*Corr. Author’s Address: Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University, Doha, Qatar, drasan@qu.edu.qa 191
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199 Received for review: 2021-10-29
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-02-09
DOI:10.5545/sv-jme.2021.7458 Original Scientific Paper Accepted for publication: 2022-02-16
Adaptive Electromagnetic Vibration Absorber  
for a Multimode Structure
Mohamed, K.S. – Amri, F. – Elboraey, M. – Nordin, N.H.D. – Muthalif, A.G.A.
Khaled S. Mohamed
1 
– Fatin Amri
2 
– Mostafa Elboraey
1 
– N.H. Diyana Nordin
2 
– Asan G.A. Muthalif
1,
*
1 
Qatar University, College of Engineering, Qatar 
2 
International Islamic University Malaysia, Department of Mechatronics Engineering, Malaysia
All structures experience vibrations due to external dynamic force excitations, such as earthquakes and wind loadings. At resonance, the 
impact of this natural dynamic force on structures may lead to structural failures. Hence, an absorber is mounted to absorb vibrations from the 
primary system. Unfortunately, passive tuned mass absorbers can only target a single frequency. Since structural buildings possess multiple 
modes, an adaptive or tune-able vibration absorber is needed to attenuate the vibration in a multi-degree of freedom (MDOF) system. In this 
work, an adaptive electromagnetic vibration absorber (AEMVA) is proposed to eliminate the effects of vibrations and is dynamically tuned 
using electromagnets. By varying the current supplied to the coil, the stiffness of the AEMVA can be adjusted, resulting in a varying absorber 
frequency. A mathematical description of the AEMVA on a three-story prototype model building is also presented. The three-story benchmark 
model was used to demonstrate the effectiveness of AEMVA in absorbing multiple vibration modes, both analytically and experimentally. 
It is shown that 68.81 %, 50.49 %, and 33.45 % of vibration amplitude reductions were achieved at the first, second, and third modes, 
respectively.
Keywords: adaptive vibration absorber, electromagnetic vibration absorber, multimode system, dynamic modelling, structural vibration 
control
Highlights
• 	 A dynamic system AEMVA with a variable natural frequency was proposed to absorb the vibration of a multi-degree of freedom 
system.
• 	 The basic theory and design for AEMVA were derived.
• 	 Experimental analysis was carried out using a benchmark model of a three-story building.
• 	 Tuning of the dynamic system proved successful in reducing the amplitude of the vibrations.
0  INTRODUCTION
Three decades ago, fewer skyscrapers existed. Due to 
limited spaces and resources, buildings are now often 
built with a higher number of levels. However, high-
rise buildings are prone to vibrations, such as wind-
induced vibrations, causing excessive deflections and 
massive failures. Since high-rise buildings possess 
multiple modes of natural frequency, a tuneable-
dynamic vibration absorber should be opted to 
eliminate unwanted vibrations.
In suppressing structural vibrations, passive 
control devices utilizing liquid or solid masses are 
widely studied. Lumped masses were used for bridge 
piers with improved efficiency of 25 % [1], liquid 
column-based dampers were used for structural 
control with effective results [2], and new damping 
methods were introduced for closely spaced natural 
frequencies for an enhanced accuracy damping 
technique [3]. Liquid-based dampers were introduced 
for controlling seismic vibrations for short-period 
structures [4], while wind-induced vibrations were 
also analysed for control in flexible structures [5]. The 
required damping level is tuned by adjusting the mass 
of the liquid or solid based on the external excitations. 
Some devices were studied and designed for vibration 
suppression through variations of stiffness. Shape 
memory helical springs [6] were studied and enhanced 
for super-elastic shape memory helical springs 
[7], which were enhanced further to temperature-
adjusted shape memory helical springs [8], and alloy 
pounding controlled dampers [9]. Magnetorheological 
elastomers [10] were also studied, and an attenuation 
controller was tested [11] for the practicality of the 
application, which was then enhanced to make use 
of conical magnetorheological elastomer isolators 
[12]. Gyro effects had been studied for a cantilever 
beam vibration isolation [13], and the technology 
was utilized in designing an intelligent glove for the 
suppression of Parkinson’s disease effects [14], all of 
which were proven beneficial in controlling vibrations. 
Apart from being heavy [15], these types of absorbers 
work well only in narrow frequency bands [16]. Also, 
the system parameters might deteriorate due to wear, 
environmental, and operational conditions [17].
Magnetorheological fluids were introduced as a 
viable solution for the development of controllable 
dampers and were extensively used in many 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
192 Mohamed, K.S. – Amri, F. – Elboraey, M. – Nordin, N.H.D. – Muthalif, A.G.A.
applications for damping. In addition to having 
nonlinear hysteretic forces [18], recent studies show 
a maximum vibration reduction of 35 % to 37.2 
% when the absorber is mounted on the first floor 
of a three-story building which was tested for a 
magnetorheological damper for earthquake-induced 
vibrations [19] and was enhanced to include neural 
networks [20], which were later enhanced further to 
include an intelligent bi-state controller [21], which 
proved beneficial but left room for improvements. 
Therefore, it is challenging to create high-efficiency 
magnetorheological (MR) fluid dampers that take 
advantage of the fluid features.
To overcome these issues, a vibration absorber 
capable of tuning its natural frequency in a wide 
frequency band, especially in a structure with multiple 
degrees of freedom, should be implemented. The force 
behaviour should be modelled and fully controlled 
with an understandable non-complex model to achieve 
high efficiencies exceeding the methods previously 
mentioned and be straightforward with fabrication.
In this work, the stiffness of the absorber is varied 
using electromagnetic coils. Variations in the current 
level applied to the magnetic coils directly influence 
the value of the generated magnetic field [17] and 
[22]. As a result, the damper’s stiffness changes 
accordingly, thus changing the absorber’s frequency 
to match the multimode structure’s frequency. This 
allows for a damper that is suitably controlled for a 
wide frequency band.
1  ADAPTIVE VIBRATION ABSORBER  
USING ELECTROMAGNETS
A three-story building prototype model is used in 
this work; the floors were made of aluminium, and 
side support beams were made of stainless steel. 
Fig. 1 shows the prototype and schematic diagram, 
respectively. Stainless steel supporting columns are 
used, and equivalent stiffness for each floor can be 
modelled using Eqs. (1) and (2):
 k
EI
L
c
=
12
3
, (1)
 I
bd
=
3
12
, (2)
where k
c
 is the stiffness for each column, and since 
we have four columns for each floor connected in 
parallel, the effective stiffness for each floor is equal 
to 4k
c
. I is the moment of inertia, E is the modulus 
of rigidity for stainless steel, b is the width for each 
column, d is the thickness of each column, and L
 
