Wave propagation in functionally graded piezoelectric sandwich doubly-curved nanoplates based on nonlocal strain gradient theory

doi:10.1007/s10483-026-3369-7

Abstract

Abstract:

This study examines the wave propagation behavior of functionally graded (FG) piezoelectric sandwich doubly-curved nanoplates subjected to thermo-electric loading. The sandwich nanoplates are composed of a piezoelectric layer and an FG interlayer, deposited on a viscoelastic substrate, where the material parameters of the FG interlayer are influenced by temperature variations. By establishing a nonlocal strain gradient constitutive equation that incorporates piezoelectric and thermal effects, the displacement and strain fields of doubly-curved structures are formulated within the framework of first-order shear deformation theory (FSDT). The governing equations are derived using Hamilton’s principle, and then the dispersion relations for the doubly-curved nanoplates are computed through harmonic solution methods. Finally, the systematic analysis is conducted to investigate the effects of curvature parameters, scale parameters, FG indices, and foundation parameters on the wave propagation characteristics. The findings contribute to a deeper understanding of the wave propagation behavior of complex doubly-curved sandwich structures.

Key words: piezoelectric sandwich structure, nonlocal strain gradient theory (NSGT), viscoelastic foundation, doubly-curved plate, wave propagation

2010 MSC Number:

TB34

Jie WANG, Juan LIU, Yinghui LI, Cheng LI, Bo ZHANG, Biao HU, Huoming SHENG. Wave propagation in functionally graded piezoelectric sandwich doubly-curved nanoplates based on nonlocal strain gradient theory. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 767-790.

TrendMD

Figures/Tables 15

Fig. 1

Table 1

Material parameters of PZT-5A"

Material parameter	PZT-5A
Elasticity constant/GPa	$c 11 = 99.201,$ $c 12 = 54.016,$ $c 13 = 50.778,$ $c 22 = 99.201,$ $c 23 = 50.778,$ $c 33 = 86.856,$ $c 44 = c 55 = 21.1,$ $c 66 = 22.6$
Thermal modulus/ $(N ⋅ K − 1 ⋅ m − 2)$	$β 11 = 0.9 × 10 − 6,$ $β 22 = 0.9 × 10 − 6$
Piezoelectric constant/ $(C ⋅ m − 2)$	$e 31 = 12.322,$ $e 32 = 12.322,$ $e 33 = 15.118,$ $e 15 = e 24 = 12.322$
Dielectric constant/ $(C ⋅ V − 1 ⋅ m − 1)$	$s 11 = 1.53 × 10 − 9,$ $s 22 = 1.53 × 10 − 9,$ $s 33 = 1.5 × 10 − 9$
Density/ $(kg ⋅ m − 3)$	$ρ = 7 750$
Poisson’s ratio	$ν = 0.31$

Table 1

Table 2

Thermal and physical parameters of ZrO2 and Ti-6Al-4V"

Material	Parameter	P₀	P₁	P₂	P₃
ZrO₂	$E r$ /GPa	$244.27 × 109$	$− 1.371 × 10 − 3$	$1.214 × 10 − 6$	$− 3.68 × 10 − 10$
Ti-6Al-4V	$β r$ / $(N ⋅ K − 1 ⋅ m − 2)$	$12.766 × 10 − 6$	$− 1.491 × 10 − 3$	$1.006 × 10 − 6$	$− 6.778 × 10 − 11$
	$E m$ /GPa	$122.56 × 109$	$− 4.586 × 10 − 4$	0	0
	$β m$ / $(N ⋅ K − 1 ⋅ m − 2)$	$7.578 × 10 − 6$	$6.638 × 10 − 4$	$− 3.147 × 10 − 6$	0

Table 2

Fig. 2

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