Thermo-mechanical dynamics analysis of smart FG-GPL nanocomposite beams by DQ-FEM Cover

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Thermo-mechanical dynamics analysis of smart FG-GPL nanocomposite beams by DQ-FEM

Acta Mechanica et Automatica

Volume 19 (2025): Issue 4 (December 2025)

By: Mohammed Yassine Mazari , Ismail Bensaid , Ahmed Saimi , Abdelmadjid Cheikh , Ihab Eddine Houalef and Billel Hamza

Open Access

|Dec 2025

Figures & Tables

Dimensions of a GPLRC beam (a), different types of distributions (b)

Convergent of the vibration frequency of a piezoelectric beam armed with GPLs as a function of the amount of grid points

The convergence of the natural frequency of a piezoelectric beam reinforced with graphene platelets as a variable dependent on the quantity of components

The no-dimensional frequency in relation to the quantity of layers (NL) with respect to various forms

The no-dimensional The impact of the beam's span-to-thickness portion on the natural frequency of GPLRC beams (a) ∆T = 0K and (b) ∆T = 100K

The impact of the L/h portion on the no dimensionless natural frequency related to GPLRC beams (a) ∆T = 0K and (b) ∆T = 100K

The impact of GPL dimensions and geometry on the vibratory frequency of FG-X type GPRLC beam (a) ∆T = 0K and (b) ∆T = 100

The impact of the weight portion and temperature increase on the no dimensional vibration frequency of GPLRC beams

The influence of the external electric voltage and piezoelectric component on the vibration frequency of FG-GPLRC beams

Natural Frequencies as Three-Dimensional Bar Chart Under different values of External Electric Voltages and Temperature Differences values

Impact of boundary conditions on the natural frequency of GPLRC beams

Material constituents and properties

Materials	Piezoelectric	GPLs
E(Gpa)	1.4	1010
v	0.29	0.186
ρ(g/cm³)	1.92	1.06
α(10^–6K^–1)	60	5
A₃₁(10^–3C/m²)	50.535	50.535 e₀
A₃₃(10^–3C/m²)	13.212	13.212 e₀
A₁₅(10^–3C/m²)	-15.93	-15.93 e₀
s₁₁(10^–9C/Vm)	0.5385	0.5385 e₀
s₃₃(10^–9C/Vm)	0.59571	0.59571 e₀

Dynamic results of FG-GPLRC piezoelectric beam diverse types of distribution and different values of the length-to-thikness pro-portion L/h

W_GPL	Patterns	UD	FG-X	FG-O	FG-A
0.1%	L/h=5	0.1581	0.1765	0.1373	0.1569
	L/h =10	0.0448	0.0448	0.0348	0.0398
	L/h 15	0.0179	0.0200	0.0155	0.0177
	L/h =20	0.0101	0.0112	0.0087	0.0100
0.3%	L/h=5	0.2237	0.2618	0.1776	0.2194
	L/h =10	0.0567	0.0665	0.0450	0.0557
	L/h 15	0.0253	0.0296	0.0201	0.0248
	L/h =20	0.0142	0.0167	0.0113	0.0140
0.5%	L/h=5	0.2741	0.3257	0.2104	0.2673
	L/h =10	0.0695	0.0827	0.0533	0.0678
	L/h 15	0.0310	0.0368	0.0238	0.0302
	L/h =20	0.0174	0.0207	0.0134	0.0170

Convergence study of DQFEM related to linear free vibration nanocomposite beam armed with GPLs

Ne	N	UD	FG-X	FG-O	FG-A
1	4	0.3061	0.3637	0.2351	0.3062
	6	0.2742	0.3258	0.2105	0.2674
	8	0.2741	0.3257	0.2104	0.2673
	10	0.2741	0.3257	0.2104	0.2673
2	4	0.2752	0.3270	0.2113	0.2686
	6	0.2741	0.3257	0.2104	0.2673
	8	0.2741	0.3257	0.2104	0.2673
	10	0.2741	0.3257	0.2104	0.2673
3	4	0.2743	0.3259	0.2106	0.2676
	6	0.2741	0.3257	0.2104	0.2673
	8	0.2741	0.3257	0.2104	0.2673
	10	0.2741	0.3257	0.2104	0.2673

Comparative of non-dimensional frequency with Wu et al_ 7 for various GPL distributions at ∆T = 0 K, L/H = 10, and WGPL=0_3%

	Pure epoxy	UD	FG-X	FG-O	FG-A
Wu et al.[6]	0.5998	0.8475	0.9293	0.7508	0.8164
Present	0.5977	0.8445	0.9300	0.7401	0.8158

Comparative of the non-dimensional fundamental frequency ω1 for Ps/Pcr=0 between the present results and those of Wu et al_ under different temperature conditions

∆T	Present	Wu et al.[6]
0 K	0.9666	0.9289
50 K	0.9275	0.8883
100 K	0.8865	0.8501

Comparative examination of the natural frequencies of various boundary conditions with varying L/h ratios

BC		L/h=10	L/h=30	L/h=100
S-S	Şimşek [37]	2.695	2.737	2.742
S-S	Present	2.739	2.775	2.779
C-F	Şimşek [37]	0.969	0.976	0.977
C-F	Present	0.976	0.982	0.983
C-C	Şimşek [37]	5.811	6.167	6.212
C-C	Present	5.947	6.242	6.279

Frequency values of functionally graded multilayer X-GPLRC beams with varying boundary conditions and slenderness ratios

BC	L/h=5	L/h=10	L/h=15	L/h=20
S-S	0.3257	0.0827	0.0368	0.0207
C-C	0.7302	0.1888	0.0844	0.0476
C-S	0.5071	0.1297	0.0579	0.0326
C-F	0.1180	0.0297	0.0132	0.0074

Dynamic Change in the non-dimensional frequency of the S-S beams for different temperatures changes, different patterns and various values for weight fraction

∆T	w_GPL	0.1%	0.3%	0.5%
0	UD	0.1581	0.2237	0.2741
	FG-X	0.1765	0.2618	0.3257
	FG-O	0.1373	0.1776	0.2104
	FG-A	0.1569	0.2194	0.2673
100	UD	0.1413	0.2000	0.2451
	FG-X	0.1616	0.2419	0.3017
	FG-O	0.1175	0.1467	0.1711
	FG-A	0.1415	0.1983	0.2417
200	UD	0.1221	0.1730	0.2122
	FG-X	0.1452	0.2201	0.2757
	FG-O	0.0936	0.1071	0.1194
	FG-A	0.1240	0.1741	0.2122

DOI: https://doi.org/10.2478/ama-2025-0081 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

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Language: English

Page range: 719 - 732

Submitted on: Apr 27, 2025

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Accepted on: Sep 28, 2025

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Published on: Dec 31, 2025

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

free vibration,

Quasi-3D beam theory,

thermal effect,

rule of mixture,

graphene reinforced composite beam GPL

Related subjects:

Electrical engineering,

Mechanical engineering,

Bioengineering and biomedical engineering,

Civil engineering,

Environmental engineering

© 2025 Mohammed Yassine Mazari, Ismail Bensaid, Ahmed Saimi, Abdelmadjid Cheikh, Ihab Eddine Houalef, Billel Hamza, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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