is the 
length of each column. The stiffness around each floor 
a)           b) 
Fig. 1.  a) 3-story building model, b) schematic of the absorber/3-story building
Table 1.  Properties of building model
Floors (aluminium) Columnal supports (Stainless steel)
Length of each floor 200 mm Length of each column 200 mm
Width of each floor 150 mm Width of each column 40 mm
Thickness of each floor 15 mm Thickness of each column 1 mm
Mass of each floor 1.50 kg Modulus of elasticity 200 GPa
Density of aluminium 2.7×10
–6
 kg·mm
–3
Stiffness for each column 1 N/mm

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
193 Adaptive Electromagnetic Vibration Absorber for a Multimode Structure 
is obtained using Eqs. (1) and (2), and the properties 
are given in Table 1.
The adaptive electromagnetic vibration absorber 
(AEMVA) mounted on top of the three-story building 
model studied in this work is shown in Fig. 1b. Four 
electromagnets and a prototype model of a three-story 
building Fig. 1b were used to study the efficiency of 
the AEMVA to absorb the vibration of the structure. 
The equation of motion for the structure can be 
represented in Eq. (3):
 MCKf   xxx  , (3)
where M is the mass matrix, C is the damping matrix, 
K is the stiffness matrix, and f is the force function. For 
this project, any damping coefficients are neglected, 
and hence Eq. (4) summarizes the coefficients for Eq. 
(3).
   
