materials

Article
An Influence of Actuator Gluing on Elastic Wave Excited in
the Structure
Dominika Ziaja *,† and Michał Jurek †

Department of Structural Mechanics, Rzeszow University of Technology, ul. Poznańska 2,

35-084 Rzeszów, Poland; mjurek@prz.edu.pl
* Correspondence: dziaja@prz.edu.pl; Tel.: +48-17-865-1622
† These authors contributed equally to this work.

Abstract: In this article, the practical issues connected with guided wave measurement are studied:
(1) the influence of gluing of PZT plate actuators (NAC2013) on generated elastic wave propagation,
(2) the repeatability of PZT transducers attachment, and (3) the assessment of the possibility of
comparing the results of Laser Doppler Vibrometry (LDV) measurement performed on different
2D samples. The consideration of these questions is crucial in the context of the assessment of
the possibility of the application of the guided wave phenomenon to structural health-monitoring
systems, e.g., in civil engineering. In the examination, laboratory tests on the web of steel I-section
specimens were conducted. The size and shape of the specimens were developed in such a way
that they were similar to the elements typically used in civil engineering structures. It was proved
that the highest amplitude of the generated wave was obtained when the exciters were glued using
wax. The repeatability and durability of this connection type were the weakest. Due to this reason,
it was not suitable for practical use outside the laboratory. The permanent glue application gave
a stable connection between the exciter and the specimen, but the generated signal had the lowest
amplitude. In the paper, the new procedure dedicated to objective analysis and comparison of the
elastic waves propagating on the surface of different specimens was proposed. In this procedure, the
genetic algorithms help with the determination of a new coordinate system, in which the assessment
of the quality of wave propagation in different directions is possible.

Keywords: guided waves; laser Doppler vibrometry; genetic algorithms

Citation: Ziaja, D.; Jurek, M. An

Influence of Actuator Gluing on
Elastic Wave Excited in the Structure. 1. Introduction
Materials 2024, 17, 2160. https://
Guided wave propagation is one of the mechanical phenomena used in the damage
doi.org/10.3390/ma17092160
detection of engineering structures [1,2]. Particles of a solid continuous medium, thrown
Academic Editor: Fengming Li out of equilibrium, vibrate. The excited waves, traveling throughout the material, reflect
Received: 6 March 2024
from boundaries or defects in the material. It does not destroy the element. For this reason,
Revised: 5 April 2024
the analysis of wave propagation is a valuable source of information about the structure of
Accepted: 24 April 2024 the material, as well as the condition of the examined specimen.
Published: 6 May 2024 The NDT techniques, connected with guided wave measurements, can be divided
into (1) contact-less and (2) contact methods. In the first case, Laser Doppler Vibrometry
(LDV) is used, while in the second one, wave measurement can be made using ultrasonic
probes, piezoelectric wafers and piezocomposite transducers, inter-digital transducers, or
Copyright: © 2024 by the authors. fiber-optic sensors [1]. Regardless of the selected wave measurement method, the wave
Licensee MDPI, Basel, Switzerland. has to be excited in the material. It also can be made contact-less (e.g., using air-coupled
This article is an open access article excitation or laser sources [3]) or using exciters touching to the examined surface [4]. As the
distributed under the terms and most popular exciters, PZT wafers/elements can be pointed. They are glued on the surface
conditions of the Creative Commons
of the structure or inside it (e.g., between layers of composites [5] or embedded inside
Attribution (CC BY) license (https://
the specimen on a reinforcement bar [6]). The last case is possible only if SHM system
creativecommons.org/licenses/by/
installation was planned before the production of the structure. In many cases, the decision
4.0/).

Materials 2024, 17, 2160. https://doi.org/10.3390/ma17092160 https://www.mdpi.com/journal/materials

