the signal-to-noise ratio in TR.

To perform the TR experiment, two piezoelectric disk

transducers (PZT 1, 1.25 cm=1 MHz, and PZT 2, 5 mm)

are placed on the plate at points C and B [Fig. 1(a)], with

the latter acting both as a receiver and as an actuator in the

forward and backward TR propagation steps, respectively.

Higher order harmonics are locally generated in the linear

elastic plate by inducing the wave field to interact with an

obstacle (e.g., a small cylinder, 8 mm in diameter and

20 mm high, placed on the surface of the sample at a point

D) whose contact surface has been previously humidified.

The emergence of nonlinearity can be ascribed to two

different reasons: the first is the fact that the two surfaces

are in “clapping” contact [44], mimicking the behavior of a

(a) (b)

FIG. 4. Snapshots of the von Mises stress (in Pa) inside the

chaotic cavity showing the energy focusing by (a) the C-shaped

phononic structure in comparison with (b) a homogeneous

chaotic cavity at t ¼ 160 μs.

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macroscopic crack in the sample; the second is due to the

intrinsic nonlinear elastic behavior of water [45], amplified

by the presence of the small cylinder. The sample (with and

without the nonlinear element) is excited by a source of the

form

YðtÞ¼Y

¼ A

sinð2πf

tÞHðt

Þ; ð1Þ

where A

is the amplitude of the sine function and Hðt

Þ is

the Hanning window centered in t

with a width corre-

sponding to 21 cycles of the sine wave of the frequency f

The time and frequency domain representations of the

signal received by PZT 2 are shown in Figs. 5(a) and 5(b),

respectively. In the case without the nonlinear scatterer,

only noise is recorded inside the cavity (the red signal),

whereas, in the presence of the artificial nonlinearity, a

resonance peak appears (the blue signal) around the second

harmonic (i.e., f

¼ 2f

¼ 400 kHz).

The TR-NEWS experiment is thus performed as follows:

the PZT 1 transducer emits a signal Y ¼ Y

[Eq. (1)]; the

signal detected by PZT 2 [the blue signal in Fig. 5(a)]is

time reversed and transmitted back in the sample. SLDV

measurements are performed on a spatial grid covering a

30 × 30 mm

region around the nonlinear source (removed

in the back propagation experiment) consisting of 200 ×

200 equally spaced grid points. The laser vibrometer is

positioned perpendicularly at 50 cm from the surface to

record the out-of-plane velocities of the points over the

target area. Multiple (128) measurements are performed

and averaged for each node, to filter out part of the noise.

After the backward propagation, time compression of the

signal and spatial focusing of the wave field are observed

at the nonlinear scatterer location. Figure 5(c) reports an

example of a time recompressed signal detected with

the SLDV. Also, at the focal time, the spatial map of the

recorded velocities reveals focusing at the location of the

defect, with a considerable concentration of energy, as

shown in Fig. 5(d).

The bandwidth and performance of the C-shaped mirror

is evaluated by means of an additional experiment: PZT 1 is

used to emit pulses [Eq. (1)] with variable frequencies in

BG1 (170 <f

< 240 kHz) and a controlled nonlinearity

is introduced by replacing the nonlinear scatterer with a

transducer PZT 3 emitting pulses [Eq. (1)] in the same time

interval with amplitude A

¼ kA

(k ≪ 1) and frequency

¼ 2f

, thus simulating the generation of second order

harmonics. Signals received in the cavity are time reversed

and the signal is detected by PZT 3. The quality of the

focusing is evaluated as the ratio between the amplitude of

the signal at the focal time and the root mean square (rms)

of the signal excluding the peak. Results are shown in

Fig. 6. Four frequency ranges are identified. (i) For 170 <

< 180 kHz and 235 <f

< 240 kHz, the focusing is

very poor even for high levels of nonlinearity (large k) since

does not fall in BG2, so there is no effect of the mirror

[see also Fig. 6(c)]. (ii) For 180 <f

< 190 kHz, focusing

is poor, even though the mirror is expected to be effective.

This is due to the presence of a band gap in PC1 at f

that

prevents the second harmonic from reaching the device.

(iii) For 190 <f

< 235 kHz, the presence of the mirror

falls in BG2) allows a significant improvement in the

quality of the focusing [see also Figs. 6(b) and 6(d)]. Thus,

the PC2 is effective even for very small nonlinearity levels

(k ¼ 0.005), for which focusing is absent outside the mirror

operating frequencies.

In conclusion, we have presented combined experimen-

tal and numerical results to demonstrate the feasibility of a

novel passive sensor for signals generated by nonlinear

elastic scatterers, such as cracks and delaminations. To do

this, we have exploited the advanced frequency filtering

and spatial focusing properties of phononic crystals, and we

have proved the applicability of the sensor to time-reversal

experiments that allow us to determine the spatial location

(a) (b)

()

)(

()

)(

Norm. out-of-plane velocity

FIG. 5. (a) Time and (b) frequency domain representations of

the signals without (red) and with (blue) the nonlinear (NL)

source acquired inside the C-shaped mirror. Note the difference in

frequency content. Evidence for (c) time and (d) spatial refocus-

ing onto the nonlinear source location.

FIG. 6. Bandwidth of the proposed device for time reversal.

(a) Quality of the focusing (signal-to-noise ratio ) vs frequency.

(b)–(d) Time-reversed signals for various nonlinearity levels and

frequencies.

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of damage. A time-reversal experiment was carried out,

showing good refocusing in time and space onto the

nonlinear source, demonstrating the feasibility of the

proposed device for damage localization in structures.

The imaging results indicate that the PC mirror is necessary

to achieve ultrasensitive detection, particularly when the

nonlinear signature of the features to be localized is very

small, and could provide additional functionalities such as

frequency-selective focalization on multiple nonlinear

scatterers with different characteristic frequencies.

In the future, we aim to improve the design of this PC

sensor addressing issues such as optimized filter or focusing

mirror designs, exploitation of multiple band gaps, or

frequency tunability using piezoelectric patches, and its

effective application to external tested structures with

reduced signal losses. Nevertheless, the results presented

in this Letter already provide the proof of concept for an

efficient, portable damage sensor with applications for

passive continuous structural health and acoustic emission

monitoring in, e.g., civil engineering and the aerospace

industry.

M. M. has received funding from the European Union’s

Horizon 2020 research and innovation program under

Marie Skłodowska-Curie Grant Agreement No. 658483.

A. K. has received funding from the European Union’s

Seventh Framework program for research and innovation

under Marie Skłodowska-Curie Grant Agreement

No. 609402-2020 researchers: Train to Move (T2M).

N. M. P. is supported by European Research Council

PoC 2015 “Silkene” No. 693670, by the European

Commission H2020 under Graphene Flagship Core 1

No. 696656 (WP14 “Polymer Nanocomposites”) and

FET Proactive “Neurofibres” Grant No. 732344. F. B. is

supported by Neurofibres Grant No. 732344.

antonio.gliozzi@polito.it

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PHYSICAL REVIEW LETTERS

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Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

Figures

Citations

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References

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Frequently Asked Questions (1)

Q1. What are the contributions mentioned in the paper "Proof of concept for an ultrasensitive technique to detect and localize sources of elastic nonlinearity using phononic crystals" ?