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Guiping Liang, Haiming Fu, Sekar Ganapathy, Jyoti Bhola*, Vidya G. Doddawad,
Shashikant V. Athawale, and Komal Kumar Bhatia
Experimental and simulation research on the
diﬀerence in motion technology levels based on
received March 17, 2022; accepted June 1, 2022
Abstract: Wearable and movable lodged health moni-
toring gadgets, micro-sensors, human system locating
gadgets, and other gadgets started to appear as low-
power communication mechanisms and microelectronics
mechanisms grew in popularity. More people are inter-
ested in energy capture technology, which turns the
energy created by motion technology into electric energy.
To understand the diﬀerence in motor skill levels, a non-
linear feature-oriented method was proposed. A bi-stable
magnetic-coupled piezoelectric cantilever was designed
to detect the horizontal diﬀerence of motion technology.
The horizontal diﬀerence was increased by the accelera-
tion generated by the oscillation of the leg and the impres-
sion betwixt the leg and the ground during the movement.
Based on the Hamiltonian principle and motion technique
signal, a nonlinear dynamic model for energy capture in
motion technique is established. According to the shaking
features of human leg motion, a moveable nonlinear shaking
energy-gaining system was the layout, which realized the
dynamic characteristics of straight, nonlinear, mono-stable,
and bi-stable. The experimental outcome shows that nonli-
nearity can eﬀectively detect the diﬀerence of motion techni-
ques. The experimental results of diﬀerent human movement
states conﬁrm the beneﬁts of the uncertain bi-stable human
power capture mechanism and the eﬀectiveness of the electro-
mechanical combining design established. The nonlinear
mono-stable beam moves in the same way as the straight
mono-stable beam in the assessment, but owing to its
higher stiﬀness, its frequency concentration range (13.85 Hz)
is moved to the right compared to the linear mono-stable
beam, and the displacement of the cantilever beam is
reduced. If the velocity is 8 km/h, the mean energy of the
bi-stable method extends to the utmost value of 23.2 μW.
It is proved that the nonlinear method can understand the
diﬀerence in the level of motion technique eﬀectively.
Keywords: nonlinear characteristics, sports technology,
Sports technology is a multi-level system that is com-
posed of various technical links and has highly ordered
and complex structural characteristics. The quality eﬀect
is determined by the coordination degree of each sub-
system and each factor in the system, and the overall
coordination eﬀect determines the performance of the
motion technology. The process of sports technology
training is to adjust various factors aﬀecting its quality
and coordinate the relationship and connection among
various factors guided by the eﬀect of training implemen-
tation. The sports technology training system is a very
sensitive complex network system that is entangled by var-
ious factors and relationships . With fresh ideas and
accomplishments, the human species has really upped their
Guiping Liang: Guangzhou Huaxia Vocational College, Guangzhou,
Guangdong, 510935, China, e-mail: GuipingLiang985@126.com
Haiming Fu: Guangzhou Huaxia Vocational College, Guangzhou,
Guangdong, 510935, China, e-mail: HaimingFu252@163.com
Sekar Ganapathy: Department of Electronics and Communication
Engineering, Sri Ramakrishna Institute of Technology, Coimbatore,
Tamil Nadu, India, e-mail: email@example.com
* Corresponding author: Jyoti Bhola, Department of Electronics &
Communication Engineering, Model Institute of Engineering and
Technology, Jammu, J&K, India, e-mail: firstname.lastname@example.org
Vidya G. Doddawad: JSS Dental College and Hospital, JSSAHER,
Mysore, India, e-mail: email@example.com
Shashikant V. Athawale: Department of Computer Engineering,
AISSMS COE, Savitribai Phule Pune University, Pune, India,
Komal Kumar Bhatia: Department of Computer Engineering, Faculty
of Informatics & Computing, J.C. Bose University of Science &
Technology, Ertwhile YMCA University of Science & Technology,
Faridabad, 121004, Haryana, India,
Nonlinear Engineering 2022; 11: 629–636
Open Access. © 2022 Guiping Liang et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0
game when it comes to constructing durable technology.
The ideal fan experience in sports is fully engaged, and
everyone has begun to employ several methods to raise
the passion and excitement of their most ardent supporters
[2,3]. Sports motion analysis investigates athletes’biome-
chanics using motion capture software, cameras, and mar-
kers. Many sports need complex, detailed moves in addition
to quick speeds. It is tough to assess them appropriately in
two-dimensional footage. Motion capture software may be
used to assess these motions in three dimension [4,5].