Materials 2024, 17, 2160 2 of 14

to structure monitoring is made after that, so this solution is not possible. In the case of
real structures operating in real conditions, the problem is the inability to ensure stable and
repeatable excitation conditions using the air-coupled method. The influence of the external
environment can significantly affect the excited wave. Due to these reasons, it seems like
the gluing of exciters on the structure surface gives the greatest scope of applications for
SHM [7,8]. However, as shown in this article, the case of gluing exciters influences excited
wave propagation.
The guided waves excited using PZT sensors were applied in defect detection in
welded composite joints [9], estimation of the depth of cracks in thick steel beams [10] or
plates [11], or de-bonding detection between concrete block and CFRP reinforcement [12].
This measurement technique was also used to monitor concrete curing [7] and corrosion
identification [13]. Surface-mounted PZT exciters were used in delamination detection
in thick composite laminates [14] and debonding detection between the steel deck and
ultra-high performance concrete layer of a lightweight composite bridge [15].
The influence of the thickness of the bonding layer between PZT transducers and host
structures was studied by Kaur and Bahalla in [16,17]. They tried to use the PZT transducers
for energy harvesting and showed that the higher the thickness of the bonding and the
lower the shear modulus of the bond layer, the smaller the amount of obtained energy.
They did not observe the inverse piezoelectric effect (the guided wave was not excited, but
it can be supposed that the bonding layer also influences the vibration generated by PZT
transducers to the host structures).
One more thing should be noted, namely, if the gluing of sensors is important, can
the exciters be glued twice in the same way? This question is significant in SMH system
configurations. It is possible that during the exploration of the structure, the exciter will be
broken and require to be exchanged [8]. Will the new exciter (even in the same size, type,
and excitation signal) generate the same wave in the structure? Tracking the examples in
the literature can show, that there is a lack of direct answers. In many articles, individual
solutions are presented [11,13,18–21]. Despite how interesting they are, they do not raise
issues of sensor attachment influence on excited and registered signals. In the articles on the
use of elastic waves [12,22], the authors take into account diverse sets of samples and the
influence of sample characteristics on the wave parameters, but the issue of the influence
of bonding on the excited wave is not discussed or considered. Potential discrepancies
between the analyzed signals can be results from gluing the sensors, which was mentioned
in [22], or the specimen surface roughness [7]. So, simply comparing the signals obtained
during examination on different specimens, without taking into account the influence of
the sensors sticking, can be risky.
Another problem connected with sensors attaching is the repeatability of measurement
on different specimens [22]. The development of appropriate procedures for the comparison
of excited signals in many specimens is important from a practical point of view. Due
to the sensor gluing, the real excited wave can be different from the generated one.The
main purpose of this article is to show that the problems with the repeatable sticking of the
PZT transducers exist and need to be taken into account before applying the guided wave
measurement to the SHM of real structures.
In this article, such issues are also discussed: (1) qualitative and quantitative com-
parison of measurements made in different areas, and (2) comparison of the influence of
different glues on wave excited with surface-stuck PZT.

2. Material and Methods

The examinations were conducted on steel specimens. The shape of the specimens
resulted from their similarity to the parts of real, engineering steel structures in the range
of the shape as well as the dimension. Under observation were the parts of the webs
of the I-section beams (despite their vertical location on the measuring stand). Each of
the beams was made with IPE300, so the thickness of the web should be 7.1 mm with
1 mm accuracy. The material properties were experimentally determined using ultrasound
Materials 2024, 17, 2160 3 of 14

techniques (Young’s modulus E = 216.65 GPa, Poisson’s coefficient ν = 0.285, and shear
modulus G = 84.28 GPa).
The elastic wave propagation observation was made by a non-contact measurement
technique, which was Laser Doppler Vibrometry (LDV). This technique allows measure-
ments in a very dense mesh of measuring points. Thanks to that, the visualization of
propagating waves is possible. The measuring stand is shown in Figure 1. It consists of
the equipment for wave excitation: the signal generator (TTi Thurlby Thandar Instruments
typu TG1010i Function Generator, Huntingdon, UK), amplifier (Piezo Systems Inc. EPA-
104, Cambridge, MA, USA), PZT sensors, and, for wave registration, Polytec Scanning
Vibrometer PSV-400-3D (Waldbronn, Germany). Due to the measurement being bounded
to a direction perpendicular to the surface of specimens, only one scanning head was used.

Figure 1. (a) Measuring stand and (b) the specimen under examination.

