Static and dynamic responses of a piezoelectric semiconductor beam under different boundary conditions

doi:10.1007/s10483-026-3345-8

Abstract

Abstract:

Due to the intrinsic interaction between piezoelectric effects and semiconducting properties, piezoelectric semiconductors (PSs) have great promise for applications in multi-functional electronic devices, requiring a deep understanding of the multi-field coupling behavior. This work investigates the free vibration and buckling characteristics of a PS beam under different mechanical boundary conditions. The coupling fields of a PS beam are modeled by combining the Timoshenko beam theory for mechanical fields with a high-order expansion along the beam thickness for electric fields and carrier distributions. Based on the hypothesis of small perturbation of carrier density, the governing equations and boundary conditions are derived with the principle of virtual work. The differential quadrature method (DQM) is used to solve the boundary-value problem. The analytical solutions for a simply supported-simply supported (SS) PS beam are also obtained for verification. The convergence and correctness of the solutions obtained with the DQM are first evaluated. Subsequently, the effects of initial electron density, boundary conditions, and geometric parameters on the vibration and buckling characteristics are explored through numerical examples, where the finite element simulations are also included. The interaction mechanism of multi-physics fields is revealed. The scale effect on the static and dynamic responses of a PS beam is demonstrated. The derived model and findings are useful for the analysis and design of PS-based devices.

Key words: piezoelectric semiconductor (PS), beam, vibration, buckling, differential quadrature method (DQM), finite element

2010 MSC Number:

O343

Guoquan NIE, Zhiwei WU, Jinxi LIU. Static and dynamic responses of a piezoelectric semiconductor beam under different boundary conditions. Applied Mathematics and Mechanics (English Edition), 2026, 47(2): 303-324.

TrendMD

Figures/Tables 13

Fig. 1

Table 1

Material parameters of an n-type GaN PS beam[27]"

Elastic constant/ $(N ⋅ m − 2)$	$c 11 = 298.4 × 109,$ $c 12 = 121.0 × 109,$ $c 13 = 142.5 × 109,$ $c 33 = 289.2 × 109,$ $c 44 = 23.1 × 109$
Piezoelectric constant/ $(C ⋅ m − 2)$	$e 15 = − 0.31,$ $e 31 = − 0.52,$ $e 33 = 0.61$
Dielectric constant/ $(C ⋅ V − 1 ⋅ m − 1)$	$κ 11 = 8.41 × 10 − 11,$ $κ 33 = 298.4 × 10 − 11$
Electron mobility coefficient/ $(m 2 ⋅ V − 1 ⋅ s − 1)$	$μ 11 = 653 × 10 − 4,$ $μ 33 = 982 × 10 − 4$
Electron diffusion coefficient/ $(m 2 ⋅ s − 1)$	$d 11 = 17.0 × 10 − 4,$ $d 33 = 25.5 × 10 − 4$

Table 1

Table 2

Calculated dimensionless frequency, damping, and critical buckling load using different numbers of grid points (N)"

$N$	$Re (ω 1)$	$Im (ω 1)$	$P cr$
7	0.274 51	$8.582 4 × 10 − 6$	0.092 32
9	0.274 41	$8.516 7 × 10 − 6$	0.092 25
11	0.274 41	$8.516 5 × 10 − 6$	0.092 26
13	0.274 41	$8.516 9 × 10 − 6$	0.092 26
15	0.274 41	$8.516 9 × 10 − 6$	0.092 26
17	0.274 41	$8.516 9 × 10 − 6$	0.092 26

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

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