With the increasing growth of low-power communi-
cation mechanisms and microelectronics mechanisms,
wearable and moveable lodged health monitoring gad-
gets, micro-sensors, human system locating gadgets, and
so on began to appear. However, since the number of
these gadgets relies on accumulator power and needs to
be replaced consistently to maintain long-term use, pur-
suing dependable energy origin to power these gadgets
and reducing their vulnerability to outer batteries have
become a main technical requirement for research in this
ﬁeld. Therefore, energy capture technology, which con-
verts the energy generated by motion technology into
electric energy, has attracted more and more attention
. Wearable athletic equipment is currently available
in a range of sizes and styles, with new ones being pro-
duced regularly. Devices are being incorporated into the
fabric of athletic clothing, ﬁtted into sports gear like balls
or bats, and worn by athletes as small devices attached to
the body in the form of a belt or skin patch [7,8]. Sensors
and equipment used by athletes would have to be practi-
cally invisible and weightless, as well as ﬂexible, strong,
and impact resistant. At the same time, they must gen-
erate precise biometric measurements such as move-
ment, heart rate, respiration, and impact. StretchSense
fabric, for example, is developed to suit all of these needs
[9,10]. In current years, scholars at home and abroad
have read about the energy capture methods of motion
technology, such as electromagnetic, thermoelectric, and
piezoelectric. Piezoelectric vibration energy capture device
has become the distinct of research on human shaking
energy capture mechanism because of its features of simple
inﬁnitesimal and raised power density. An oscilloscope col-
lects three voltage signals synchronously in motion tech-
nology, and the voltage signals are subsequently translated
into appropriate acceleration, displacement, and gained
voltage signals. More people are interested in energy cap-
ture technology, which turns the energy created by motion
technology into electric energy. The energy capture tech-
niques of motion technology, such as electromagnetic,
thermoelectric, and piezoelectric, have been studied by
academics both at home and abroad. Because of its
properties of simple inﬁnitesimal and increased power
density, the piezoelectric vibration energy capture device
has become the focus of research on human shaking
energy capture mechanisms.
Movement technical structure is complex, the factors
aﬀecting its quality eﬀect for diﬀerent training stages and
diﬀerent athletes role are diﬀerent, having a certain dif-
ference and variability, which determines the interaction
between them on the quality of the movement technology
can achieve diversiﬁcation, namely to diﬀerent athletes
to produce the same result of eﬀect factors cannot; in the
same way, the factors that aﬀect the same performance of
the same athlete can be diﬀerent . A motion sensor
can detect the movement of an object or a person in
relation to its surroundings. A portable motion sensor
can gather and store information about a person’s move-
ment, which may later be analyzed. It uses acceler-
ometers and gyroscopes to capture a person’s movements
[12,13]. For example, a high jump in the ﬁnal session of
the World athletics championship can also jump over
2.35 m, and pat’s technical index of large diﬀerences,
the Chinese outstanding high jump athletes also skip
the technical index of 2.24 m is also a larger diﬀerence;
it shows that aﬀecting the quality of the high jump move-
ment technology of the nonlinear interaction between
multiple factors makes the performance of the obtained
to choose various methods and approaches . There-
fore, domestic and foreign researches continue. Cui et al.
studied the diﬀerences between sitting volleyball tech-
nology and sports classes for para-athletes . Sathiya-
moorthi et al. studied the comparison of life skills of
college PE and non-PE majors from the perspective of
socioeconomic status . The purpose of Ferreira Gon-
zalez et al.’s study was to investigate the diﬀerences in
inhibitory control and motor adaptation between dif-
ferent types of locomotives (i.e., closed and open skill
locomotives). Gao et al.used magnetic levitation
to create a multi-stable vibration energy harvesting device.
Only magnetic contact was employed in the fabrication
of the harvester, which had a multi-well restoring force
potential. Other investigations, on the other hand, used a
combination of magnets and piezoelectric cantilevers to
build bi-stable and multi-stable energy harvesters [19–21].
The use of a third-order polynomial ﬁttocharacterize
the nonlinear magnetic force, according to Lan and Qin
, can result in instabilities at small displacements near
equilibrium and severe degradation at greater deﬂections.