m
m
m
m
x
x
x
x
aa
1
2
3
1
2
3
000
00 0
00 0
000


























 




 
 













kk k
kk kk
kk kk
kk
aa
aa
12 2
22 33
33
00
0
0
00
x x
x
x
x
f
a
1
2
3
1
0
0
0

























, (4)
where  x is the acceleration, and x is the horizontal 
displacement of the building. Subscripts 1, 2, and 3 
represent the floor of the building, and subscript a 
refers to the absorber, making m
a
 the mass of the 
AEMVA absorber. In addition, m is the floor mass, 
and k denotes the stiffness. Each floor’s mass and 
stiffness coefficients are as summarized in Table 1, 
while the absorber’s mass m
a
 and stiffness coefficient 
k
a
 are to be examined in Section 3 for the proper 
tuning of the absorber.
2  ADAPTIVE ELECTROMAGNETIC VIBRATION ABSORBER 
MODELLING AND DESIGN
For the magnetic field at a point P with a distance D 
outside a ring of wire with radius R, the magnetic field 
from a small wire segment at the top of the ring can be 
modelled.
 dB
dx







0
22
22
4
I
DR
R
DR
encl.
. (5)
Use Fig. 2 and Eq. (5) after accounting for the 
opposite vertical field directions. I
encl.
 is the current 
supplied I
supp.
 multiplied by the number of coils used. 
By integrating the magnetic field over all the small 
segments of the coil dx

, where the integration is the 
circumference of the circle, Eq. (6), the total field for 
a single loop at point P would arise [23].
 

B
single loop




0
2
22
3
2
2
I R
DR
encl.
. (6)
Eq. (6) represents the magnetic field strength for 
a single wire turn. For a solenoid integrating over all 
the coil turns is required, Fig. 2 is used.
Fig. 2.  Mathematical model representation for the damper
Rewriting Eq. (6) to include the previous findings 
gives Eqs. (7) and (8), where n is the number of coils 
per unit length of the solenoid.
 
II ndx
encl app ..
�� =
 (7)
 

B
total

  


0
2
2
2
32
2
I ndx
R
Dx R
app.
/
, (8)
integrating across the limits of x which is the length 
over the solenoid we obtain Eq. (9):

B
Total


  













0
2
2
22
2
In
DL
DL R
D
DR
app.
)
. (9)
For the force between the two nearby aligned 
electromagnets, we can use the Magnetic-Charge 
model to model the force from one magnet to the 
other as in Eq. (10):
 F
A
repulsion


B
Total
2
0

. (10)
Modelling the electromagnets as a spring so 
forces can be modelled using Fig. 2 and Eq. (11): 
 Fk D
repulsion a
 , (11)

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
194 Mohamed, K.S. – Amri, F. – Elboraey, M. – Nordin, N.H.D. – Muthalif, A.G.A.
where D is the distance between the two 
electromagnets.
This gives Eq. (12) for the semi-spring constants:
 
k
A
x
In
DL
DL R
D
DR
a
Carbon steel core app





  





22
0
2
2
22



.
)
 






. (12)
We also have two springs connected to the mass 
in the middle, which means they are connected in 
parallel, and the equivalent stiffness we are looking 
for is 2k
a
 which gives Eq. (14) for all three vibration 
modes as follows, making use of Eq. (13) for the 
natural frequency using the mass and the stiffness, and 
hence our unit for the natural frequencies is in radians 
per second:
 
n
equivalent
k
m
 . (13)
The final equation used for the natural frequencies 
of the system is Eq. (14); the physical parameters and 
properties of electromagnets are summarized in Table 
2, and an iron core can be seen in Fig. 3a and b, which 
shows the full assembled absorber. The design was 
meant to maximize the repulsion force between two 
electromagnets of opposite polarity opposing each 
other.
  



