Effect of the tetra-chiral auxetic cell and layer geometries on the thermomechanical vibration response of magneto-electro-elastic smart sandwich nanoplates

doi:10.1007/s10483-026-3420-6

摘要/Abstract

Abstract:

This work investigates the thermomechanical vibration response of magneto-electro-elastic (MEE) smart sandwich nanoplates incorporating a tetra-chiral auxetic core. The analysis is performed within the framework of nonlocal strain-gradient elasticity combined with a four-variable refined shear deformation theory, enabling the simultaneous consideration of size-dependent effects, geometric chirality, and multi-field coupling. The studied configuration consists of a porous tetra-chiral auxetic core bonded to piezo-electro-magnetic face layers and subjected to thermal loading together with external electric and magnetic potentials. The effective elastic properties of the tetra-chiral auxetic core are evaluated by a unit-cell approach. The governing equations of motion are derived via Hamilton’s principle and solved analytically by Navier’s method. The model accuracy is verified through comparisons with the previously published results. A detailed parametric investigation is conducted to examine the effects of the auxetic geometric parameters, core-to-face thickness ratios, face-layer material composition, applied electric and magnetic fields, and nonlocal length-scale parameters on the fundamental vibration characteristics of the proposed smart sandwich nanoplates. The results indicate that the magnetic loading and strain-gradient effects enhance structural stiffness and stability, whereas the electric potential and nonlocal parameter introduce softening. Overall, the tetra-chiral auxetic cores provide an efficient mechanism for tuning and controlling the vibration behavior of smart sandwich nanoplates operating in coupled thermal and multi-field environments.

Key words: tetra-chiral auxetic lattice, magneto-electro-elastic (MEE) sandwich nanoplate, thermomechanical vibration, nonlocal strain-gradient elasticity, smart structure

中图分类号:

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1691-1722.

T. DAS, M. T. OZDEMIR, M. S. GUL, I. ESEN. Effect of the tetra-chiral auxetic cell and layer geometries on the thermomechanical vibration response of magneto-electro-elastic smart sandwich nanoplates[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1691-1722.

图/表 12

Material	Property	P₀	P₁	P₂	P₃
BaTiO₃	ν	0.3	0	0	0
	κ/(W·m^-1K^-1)	3.762	$− 8.505 × 10 − 4$	$1.328 × 10 − 6$	$− 7.973 × 10 − 10$
	α/K^-1	$1 × 10 − 5$	$− 3.0 × 10 − 4$	$4.0 × 10 − 6$	$1.0 × 10 − 9$
	ρ/(kg·m^-3)	5 800	0	0	0
	$C 11$ /Pa	$1.74 × 1011$	$− 1.552 × 10 − 4$	$6.125 × 10 − 9$	$− 9.0 × 10 − 11$
	$C 55$ /Pa	$4.493 × 1010$	$− 1.552 × 10 − 4$	$6.125 × 10 − 9$	$− 9.0 × 10 − 11$
CoFe₂O₄	ν	0.3	0	0	0
	κ/(W·m^-1K^-1)	4.703	$− 0.001$	$1.661 × 10 − 6$	$− 9.967 × 10 − 10$
	α/K^-1	$7.5 × 10 − 6$	$− 3.01 × 10 − 4$	$4.02 × 10 − 6$	$− 1.01 × 10 − 9$
	ρ/(kg·m^-3)	5 300	0	0	0
	$C 11$ /Pa	$2.898 7 × 1011$	$− 1.552 × 10 − 4$	$6.125 × 10 − 9$	$− 9.0 × 10 − 11$
	$C 55$ /Pa	$4.733 × 1010$	$− 1.552 × 10 − 4$	$6.125 × 10 − 9$	$− 9.0 × 10 − 11$

$a / h$	$μ 2 / nm 2$	TSDT
$a / h$	$μ 2 / nm 2$	Ref. [65]	Ref. [51]	Present
10	0	9.35	9.302 9	9.321
	1	8.54	8.501 6	8.512
	2	7.91	7.877 1	7.902
	3	7.41	7.372 6	7.398
	4	6.99	6.954 2	6.983
	5	6.63	6.599 7	6.619
20	0	2.39	2.386 4	2.391
	1	2.18	2.180 8	2.173
	2	2.02	2.020 6	2.012
	3	1.89	1.891 2	1.893
	4	1.79	1.783 9	1.792
	5	1.70	1.692 9	1.689

e₀	( $m, n$ )	μ/nm
		Ref. [51]				Present
		1	2	3	4	1	2	3	4
0.2	(1, 1)	20.867 19	20.698 57	20.426 39	20.062 77	20.912	20.731	20.458	20.081
	(2, 2)	81.239 06	78.743 64	75.051 23	70.657 99	81.104	78.612	74.982	70.521
	(3, 3)	175.115 9	163.933 3	149.273 2	134.094 6	174.832	163.521	148.964	133.782
0.4	(1, 1)	21.153 58	20.982 64	20.706 73	20.338 12	21.238	21.061	20.781	20.412
	(2, 2)	82.145 83	79.622 5	75.888 93	71.446 65	82.031	79.487	75.624	71.213
	(3, 3)	176.413 2	165.147 7	150.379 0	135.088 0	176.084	164.732	149.815	134.527
0.6	(1, 1)	21.640 47	21.465 60	21.183 33	20.806 24	21.698	21.524	21.241	20.872
	(2, 2)	83.702 69	81.131 59	77.327 21	72.800 74	83.518	81.004	77.112	72.564
	(3, 3)	178.725 2	167.312 1	152.349 9	136.858 4	178.391	166.987	151.982	136.274
0.8	(1, 1)	22.579 63	22.397 17	22.102 65	21.709 19	22.613	22.428	22.136	21.756
	(2, 2)	86.706 72	84.043 34	80.102 42	75.413 51	86.314	83.782	79.864	75.098
	(3, 3)	183.268 7	171.565 4	156.222 8	140.337 5	182.741	171.182	155.847	139.962

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