Quinn et al.looked at the large-amplitude branch of a
mono-stable energy harvester’s response and found that the
right design might enhance performance signiﬁcantly. A
theoretical analysis for mono-stable energy harvesters was
630 Guiping Liang et al.
provided by Sebald et al.. The mono-stable harvester
was proved to be capable of obtaining maximum harvested
power. A bi-stable magnetically coupled piezoelectric can-
tilever was used to detect a horizontal diﬀerence of motion
technology. The horizontal diﬀerence was enhanced due to
the acceleration caused by the leg swing and the impact
between the leg and the ground during the action. Using
the Hamiltonian principle and motion technique signal, a
nonlinear dynamic model for energy capture in motion is
built. Experimental ﬁndings of diverse human movement
states validate the beneﬁts of the nonlinear bi-stable
human energy capture mechanism and the eﬃcacy of
the electromechanical combining representation created.
The piezo-thermoelastic shell continuum’sshellthermo-
electromechanical equations and boundary conditions are
derived using Hamilton’s concept. The energy ﬂuctuations
over any given time period are assumed to be zero, according
to Hamilton’s concept. All energy associated with a piezo-
thermoelastic shell continuum exposed to mechanical,
thermal, and electric inputs is taken into consideration.
Acoustic waves, electrical transmission diﬃculties, plasma
waves, and other spatially extended systems may all be
studied using nonlinear dynamics models. A linear chain
of discrete oscillators with the nearest neighbor has been
used to represent these diﬃculties. Of course, continuum
physics, such as acoustics or ﬂuid mechanics, which
employ partial diﬀerential equations in space and time,
is the limit of such models. When the oscillators’coupling
is nonlinear, a phenomenon occurs.
Based on the current research, this research provides
a nonlinear characteristics technique. To detect the hor-
izontal diﬀerence of motion technology, a bi-stable mag-
netic-coupled piezoelectric cantilever was constructed.
The acceleration caused by the leg oscillation and the
impression between the leg and the ground during move-
ment increased the horizontal diﬀerence. A nonlinear
dynamic model for energy capture in motion method is
developed using the Hamiltonian principle and motion
technique signal. According to the vibration features
of human leg motion, a moveable nonlinear shaking
energy catching system was designed, which realized
the dynamic characteristics of straight, nonlinear, mono-
stable, and bi-stable. Nonlinearity may eﬃciently identify
the diﬀerence in motion approaches, according to the
results of the experiments. The beneﬁts of the nonlinear
bi-stable human power capture mechanism, and the eﬃ-
cacy of the electromechanical coupling model created is
conﬁrmed by the experimental ﬁndings of various human
2 Experimental data
2.1 Nonlinear dynamics model
The magnetically coupled piezoelectric cantilever beam
structure is designed, in which the rotation angle α, the
and the length hof the cantilever beam are
variable and the outer magnet can be disassembled .
By adjusting the prior parameters, dissimilar nonlinear
repairing forces can be acquired, to obtain the piezo-
electric cantilever beam with dissimilar potential wells.