n
Carbon steel core app
A
x
In
DL
DL R
D
DR



  








0
2
2
22
2 
.
)
 



m
absorber
.
 (14)
Table 2.  Electromagnets properties
Electromagnets (Carbon steel)
Inner diameter 15 mm Diameter of copper coil 5 mm
Outer diameter 30 mm Number of coils 300
Length of core 24 mm Mass of each core 150 g
Thickness of outer layer 4 mm Range of current supplied 0 A to 3 A
Relative magnetic permeability 100
a)           b) 
Fig. 3.  a) Electromagnetic core, and b) AEMVA model
3  SIMULATION STUDIES  
OF ELECTROMAGNETIC VIBRATION ABSORBER (AEMVA)
Simulation studies were conducted for the system’s 
response with and without the absorber. The 
parameters in the simulation studies are listed in 
Tables 1 and 2. Using Eq. (4), the natural frequencies 
of the three-story building are shown in Table 3. 
An excitation input was applied to the building 
and based on Eq. (4), the response of the first floor 
at three modal frequencies was observed. Without 
an absorber, the displacement of the first floor is 
displayed in Fig. 4. Mode shapes at each nodal 
frequency are also shown in Fig. 5. Likewise, Fig. 
6 shows the first floor’s responses at three natural 
frequencies when the absorber is tuned to absorb 
each frequency. Frequencies are given in Hz, and 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
195 Adaptive Electromagnetic Vibration Absorber for a Multimode Structure 
Fig. 4.  Frequency response of the building model without absorber
a)             b)             c) 
Fig. 5.  a) Mode shape of the first resonant frequency, b) mode shape of the second resonant frequency, 
and c) mode shape of the third resonant frequency
amplitude is given in-floor displacement per unit force 
of excitation.
The simulation results show that with proper 
tuning of the electromagnetic stiffness, the AEMVA 
can effectively be used to reduce the vibration 
response of the structure.
4  EXPERIMENTAL SETUP
An experimental setup used to implement the AEMV A 
is shown in Fig 7. An accelerometer is attached to 
the third floor of the building model to measure the 
acceleration signal resulting from the vibration. This 
acceleration signal is used to construct the fast Fourier 
transform (FFT) diagrams and used to construct the 
amplitude-time signal for any time-domain analysis 
required.
An exciter consisting of a motor and an unbalance 
disk is mounted on the first floor of the building to 
exert the force needed to excite the building. The plate 
used for the first floor had a thickness of 5 mm to 
account for the weight of the exciter. A speed controller 
was used to adjust the motor’s rotating frequency. The 
absorber was mounted atop the building, and power 
supplies used were connected to the electromagnets 
for the current variation as required. The polarity 
for each electromagnet was adjusted so the two 
electromagnets facing each other repel. 
A Dewesoft Sirius Modular data acquisition 
system and software were used to acquire and process 
the accelerometer signals. The whole setup was 
mounted on a heavy steel plate for proper structure 
grounding, as in Fig. 7.
5  EXPERIMENTAL RESULTS
The effect of attaching AEMVA to the structure at the 
three resonant frequencies after adjusting the magnetic 
field to provide the necessary stiffness is shown in Fig. 
8. The frequency response function of the building 
model is shown in Fig. 9. The current supplied to each 
electromagnet for each mode is shown in Table 3.
Table 3.  Theoretical and experimental resonance and current 
combinations
Modes
Theoretical resonant 
frequency ω
n
  
[Hz]
Experimental resonant 
frequencies ω
n
  
[Hz]
Current 
supplied  
[A]
First 3.024 2.42 1.80
Second 8.754 7.66 2.60
Third 12.570 12.10 3.00