The real dimension of the observed area (measured on the specimen surface) was
205 mm width and 200 mm high, and there were 5183 measuring points, arranged regularly.
The PZT exciter was glued approximately in the middle of the area.
The wave excitations were made using plate actuators NAC2013 (dimensions:
5 × 5 × 2 mm) and PZT actuators by Noliac (www.noliac.com/products/actuators/plate-
actuators/show/nac2013, accessed on 10 January 2024). During measurements, the in-
fluence of the gluing method was analyzed, so five different types of glue were tested as
shown in Table 1. In this table, also the advantages and disadvantages of the application
of each of them are formulated based on long-term, personal experiences in the field of
elastic wave measurements experiments. The identified advantages and disadvantages
result from the different chemical compositions of individual adhesives, which translate
into features such as setting speed, strength, the flexibility and durability of the connection,
and resistance to accidental loads. Moreover, the chemical composition of the adhesive and
the mechanical properties of the connection are related to the ability to transfer the excited
wave from the PZT to the analyzed element.
Two types of excitation were tested, namely, the 2.5 and 3.5 sine waves, both cases
modulated with the Hanning window. The frequency of the generated signal was different
for each of them, with the aim to obtain the same operational frequency 100 kHz, and they
were, respectively, 40 kHz and 28.571 kHz. The change in the type of excitation signal, with
the same value of operational frequency and amplitude, influences the energy of excitation.
In analyzed cases, the energy of the normalized 3.5 sine wave (21.56) was 1.28 times bigger
than for the normalized 2.5 sine wave (16.89).
The sampling frequency was 2.56 MHz, and the length of the registered signal was
3.2 ms. After preliminary observation of the wave propagation, it was determined that
in this task, the registered signal range should be narrowed down to 1 ms.The collected
signals were filtered using a bandpass filter in the passband frequency 80–160 kHz and
narrowed to the first 2600 elements (1 ms). An exemplary signal (for randomly selected
point), measured with LDV before and after filtering and narrowing, is shown in Figure 2.
In Figure 3, the maps of the neighborhood of the sensors are shown regarding the type of
sensor gluing. Each map shows the same time step of 0.2019 ms after the trigger.
Materials 2024, 17, 2160 4 of 14

Table 1. Applied fixing types.

Fixing Type No. Glue Advantages Disadvantages

1 Wax easy application unstable (possible
easy removal accidental detachment)
uniqueness of sticking
2 Multi-fix mass easy application long-drawn operation
easy removal of the sensor heats the mass
more repeatable than wax and changes its properties
3 commercial easy application poor bonding
Polyacetate-vinyl easy removal on slippery surfaces
adhesive\ accidental water-soluble
glue MAGIC detachment impossible
satisfactorily reproducible
gluing
4 Elastic ethyl easy application low amplitude
2-cyanoacrylate accidental detachment of generated signal
impossible very difficult to remove
(detaching the sensor is
associated with its damage)
5 Universal ethyl easy application low amplitude
2-cyanoacrylate accidental detachment of generated signal
impossible very difficult to remove
(detaching the sensor is
associated with its damage)

a) 10 -4
1
Velocity [m/s]

-1
0 0.5 1 1.5 2 2.5 3
Time [s] 10 -3

b) 10 -4
1
Velocity [m/s]

-1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time [s] 10 -3
c)
10 -4
1
Velocity [m/s]

0.5

-0.5

-1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time [s] 10 -3

Figure 2. (a) The exemplary signal, measured with LDV, before (blue) and after (red) filtering. With
the black dashed rectangle, the signal for further analysis is marked, and its zoom is shown in the
diagram (b) before and (c) after filtering.
Materials 2024, 17, 2160 5 of 14

Figure 3. Examples of propagating waves for different gluing types: (a) WAX, (b) MAGIC, (c) Elastic
glue. The time of measurement from the trigger: 0.2019 ms. Maps visualized by Politec software
(Polytec Scanning Vibrometer, Version 9.0).

3. Calculation Procedure
The distance between the scanning head and the surface of the specimen was 230 cm.
It is a relatively long distance, and even small changes in the position of the head influence
the direction of the laser beam so that it does not reach the same point. The measurements
lasted several weeks and required the equipment to be switched off between some of the
samples. This is the first reason why the position of the scanning head may have changed.
Another one is the necessity of changing the sample or measurement area. Due to technical
reasons, it is impossible to obtain the identical location of measuring points (with such a
dense mesh of points) concerning the sensor location. The new procedure presented here
can help the comparison of on-the-surface propagated elastic waves.The algorithm of the
procedure is shown in Figure 4.

Adopting a regular grid of points

in a new coordinate system (Base Coordinate System, BCS)
Data standarization

Conversion the measurement data from

local Measurement Coordinate System, MCS to BCS
Section 3.1.