Based on the Hamiltonian principle, the variation V
the Lagrangian function of the piezoelectric cantilever
should be constant at 0 at any time t
where δis the variation sign; E
, and E
energy, potential energy, and external excitation energy,
respectively. The deformation of the mass block at the
end of the cantilever beam is small and can be regarded
as the concentrated mass. Then, each quantity in Eq. (1)
can be expressed as:
E ρuuV ρuudV muu
0.5 d0.5 0.5
0.5 d 0.5 d 0.5 d
ii i j
In Eq. (2),V
are the volume of the inter-
mediate layer and the volume of the piezoelectric layer,
are the density of the intermediate
layer and the density of the piezoelectric layer, respec-
tively; Uis the deﬂection of the cantilever beam; m
concentrated mass at the end; N
are the numbers
of forces acting on the cantilever beam and the number of
electric quantity, respectively; f
)is the force acting on
are respectively the voltage and charge acting
on the suspension beam; S,T,D,andErepresent strain
vector, stress vector, electric displacement vector, and
electric ﬁeld intensity vector, respectively. After ﬁnishing,
the electromechanical coupling model of the magnetic
coupled pressure cantilever structure can be obtained as
Experimental and simulation research on the diﬀerence in motion technology levels 631
() () () ()
() () () ⎫
Mx t Cx t F θV t Ma t
CVt VrR θxt
where M,C,andθrepresent the equivalent mass, equiva-
lent damping, and equivalent electromechanical coupling
coeﬃcient, respectively; C
is the equivalent capacitance
of PZT; x(t)is the displacement at the end of the cantilever
beam; Ris the load resistance; V(t)is the voltage at both
ends of R;a(t)is the acceleration of outer excitation; F
the nonlinear repairing force of thecantilever beam, which
is expressed as () () ()=+ + +⋯+
n nxt nxt nxt
by polynomial ﬁtting method, where n
polynomial ﬁtting coeﬃcient. The potential energy func-
tion U(x)of the cantilever beam is obtained by inte-
grating () ∫
2.2 Experimental design
In the experiment, the metal layer in the middle of the
cantilever beam is made of stainless steel with a size of
95 mm ×10 mm ×0.27 mm, and the piezoelectric plate is
PZT-51 with a size of 12 mm ×10 mm ×0.6 mm. The two
pieces are attached in parallel. All magnets in the device
are rubidium iron boron enduring magnets. The size of
the magnet at the end of the cantilever beam is 8 mm ×
6mm ×4 mm, the diameter of the external magnet is
25 mm, and the thickness is 5 mm. To acquire the accel-
eration generated by leg swing and ground impression in
the process of motion technology and take it as the
external excitation signal a(t)of subsequent simulation,
the acceleration sensor is used to collect the acceleration
of small leg position in the process of motion. The canti-
lever ray with dissimilar ability wells is acquired by
adjusting the external magnet, and the displacement of
the cantilever beam end is measured by the laser displa-
cement sensor, to read about the nonlinear movement
characteristics of the piezoelectric cantilever beam in
the process of motion technology. The acceleration sensor is
ﬁxed to the root of the energy harvesting device, and the
displacement sensor is attached with screws. The shaking
direction of the piezoelectric cantilever beam is consistent
with the swing direction of the leg. In motion technology,
three voltage signals are collected synchronously by an oscil-
loscope, and then, the voltage signals are converted into cor-
responding acceleration signals, displacement signals, and
gained voltage signals. In the experiment, the human body
exercised on the treadmill, and the speed VT of the treadmill
was adjusted to respectively test the acceleration signal, the
energy capture voltage, and the end displacement of the can-
tilever beam at dissimilar speeds .
To study the beneﬁts of bi-stable shaking energy cap-
ture mechanism of motion technology, three kinds of
cantilever beam structures including linear mono-stable,
nonlinear mono-stable, and bi-stable were designed and
compared by modifying the position parameters of the
outer magnet. The rising repulsive magnetic force will
cause the clamped–clamped beam to bend as the canti-
lever beam approaches the center position (unstable equi-
librium position), hence increasing the distance between
the two magnets and lowering the potential energy barrier.
This is advantageous for achieving the goal of leaping
between possible wells. The repulsive magnetic force will
diminish, and the clamped–clamped beam will return
once the cantilever beam passes through the middle
position, maintaining the system’sbi-stable feature.
The speciﬁc structural parameters areas follows: nonlinear
mono-stable beams d
=58 mm, h=17 mm, and α=0°;
bi-stable beam d
=55 mm, d
=15 mm, and α=10°. The
energy capture device is a linear mono-stable beam after
removing the external magnet [12,27].
In the static horizontal position, the relationship
between restoring force and displacement under diﬀerent
steady-state conditions was measured with an advanced
digital dynamometer and digital displacement kit of mea-
suring bench. The measurement results are shown in
Figure 1. By polynomial ﬁtting, the restoring force curve
equations of the cantilever beam under diﬀerent steady-
state conditions are obtained as follows: linear mono-
stable beam, F
=24.8x; nonlinear mono-stable beam,
=− × + × +
xxx5.49 10 1.56 10 26.09
r2 85 53 ; and bi-stable
beam =− × + × + × −
xxxx6.8 10 3.12 10 6.16 10 9.6353
r3 11 7 8 5 4 3 .