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
196 Mohamed, K.S. – Amri, F. – Elboraey, M. – Nordin, N.H.D. – Muthalif, A.G.A.
a) 
b) 
c) 
Fig. 6.  a) Anti-resonance of the first mode, b) anti-resonance of the second mode, and c) anti-resonance of the third mode
Fig. 7.  Experimental setup

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
197 Adaptive Electromagnetic Vibration Absorber for a Multimode Structure 
Based on the summarized data in Table 4, Figs. 
8 and 9, it is observed that the AEMVA successfully 
absorbs all three vibration modes. Three resonance 
frequencies at 2.42 Hz, 7.66 Hz, and 12.1 Hz had 
an amplitude attenuation of 68.81 %, 50.49 %, and 
33.45 %, respectively. Notably, the third mode of 
frequency had a lower attenuation than the other 
two modes. This is due to the rapid vibration that 
resulted in the absorber colliding with the side 
electromagnets due to the small distance between 
them. The performance of the AEMVA at the third 
mode can be improved by increasing the current 
supplied to each electromagnet while increasing the 
distance between the electromagnets. This will result 
in a smoother oscillation without any collision but 
will cause excessive heating on electromagnets. The 
general trend is that reducing the distance between the 
two electromagnets or increasing the current increases 
the stiffness coefficient. However, the distance cannot 
be minimal for any effective oscillation to occur; thus, 
experimenting with the current-distance combination 
can prove effective.
6  CONCLUSION
This research used an AEMV A to reduce the vibrations 
on a three-story building prototype model. Both 
simulation and experimental studies are presented in 
this work. By tuning the AEMVA, it is shown that 
the vibrations of the building floors were reduced 
due to the variations of the magnetic flux/stiffness. 
The tuning of AEMVA was achieved by changing 
a) 
b) 
c) 
Fig. 8.  a) Performance of AEMVA at first mode with and without the absorber, b) Performance of AEMVA at second mode with and without 
the absorber, and c) Performance of AEMVA at third mode with and without the absorber

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
198 Mohamed, K.S. – Amri, F. – Elboraey, M. – Nordin, N.H.D. – Muthalif, A.G.A.
a) 
b) 
c) 
Fig. 9.  a) Frequency response function at first mode, b) frequency response function at second mode,  
and c) frequency response function at second mode
Table 4.  AEMVA performance at the resonant frequency
Modes
Resonant frequencies
[Hz]
Vibration amplitude without AEMVA 
[m/s
2
]
Vibration amplitude with AEMVA 
[m/s
2
]
Attenuation amplitude 
[ m/s
2
]
Attenuation 
[%]
First 2.42 5.90 1.84 4.06 68.81
Second 7.66 101.63 50.32 51.31 50.49
Third 12.10 164.65 109.57 55.08 33.45
the current supply to each electromagnet to match the 
resonance frequencies of the model. Both simulation 
and experimental results show that a single absorber 
can suppress the effect of vibration at a multi-modal 
structure.
One point of interest is the slight shift in 
frequencies between the theoretical and experimental 
results and the attenuation, which was almost 100 % 
for all modes in the theoretical results. The frequency 
shift is explained by how the theoretical results were 
conducted without accounting for the weight of the 
absorber on top of the structure and the weight of 
the excitation motor, which decreases the natural 
frequencies of the model. The difference in amplitude 
attenuation comes from the already assumed negligent 
damping. The constant collision of the absorber and 
side electromagnets also causes a lower-than-expected 
percentage attenuation. This was mostly observed in 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)3, 191-199
199 Adaptive Electromagnetic Vibration Absorber for a Multimode Structure 
the third mode of vibration, where the absorber’s mass 
had a higher displacing force due to the rapid structure 
vibration.
7  ACKNOWLEDGEMENTS
This work is partly supported by Qatar University 
Student Grant no: QUST-2-CENG-2020-3.
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