Estimation of PZT exciter location (genetic algorithms)

Transition to a new polar coordinate system

(beginning in the location of PZT, Comparative Coordinate System, CCS)

Division the region to circle segments

Calculation of the signal energy for each segment

Data analysis
Section 3.2.

Comparison of the signal energy between segments

in selected measurement

Comparison of signal energy between measurements

regarding glue type

Figure 4. Scheme of the procedure.

3.1. Data Standardization

The location of measuring points during measurements by LDV is made in the local
coordinate system of the tool (Measurement Coordinate System, MCS), which can be
defined by the operator. It is possible to change the MCS every time while the observed
area is changed, but in the author’s opinion, it is not necessary, as this process will not
solve the problem of aligning the measuring points. Only the time consumption of the
measurements is increased. The information of the distribution of the measurement points
relative to each other is sufficient.
Materials 2024, 17, 2160 6 of 14

Assuming that the coordinates of the p-th point P in MCS are PpMCS ( x PMCS , y PMCS ), the
new coordinate of the measuring points can be recalculated to a new Base Coordinate
System (BCS) PpBCS ( x PBCS , y BCS
P ) using the formula:

x PBCS,1 = x PMCS − min(X MCS ) (1)

y BCS,1
P = y PMCS − min(Y MCS )
x PBCS = x PBCS,1 ÷ max (XBCS,1 ) · lx
y BCS
P = y BCS,1
P ÷ max (YBCS,1 ) · ly

where:
X MCS = [ x1MCS , x2MCS , . . . , x pMCS , . . . , xnMCS ];
Y MCS = [y1MCS , y2MCS , . . . , y MCS
p , . . . , ynMCS ];
n—number of measuring points;
XBCS,1 = [ x1BCS,1 , x2BCS,1 , . . . , x BCS,1
p , . . . , xnBCS,1 ];
YBCS,1 = [y1BCS,1 , y2BCS,1 , . . . , y BCS,1
p , . . . , ynBCS,1 ];
lx—the actual width of the area as measured on the object;
ly—the actual hight of the area as measured on the object.
The BCS is a Cartesian coordinate system, in which all measuring points are located
in the first quadrant. Additionally, thanks to the normalization of coordinates and them
referencing the real dimensions of the observed area (measured on the surface of the
element), it is possible to avoid the influence of changes in the distance between the
specimen and the scanning head on the location of the measuring points. Small differences
in the distance are acceptable. This is especially important for large and heavy samples.

3.1.1. Conversion of the Measurement Data to a New Grid of Points

The data collected during LDV measurement are the time signal for each node of the
measuring mesh. In Figure 5a, the exemplary velocities in the selected time step registered
for all measuring points are shown. Due to specimen surface unevenness, the nodes of the
mesh grid, despite assumptions, are not evenly spaced. Moreover, the measurement points
that were located in places where the cables supplying the PZT transducers were located
were not subject to measurements because the cables covered the surface of the element in
which the wave propagated and the laser beam could not measure the wave. These factors
made it even more difficult to compare the wave, induced by different sensors. To solve
this problem, the conversion of the measurement data to a new regular grid of points was
proposed as described below. The results of the data conversion are shown in Figure 5,
where Figure 5a shows the data obtained with LDV measurement, while Figure 5b presents
the results of data transformation to the BCS.
Starting from the beginning of the BCS, the regular grid of new nodes Ni,j ( x Ni,j , y Ni,j ) is
determined, with a constant distance between rows (dy ) and columns (d x ). The number of
rows I and columns J can be calculated as I = ly /dy + 1, J = lx /d x + 1, so i ∈ (1, 2, . . . , I )
and j ∈ (1, 2, . . . , J ). The number of nodes is nn = I · J, and does not have to be the same as
the number of measuring points in MCS. For each node, the distance between the node
and measuring points is calculated using Equation (2):
r
 2  2
r ( Ni,j , Pp ) = x Ni,j − x PBCS + y Ni,j − y BCS
P (2)

Next, a modified Hanning function [1] with the max value equal to 1 for the selected
node and 0 for the points equally distant to rmax (defined by the operator) is used as a
weight function. See Equation (3):
Materials 2024, 17, 2160 7 of 14

(   π ·r( N ,P ) 
i,j p
0.5 · 1 + cos rmax for r ( Ni,j , Pp ) <= rmax
R( Ni,j , Pp ) = (3)
0 for r ( Ni,j , Pp ) > rmax
Finally, the velocity for the selected node is calculated by weighted averaging
Equation (4):
np
∑ p=1 A( x PBCS , y BCS
P ) · R ( Ni,j , Pp )
AMPL( Ni,j ) = np (4)
∑ p=1 R( Ni,j , Pp )

where A( x PBCS , y BCS

P ) is an amplitude of the signal registered with LDV for the p-th P point,
and AMPL( Ni,j ) is an amplitude of the signal calculated for the node Ni,j .