Figure 1: Measurement values of restoring forces of diﬀerent steady-
632 Guiping Liang et al.
By integrating each restoring force equation, the corre-
sponding potential energy function U(x)can be obtained, as
2.3 Analysis of sports techniques
To study the movement features of the human body, the
vibration data acquisition system designed earlier was
used to collect diﬀerent objects (subject A, male, height
175 cm, and mass 63 kg; Object B, male, 170 cm in height,
and 73.5 kg in mass).Atdiﬀerent motion speeds, the rela-
tionship between real-time acceleration and time change
and its spectrum are shown in Figure 3. The measured
acceleration signal will be used as the external excitation
signal of the simulation timing electric model [28,29].
As can be seen from Figure 3, the leg acceleration of
subjects A and B increase with the increase in movement
speed, reaching A maximum of about 4G, showing A
certain asymmetry. It can be seen from the spectrum
analysis that the acceleration frequency grows with the
increase in the motion velocity, and it is mainly concen-
trated at the frequency of the motion technology and its
multiplier. At the speed of 5 km/h, the motion frequencies
of subjects A and B are 0.95 and 1 Hz, while at the speed
of 8 km/h, the motion frequencies of subjects A and B are
1.4 and 1.3 Hz, showing certain individual diﬀerences.
The motion spectrum of the human body is mostly focused
in the low-frequency region, so it is diﬃcult to design low-
frequency piezoelectric cantilever beams in microstructures.
The traditional linear piezoelectric cantilever beam mostly
acquires the concept of mechanical resonance. In the pro-
cess of motion technology, the shaking energy band of the
leg moves with time, resulting in the capacity of shaking
energy catching which is greatly reduced. Therefore, this
article designs a nonlinear bi-stable piezoelectric cantilever
beam, hoping to understand the level diﬀerence of motion
3 Simulation experiment
To conﬁrm the eﬀectiveness of the established nonlinear
electro-mechanical coupling model, the acceleration signal
collected by subject A when walking at A speed of 5 km/h is
used for numerical simulation. Simulation time to model
the voltage V(t)and velocity V(t)of the initial value is set
to 0; the linear beam and nonlinear mono-stable beam dis-
placement of the initial value is set to 0; the bi-stable beam
displacement of the initial value is set to its potential well-
steady point of x
; the output voltage of the beam, the
moving parts, voltage frequency spectrum, and phase tra-
jectory is used to analyze them captive to performance.
The maximum value and mean square value of absolute
voltage in each case are calculated. Considering that the
load resistance Ris 10 Mω, the maximum voltage and
average power of the linear mono-stable beam simulation
results are 10.19 V and 1.3 μW. The maximum voltage of
the nonlinear mono-stable beam is 8.6 V, and the average
power is 0.73 μW, which is lower than that of the linear
mono-stable beam. The maximum voltage and average
power of the bi-stable beam are 19.5 V and 5.1 μW, respec-
tively. The simulation results show that compared with the
linear mono-stable beam, the nonlinear mono-stable beam
produces a smaller voltage output. The main reason is that
the modulated nonlinear mono-stable beam has a larger
stiﬀness and behaves as a hard characteristic, so its ampli-
tude is smaller under the same excitation signal. The
frequency range of the linear mono-stable beam is con-
centrated at 12.55 Hz, while the frequency range of the
nonlinear mono-stable beam is concentrated at 13.95 Hz,
which is 1.4 Hz behind the linear mono-stable beam,
mainly due to the larger stiﬀness of the nonlinear mono-
stable beam. Compared with the linear and nonlinear
mono-stable beam, the bi-stable beam has a better hori-
zontal diﬀerence eﬀect, and its power output is increased
several times. The introduction of the nonlinear restoring
force in the bi-stable system makes the stiﬀness of the
cantilever beam very small, and even negative stiﬀness
appears within a certain range, and the bi-stable system
Figure 2: Potential energy curves of diﬀerent steady-state
Experimental and simulation research on the diﬀerence in motion technology levels 633
has two stable equilibrium points. After being excited, the
end of the cantilever beam will cross the potential well and
do a reciprocating motion between the two equilibrium
points, which increases the horizontal diﬀerence. As can
be seen from the voltage spectrum diagram, the frequency
range of the cantilever beam is mainly concentrated in the
range of 4–8 Hz. Compared with the linear mono-stable
beam and the nonlinear mono-stable beam, the frequency
of the cantilever beam has an obvious forward shift, which
is mainly caused by the nonlinear magnetic force making
the stiﬀness of the cantilever beam smaller.
