Multi-physics coupling of piezoelectric laminated beam with temperature-dependent material property

doi:10.1007/s10483-026-3418-8

摘要/Abstract

Abstract:

Piezoelectric laminated beams (PLBs) have attracted increasing attention because of their high energy density and ease of integration. However, the temperature sensitivity of their material parameters poses a critical challenge for accurately predicting their response under thermal and vibration excitations. To bridge this gap, we construct a coupled thermo-electro-elastic forced vibration model of the PLB configuration with a tip mass, characterized by a temperature-dependent material property, and derive its closed-form solutions. Furthermore, the dynamic responses induced by thermal and vibration excitations are decoupled and analyzed. The decoupling analysis indicates that the global displacement is predominantly governed by the displacement induced by the thermo-electric coupling effect under static and low-frequency thermal-vibration excitations, with the displacement amplitude on the order of micrometers. Due to the insignificant displacement, the thermal strain is excluded from the multi-physics coupling model, allowing for individual investigation of the effect of temperature-dependent material property on the dynamic response. The results show that the structural resonant frequency decreases with the increasing thermal source intensity, which is attributed to the deterioration of the flexural rigidity. The corresponding maximum voltage and power decrease by 4.5% and 9.7% with the increasing surface thermal source intensity from 0 kW/m² to 2.0 kW/m², respectively. Overall, this study is promising to promote the investigation of multi-physics coupling and provides critical insights into the performance degradation of piezoelectric structures under the combination of thermal and vibration excitations.

Key words: multi-physics coupling, temperature-dependent material property, thermo-electric coupling effect, energy harvesting, Green’s function

中图分类号:

O327

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1811-1834.

Huirong ZHANG, Gantong CHEN, Bohao DUAN, Shengxi ZHOU. Multi-physics coupling of piezoelectric laminated beam with temperature-dependent material property[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1811-1834.

图/表 14

r_m	$T (y 0) / ° C$	e₁/%	r_m	$T (y 0) / ° C$	e₁/%
1	64.000 1		30	64.000 0	$< 0.5$
5	64.000 0	$< 0.5$	40	64.000 0	$< 0.5$
10	64.000 0	$< 0.5$	50	64.000 0	$< 0.5$
20	64.000 0	$< 0.5$	FEM result	64.000 0	$< 0.5$
Note that the precision of the numerical results is determined as $1 × 10 − 4 .$ $e 1 = \| T i (y 0) − T j (y 0) \| / T i (y 0);$ $e 2 = \| T FEM (y 0) − T 50 (y 0) \| / T FEM (y 0) < 0.5 % .$ The superscripts i and j indicate the orders, and $j < i,$ where $j = 1,$ 5, 10, 20, 30, 40; $i = 5,$ 10, 20, 30, 40, 50. $T FEM (y 0)$ denotes the FEM result

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