Figure 5. Exemplary view of (a) data obtained with LDV measurement, and (b) data after transforma-
tion to the BCS.

3.1.2. Estimation of PZT Exciter Location

The wave propagation analysis should be made with consideration of the measuring
point distance from the exciter. In view of the imprecise description of the location of the
measurement grid nodes in relation to the sensor, and thus also the nodes of the new mesh,
it became necessary to set the PZT location in another way. In this aim, genetic algorithms
were used, assuming that the material was homogeneous and the elastic wave propagated
in every direction in the same way.
For genetic algorithm implementation, the MATLAB environment was used. The ’ga’
function was used with default parameters (random initial population with a uniform
distribution; population size = 50; the fraction of the population at the next generation = 0.8;
stops criterion: the average relative change in the best fitness function value <= 1 × 10−6
and maximum number of iterations = 200). No linear or non-linear constraints were applied.
Only a set of lower and upper bounds on the design variables (coordinates of the center of
the circle) were limited to the dimensions of the analyzed area. The influence of parameter
changes on the calculation result was not analyzed.
Based on 20 first time steps (before excitation), the noise level was estimated. The mean
value AMPL and the standard deviation σAMPL were established considering all nodes of
the mesh grid. Then, for further analysis, another 41 time steps were selected. These were
the steps in which the wider-and-wider propagated wave was observed. It was the first
flight of the wave (without reflections from edges of specimen). As crucial points for the
determination of the sensor location, the points satisfying Equation (5) were selected:

Bs = { Ni,j : AMPLs ( Ni,j ) >= AMPL + 3 · σAMPL } (5)

where s is the time step number.

Materials 2024, 17, 2160 8 of 14

BCS , y BCS ] were established for each

The coordinates of the circle center of gravity [ xc,s c,s
time step using genetic algorithms, Equation (6):
BCS BCS
[ xc,s , yc,s ] = ga( f o , Rc , Bs ) (6)

where f o is the objective function defined in Equation (7), and

Rc —radius of the circle in the presented examinations, assuming that Rc = 70 mm :
 q 2
f o = ∑ ∑ Rc − ( x Ni,j − xc,sBCS )2 + ( y BCS 2
Ni,j − yc,s ) for Ni,j ∈ B (7)
i j
BCS BCS
∑s xc,s ∑s yc,s
,xcBCS =
ycBCS = (8)
S S
where S is the number of considered time steps.
The crucial points in the first, the middle, and the last time steps of exemplary con-
sidered sequence are shown in Figure 6. In these figures, also the location of circles
approximated using the genetic algorithm are shown. The middle point of the circles
corresponds to the PZT exciter location.

a) time 0.1910 s b) time 0.2105 s c) time 0.2223 s

{ xBCS
C,490
=0.1030, y BCS
C,490
=0.0944 } { xBCS
C,540
=0.1005, y BCS
C,540
=0.0985 } { xBCS
C,570
=0.1035, yBCS
C,570
=0.1008 }

0.2 0.2 0.2

0.15 0.15 0.15

y [m]

y [m]

y [m]
0.1 0.1 0.1

0.05 0.05 0.05

0 0 0
0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2
x [m] x [m] x [m]

significant points approximated circle location

Figure 6. Significant points and GA-approximated locations of circle in (a) 490th, (b) 540th,
(c) 590th time steps, for one selected exciter and its excitation.

An example of the application of the proposed procedure is shown in Figure 6. The

guided wave registered for all points of the grid in one selected moment in time can be
visualized as a color map in 2D space. The applied color scale consists of two colors: blue
for the points filling the Equation (5), and white for those with a smaller amplitude. The
white ones are omitted in further analysis of the selected step. Each time step is taken
into consideration by the genetics algorithm separately, so the obtained coordinates of the
gravity center of the circle (shown with a black line) can be varied. It is the result of the
nonideal character of the experimentally obtained data (noises, measurement uncertainties,
imperfections of the specimen, etc., but primarily differences caused by the adhesion of
the exciter). It is why more than one time step is used to determine the center location and
justifies the use of Equation (8). The middle point of the circles corresponds to the PZT
exciter location.