4 Results and discussion
The genetic characteristics of athletes are generated inside
the human body system, which does not change with the
change of external conditions. It dominates the evolution
and development of athletes’competitive ability throughout.
Therefore, genetic characteristics are the order parameters of
competitive ability system evolution. Genetic characteristics
can reveal the potential of various innate qualities that aﬀect
the human body’s competitive ability and reﬂect the devel-
opment level of body shape, physiological function, and
Figure 3: Acceleration signal and its spectrum at diﬀerent velocities: (a)acceleration signal of A, (b)acceleration signal of B, (c)acceleration
frequency of A, and (d)acceleration frequency of B.
634 Guiping Liang et al.
sports quality that changes with age. It determines the devel-
opment level of athletes’physical ability, skills, tactical
ability, sports intelligence, and psychological ability, and
thus the selection of sports materials, sports training, sports
competition, and sports management of the entire process of
competitive sports composition.
According to the characteristics of diﬀerent events,
the characteristics of diﬀerent athletes and the law of
human growth and development, sports selection, sports
training, sports competition, and sports management
should be carried out on the basis of human genetic char-
acteristics, so that athletes’competitive potential can be
explored systematically and their competitive ability can
be continuously developed. When selecting materials
for sports, the characteristics of sports items should be
fully considered. According to the genetic characteristics,
scientiﬁc testing and prediction methods should be used
to improve the success rate of material selection. During
sports training, the training content, training method,
training means, and load control should be diﬀerent
due to the diﬀerent age characteristics, project character-
istics, and stage tasks of athletes. The success or failure of
sports training, sports direct embodiment, genetic char-
acteristics use the motion indirectly, the process of sports
competition, not according to the vested interest force
teenager athletes prematurely in adults. This frequently
leads to early special or excessive training, as well as
drug use, which causes signiﬁcant harm to the adoles-
cent body and the competition. Sports management is the
prerequisite to ensure the successful selection of sports
materials, sports training, and sports competition. It is
necessary to formulate a feasible management system
according to the characteristics of different sports and
athletes, especially for young athletes to formulate a com-
plete set of training mechanisms including the cultivation of
humanistic quality. The motion of the nonlinear mono-
stable beam in the evaluation is the same as that of the
straight mono-stable beam, but due to its larger stiﬀness,
its frequency concentration range (13.85 Hz)is moved to
the right compared with that of the linear mono-stable
beam, and the displacement of the cantilever beam is
smaller than that of the linear mono-stable beam. In the
process of motion, the bi-stable beam vibrates greatly across
and between the potential wells due to the swing of the leg
and the inﬂuencebetweenthebi-stable beam and the
ground, resulting in high voltage. In addition, the bi-stable
beam crosses the potential well extra frequently due to the
increase in speed, so the power output generated at a larger
motion speed is greater.
A strategy for nonlinear features is presented in this
research. The horizontal diﬀerence of motion technology
was detected using a bi-stable magnetically linked piezo-
electric cantilever. The acceleration created by the leg
swing and the collision between the leg and the ground
during the movement increased the horizontal diﬀerence.
A nonlinear dynamic model for energy capture in motion
method is developed using the Hamiltonian principle and
motion technique signal. A portable nonlinear shaking
energy-capturing system was built based on the shaking
characteristics of human leg motion, and it realized the
dynamic characteristics of straight, nonlinear, mono-
stable, and bi-stable. Nonlinearity may eﬃciently identify
the diﬀerence in motion approaches, according to the
results of the experiments. The beneﬁts of the nonlinear
bi-stable human energy capture mechanism and the eﬀec-
tiveness of the electromechanical combining representa-
tion established are conﬁrmed by the experimental results
of various human movement states. When traveling at
8 km/h, the bi-stable system’s total power reaches a max-
imum of 23.2 W. It has been demonstrated that the non-
linear approach can eﬀectively interpret the diﬀerence in
the degree of motion methodology.
Acknowledgments: Authors are thankful to the Guangdong
Provincial Department of Education, Soliton of some non-
linear wave equations, Project No: 2017GKTSCX111.
Author contributions: All authors have accepted respon-
sibility for the entire content of this manuscript and
approved its submission.
Conﬂict of interest: Theauthorsstatenoconﬂict of interest.
Data availability statement: The data used to support the
ﬁndings of this study are available from the corresponding
author upon request.
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