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Bending and Vibration Analysis of Magneto-Electro Bilaterally Coated Quasi-3D Microbeam Via DQ-FEM Cover

Bending and Vibration Analysis of Magneto-Electro Bilaterally Coated Quasi-3D Microbeam Via DQ-FEM

Acta Mechanica et Automatica
Volume 19 (2025): Issue 3 (September 2025)
By: Besma KHOUANI,  Ahmed SAIMI and  Ismail BENSAID  
Open Access
|Sep 2025

Figures & Tables

Fig. 1.

Piezo-bilaterally FG microbeam model
Piezo-bilaterally FG microbeam model

Fig. 2.

Comparative analysis of the bending of a doubly S-S microbeam exposed to an even distribution of load
Comparative analysis of the bending of a doubly S-S microbeam exposed to an even distribution of load

Fig. 3.

Comparative analysis of electrical potential of a doubly S-S microbeam exposed to an even distribution of load
Comparative analysis of electrical potential of a doubly S-S microbeam exposed to an even distribution of load

Fig. 4.

Comparative analysis of magnetic potential of a doubly S-S microbeam exposed to an even distribution of load
Comparative analysis of magnetic potential of a doubly S-S microbeam exposed to an even distribution of load

Fig. 5.

Deflection of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))
Deflection of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))

Fig. 6.

Electric potential of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))
Electric potential of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))

Fig. 7.

Magnetic potential of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))
Magnetic potential of MEE bilaterally microbeam with various boundary conditions (kz = 1, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%))

Fig. 8.

Simply supported microbeam midspan deflection with various thickness and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (kz = 1, b = 2h, L = 20h,)
Simply supported microbeam midspan deflection with various thickness and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (kz = 1, b = 2h, L = 20h,)

Fig. 9.

Electric (a) and magnetic (b) potentials at simply supported microbeam midspan with various thickness and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (kz = 1, b = 2h, L = 20h,)
Electric (a) and magnetic (b) potentials at simply supported microbeam midspan with various thickness and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (kz = 1, b = 2h, L = 20h,)

Fig. 10.

Simply supported microbeam midspan deflection with various FG fraction index and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (h = 20μm, b = 2h, L = 20h,)
Simply supported microbeam midspan deflection with various FG fraction index and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (h = 20μm, b = 2h, L = 20h,)

Fig. 11.

Electric (a) and magnetic (b) potentials at simply supported microbeam midspan with various FG fraction index and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (h = 20μm, b = 2h, L = 20h,)
Electric (a) and magnetic (b) potentials at simply supported microbeam midspan with various FG fraction index and MEE inner material mixture percentage BaTiO3 – CoFe2O4 (h = 20μm, b = 2h, L = 20h,)

Fig. 12.

Electric and magnetic potentials distribution of simply supported microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)
Electric and magnetic potentials distribution of simply supported microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)

Fig. 13.

Electric and magnetic potentials distribution of clamped microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)
Electric and magnetic potentials distribution of clamped microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)

Fig. 14.

Electric and magnetic potentials distribution of clamped free microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)
Electric and magnetic potentials distribution of clamped free microbeam with kz = 5, h = 20μm, b = 2h, L = 20h, BaTiO3(50%) – CoFe2O4(50%)

Fig. 15.

Deflection with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h
Deflection with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h

Fig. 16.

Electric potential with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h
Electric potential with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h

Fig. 17.

Magnetic potential with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h
Magnetic potential with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h

Fig. 18.

Natural frequencies with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h
Natural frequencies with respect to length-thickness ratio of simply supported microbeam with kz = 5, b = 2h

Materials Properties of the mixture (BaTiO3 – CoFe2O4)

BaTiO3 – CoFe2O4epoxy
0%-100%20%-80%40%-60%50%-50%60%-40%80%-20%100%-0%
C112862622382262141901664.889
C13170151.6133.2124114.896.4782.407
C33269.5248226.5215.75205183.51624.889
C5545.344.8444.3844.1543.9243.46431.241
q31580.3464.24348.18290.15232.12116.0600
q33699.7559.76419.82349.85279.88139.9400
q1555044033027522011000
e310-0.88-1.76-2.2-2.64-3.52-4.40
e3303.727.449.311.1614.8818.60
e1502.324.645.86.969.2811.60
s110.082.34.535.646.758.9811.20
s330.0932.595.106.357.610.1012.60
d1102.64.585.386.027.0400
d3302020276027402520155000
μ11590473356297.523912250
μ33157127.69883.568.839.4100
ρ53005400550055505600570058001180
MLSP l7.337.297.247.217.187.10716.93

Comparison of numerical results (b = 2h, L = 20h), 50%-50% BaTiO3 – CoFe2O4

h(μm)Frequency (MHz)
1st mode2nd mode3rd mode
[12]present[12]present[12]present
14.424.0974.06916.81116.22839.64734.853
28.841.7101.7017.0076.78416.46614.796
h(μm)Midspan Deflection w/hMidspan Electric potential γ(V)Midspan Magnetic potential 𝜁(A)
[12]present[12]present[12]present
14.420.07920.0793-1.251-1.2290.01250.0122
28.840.02840.0283-0.896-0.8770.00900.0087

Natural frequency (MHz) of simply supported MEE FG microbeam (b = 2h, L = 20h,)

BaTiO3 – CoFe2O4
h(μm)kz0%-100%20%-80%40%-60%50%-50%60%-40%80%-20%100%-0%
2003.00092.85712.71082.63632.56132.40712.2472
0.52.52502.41242.29752.23912.18022.05891.9332
12.22002.12832.03481.98721.93931.84041.7380
51.51821.48401.44911.43131.41351.37661.3386
101.39191.37311.35391.34411.33441.31411.2932
151.35381.34111.32821.32161.31501.30131.2872
201.33521.32601.31661.31181.30701.29701.2867
4001.35781.28911.21911.18361.14761.07390.9974
0.51.09791.04490.99090.96340.93560.87860.8194
10.92700.88470.84150.81960.79730.75180.7045
50.52040.50780.49500.48850.48200.46870.4550
100.46030.45480.44920.44640.44360.43780.4318
150.45020.44690.44350.44180.44010.43660.4330
200.44810.44580.44350.44230.44110.43870.4362
10000.52600.49890.47130.45720.44300.41390.3836
0.50.41890.39800.37680.36600.35500.33260.3092
10.34750.33100.31410.30550.29680.27890.2604
50.17220.16770.16330.16100.15870.15410.1494
100.14730.14580.14420.14340.14270.14110.1395
150.14490.14410.14330.14290.14250.14170.1408
200.14550.14500.14450.14420.14400.14340.1429
DOI: https://doi.org/10.2478/ama-2025-0041 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 337 - 349
Submitted on: Dec 26, 2024
Accepted on: Apr 10, 2025
Published on: Sep 5, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
higher-order Q3D beam theory,
magneto-electro-elastic microbeam,
MCST,
DQ-FEM,
FGM
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Besma KHOUANI, Ahmed SAIMI, Ismail BENSAID, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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