3.1.3. Comparative Coordinate System (CCS)

The approximated location of PZT was established as an origin of the polar coordinate
system, in which the coordinates of nodes were recalculated to the new ones, according to
Equation (9): [23].
Materials 2024, 17, 2160 9 of 14

q
rCCS
N = ( x BCS
N − xc
BCS )2 + ( y BCS − y BCS )2
Ni,j c
i,j
 i,j  y 
Ni,j


 atan x N for x Ni,j > 0, y Ni,j >= 0

  i,j 
y Ni,j


 atan x Ni,j + 2π for x Ni,j > 0, y Ni,j <0


(9)

φCCS
Ni,j = 
y Ni,j



 atan x Ni,j +π for x Ni,j < 0


 π

for x Ni,j = 0, y Ni,j >0
2


 3π

2 for x Ni,j = 0, y Ni,j <0

3.2. Data Analysis

Knowing the PZT sensor size, the nodes in the area of sensor should be omitted. They
may cause interference in the data analysis (if some measurements were taken on the sensor
surface, it is not the same surface on which the wave propagated in the analyzed material).
Therefore, in further steps, the nodes with rCCSNi,j <= rsens are not included. The adopted
value of rsens equals 15 mm. Examples of propagating waves, the same as in Figure 3 but
after an application of the proposed procedure, including the removal of nodes in the near
neighborhood of the sensor, are shown in Figure 7.

Figure 7. Examples of propagating waves for PZT sensors attached with: (a) WAX, (b) MAGIC,
(c) Elastic glue, the same as in Figure 3 but after an application of the proposed procedure. The same
scale was used for all maps in this figure.

The comparison of signals collected during measurements requires taking into account
the location of the measuring node in relation to the excitation location. Thanks to the
adoption of a new CCS, the selection of appropriate points is more objective. The exemplary
signals, recorded for nodes located at the smallest distance from the origin of the polar
system (CCS) and simultaneously with the smallest value of φ Ni,j , are shown in Figure 8.
The signals are grouped considering the type of applied glue.
As can be seen, despite the identical material properties and their homogeneity, as well as
the same sensor sizes and excitation types, the registered signals may be completely different. It
seems that the observed differences are the result of the way the sensor is glued. The applied
glue influences the generated amplitude of the signal and also the possibility of sticking the
sensor in an even and repeatable way, so the wave could propagate identically in every direction.
The highest amplitude of the propagated wave was obtained for wax, but as specified
in Table 1, the sensor mounted on wax can be easily removed, e.g., by an unplanned jerk of
the cable. In such a case, it is hardly possible to re-stick the sensor in the same way. In each of
the measurements shown in Figure 8a, the shape of the registered signal is different. An even
greater lack of repeatability of gluing is observed in the case of the use of elastic or universal
glue. Despite no possibility of the accidental detachment of sensors, the application of this
type of glue is not recommended due to the very low amplitude of the generated wave.
Materials 2024, 17, 2160 10 of 14

In the aim of the assessment of the generated wave quality, the circular area with
rcirc = 80 mm and the middle point in the estimated location of the PZT sensor was adopted.
The radius of this circle was established such that even in the case that the sensor was not
in the center of the observed area, the circle would not be clipped. Then, this area was
divided into twenty identical pieces, being slices of a circle (omitting the above-mentioned
Ni,j , for which rCCS
N <= rsens ).
i,j

Figure 8. Exemplary comparison of signals collected during measurements with sensors glued on with
different types of glue: (a) WAX, (b) Multi-fix mass, (c) MAGIC, (d) Elastic glue, (e) Universal glue. The
comparison of nodes that were located closest to the origin of CCS (single selected node for each sensor).

The sum of the averaged squared amplitudes (ASAs) of the points, assumed to be sig-
nificant, was calculated for each slice, considering the selected time steps. The calculations
were made according to Equation (10):

Ea = ∑ ∑{ AMPLs ( Ni,j )}2 for Ni,j ∈ Aa (10)

s

where a is the number of a piece, Aa is the area of the a-th piece, and s is the number of the
selected time step s ∈ {490, 492, 494, . . . , 570}.
Materials 2024, 17, 2160 11 of 14

The exemplary comparison of changes in ASA for the selected pieces of the circular
area is shown in Figure 9. The differences between the energy in the pieces are clearly
visible. However, when choosing the type of sensor sticking, we should strive for relatively
uniform excitation in all directions (as long as the tested material is homogeneous).

Figure 9. Averaged squared amplitudes of wave for selected pieces of the circular areas surrounding
the exciters. The same scale was adopted to all shown examples. The excitation with 2.5 sine
wave; the left column (a,d,g) sensors mounted with wax; the middle column (b,e,h)—commercial
polyacetate-vinyl adhesive (glue MAGIC); the right column (c,f)—elastic ethyl 2-cyanoacrylate.

4. Results and Discussion

During the measurements, one (the same) sensor was used for all examinations
with removable gluing (fixing type nos. 1–3). For each fixing and excitation type, three
patterns were registered. The statistics of the collected results are shown in Figure 10. In
the diagram, the energy of the wave propagating in selected pieces of a circular area is
compared, considering the gluing type. As can be seen, for both types of excitation, the
highest energy of the wave was obtained in the case of wax use. However, the variability
of the analyzed energy is the biggest in this type of sticking. It means that the wave
did not propagate evenly in all directions, and the comparison of the wave propagation
Materials 2024, 17, 2160 12 of 14

between different points requires that this fact be taken into account. For both types of
excitation, the most even wave propagation was obtained using commercial polyacetate-
vinyl adhesive/glue MAGIC. The experiment was extended by gluing another four sensors
but this time using two types of permanent glue (elastic and universal 2-cyanoacrylate).
Four additional measurements with 2.5 sine wave excitation were collected, and the whole
procedure was repeated. The results are shown in Figure 10b. Unfortunately, the observed
wave amplitudes are significantly lower than in the previous cases, which result in a lower
level of averaged squared amplitudes of waves. Additionally, as shown in Figure 8d,e,
problems with the repeatability of the gluing are observed. The experiments were repeated
for 3.5 sine wave excitation (Figure 10c). The trends obtained for the 2.5 sine wave excitation,
which are described above, were confirmed.

Figure 10. The comparison of ASA propagating in analyzed pieces of circular area. (a) Wave excited
by one, the same, sensor NAC2013 regarding type of gluing and excitation type. (b) The comparison
of ASA generated by different sensors. Excitation type: 2.5 sine wave. (c) The comparison of ASA
generated by different sensors. Excitation type: 3.5 sine wave.

5. Conclusions
In this article, two issues were raised, important from a practical point of view in
elastic wave propagation measurements. The first one was the analysis of the influence
of gluing the PZT actuators (applied glue types are listed in Table 1) to the examined
surface on the elastic wave propagation. As shown, the highest amplitudes of waves, which
correspond to the energy of the recorded signals, were obtained using wax, and the lowest
ones using the permanent glue. Unluckily, the durability of the connections was increased
with the decrease in the wave amplitudes. The stability of the sensors sticking is necessary;
otherwise, they may accidentally be peeled off during the measurement. The paper shows
that it is impossible to re-stick the sensor in the same way. The optimal solution in the
analyzed task seems to be the application of bookbinding glue with a satisfactory amplitude
of signal and durability of the connection. However, its application is narrowed only to
rough, dry, and degreased surfaces.
The second issue is the development of the procedure dedicated to objective analysis
and comparison of the elastic waves propagating on the surface of different specimens.
In large-sized specimens, the precise location of the measurement points is impossible.
Therefore, also a new procedure was developed, which engages genetic algorithms to help
with the determination of a new coordinate system. In this system, wave propagation can
be considered for the position of the exciter (not the measuring points). The proposed
procedure also helps with the assessment of the quality of the wave propagation in different
directions, and it is planned to be used in further examination of the analysis of the next
flights of waves (e.g., after the reflection from the boundary of the material).
Materials 2024, 17, 2160 13 of 14

Author Contributions: Conceptualization, D.Z. and M.J.; methodology, D.Z. and M.J.; software,
D.Z.; writing—original draft preparation, D.Z.; writing—review and editing, M.J.; visualization, D.Z.;
project administration, D.Z.; funding acquisition, D.Z. and M.J. All authors have read and agreed to
the published version of the manuscript.
Funding: This research was a part of grant Preludium project no. 2019/35/N/ST8/01086 founded
by National Science Centre (NCN), Poland.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Date will be made available on reasonable request.
Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or
in the decision to publish the results.

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