Free vibration of piezoelectric semiconductor composite structure with fractional viscoelastic layer

doi:10.1007/s10483-025-3237-8

Abstract

Abstract:

In this study, the free vibration of a piezoelectric semiconductor (PS) composite structure composed of a PS layer, a fractional viscoelastic layer, and an elastic substrate with simply-supported boundary conditions is investigated. The fractional derivative Zener model is used to establish the constitutive relation of the viscoelastic layer. The first-order shear deformation theory and Hamilton's principle are used to derive the motion equations of the present problem. The frequency parameter is numerically resolved with the Newton-Raphson method through the eigenvalue equation. The effects of either geometric parameters, carrier density, and electric voltage applied on the surface of the composite structure or the fractional order of the Zener model on both the natural frequency and loss factor are discussed, and some interesting conclusions are drawn. This work will be helpful for designing and manufacturing PS materials and structures.

Key words: fractional viscoelastic material, free vibration, composite structure, piezoelectric semiconductor (PS)

2010 MSC Number:

O327

Yansong LI, Wenjie FENG, Lei WEN. Free vibration of piezoelectric semiconductor composite structure with fractional viscoelastic layer. Applied Mathematics and Mechanics (English Edition), 2025, 46(4): 683-698.

TrendMD

Figures/Tables 13

Fig. 1

Table 1

Comparison of vibration frequencies of PS plate for different modes"

$ω (λ 1, λ 2)$	$n 0 = 10 16$ m $− 3$		$n 0 = 10 23$ m $− 3$
$ω (λ 1, λ 2)$	Guo et al.^[32]	Present	Guo et al.^[32]	Present
$ω$ (1, 1)	0.991 1	0.991 3	0.983 3	0.983 3
$ω$ (1, 2)	2.157 1	2.157 2	2.148 8	2.148 9
$ω$ (2, 2)	3.071 3	3.071 5	3.065 0	3.065 4

Table 1

Table 2

Material properties of fractional viscoelastic (1SD-110) and PS (ZnO) materials (see Permoon and Farsadi[47] and Wang et al.[50])"

ISD-110	ZnO	ZnO
$a ∗ = 0.028 7$ MPa	$c 11 = c 22 = 209.7$ GPa	$e 15 = e 24 = − 0.48$ C/m $2$
$b ∗ = 1.035$ MPa	$c 12 = 121.1$ GPa	$ε 11 = ε 22 = 7.57 × 10 − 11$ F/m
$c ∗ = 0.011$	$c 13 = c 23 = 105.1$ GPa	$ε 33 = 9.03 × 10 − 11$ F/m
$α = 0.5$	$c 33 = 210.9$ GPa	$μ 11 = μ 22 = 0.02$ m $2$ / $(V ⋅ s)$
$ρ c = 965$ kg/m $3$	$c 44 = 42.47$ GPa	$μ 33 = 0.02$ m $2$ / $(V ⋅ s)$
	$c 55 = 42.47$ GPa	$d 11 = d 22 = 0.000 52$ m $2$ /s
	$c 66 = 44.3$ GPa	$d 33 = 0.000 52$ m $2$ /s
	$e 31 = e 32 = − 0.573$ C/m $2$	$ρ t = 5 700$ kg/m $3$
	$e 33 = 1.32$ C/m $2$

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

References 50

[1]	WANG, Z. L. Nanobelts, nanowires, and nanodiskettes of semiconducting oxides-from materials to nanodevices. Advanced Materials, 15(5), 432–436 (2003)
[2]	OLSON, D. C., PARIS, J., COLLINS, R. T., SHAHEEN, S. E., and GINLEY, D. S. Hybrid photovoltaic devices of polymer and ZnO nanofiber composites. Thin Solid Films, 496(1), 26–29 (2006)
[3]	DURAISAMY, N., KWON, K. R., JO, J., and CHOI, K. H. Development of nanostructured ZnO thin film via electrohydrodynamic atomization technique and its photoconductivity characteristics. Journal of Nanoscience and Nanotechnology, 14(8), 5849–5855 (2014)
[4]	KALANTAR-ZADEH, K., CHEN, Y. Y., FRY, B. N., TRINCHI, A., and WLODARSKI, W. A novel Love mode SAW sensor with ZnO layer operating in gas and liquid media. IEEE Ultrasonics Symposium, Institute of Electrical and Electronics Engineers, 353–356 (2001)
[5]	LIN, C. Y., CHEN, J. G., FENG, W. Y., LIN, C. W., HUANG, J. W., TUNNEY, J. J., and HO, K. C. Using a TiO₂/ZnO double-layer film for improving the sensing performance of ZnO based NO gas sensor. Sensors and Actuators B-Chemical, 157(2), 361–367 (2011)
[6]	RAHMAN, R. A., ZULKEFLE, M. A., YUSOFF, K. A., ABDULLAH, W. F. H., RUSOP, M., and HERMAN, S. H. Drying temperature dependence of sol-gel spin coated bilayer composite ZnO/TiO₂ thin films for extended gate field effect transistor pH sensor. Materials Science and Engineering, 340, 012018 (2018)
[7]	FERNANDES, J. C. and MULATO, M. Synthesis and electrical characterization of ZnO and TiO₂ thin films and their use as sensitive layer of pH field effect transistor sensors. MRS Online Proceedings Library, 1675, 53–58 (2014)
[8]	RASHEED, H. S., AHMED, N. M., MATJAFRI, M. Z., ALHARDAN, N. H., AL-MESSIERE, M. A., SABAH, F. A., and AL-HAZEEM, N. Z. Multilayer ZnO/Pd/ZnO structure as sensing membrane for extended-gate field-effect transistor (EGFET) with high pH sensitivity. Journal of Electronic Materials, 46(10), 5901–5908 (2017)
[9]	LI, J., HUANG, C. X., ZHAO, C. Y., DING, X. W., ZHANG, J. H., JIANG, X. Y., and ZHANG, Z. L. High performance ZnSnO thin film transistor with ZrO₂ gate insulator formed by atomic layer deposition. Journal of Nanoelectronics and Optoelectronics, 13(2), 214–220 (2018)
[10]	YANG, J. H., CHOI, J. H., CHO, S. H., PI, J. E., KIM, H. O., HWANG, C. S., PARK, K. C., and YOO, S. Highly stable AlInZnSnO and InZnO double-layer oxide thin-film transistors with mobility over 50 cm²/V · s for high-speed operation. IEEE Electron Device Letters, 39(4), 508–511 (2018)
[11]	TAKEUCHI, M., YAMADA, H., KAWAMURA, H., GOTO, Y., NOMURA, T., FUJINO, H., YOSHINO, Y., MAKINO, T., and ARAI, S. Stress adjustment and characteristics improvement in a 1.8GHz range film bulk acoustic wave resonator by using multi-layer structure of ZnO/A1₂O₃/SiO₂. Materials Research Society Symposium Proceedings, 741, 59 (2003)
[12]	LUO, J. T., LUO, P. X., XIE, M., DU, K., ZHAO, B. X., PAN, F., FAN, P., ZENG, F., ZHANG, D. P., ZHENG, Z. H., and LIANG, G. X. A new type of glucose biosensor based on surface acoustic wave resonator using Mn-doped ZnO multilayer structure. Biosensors & Bioelectronics, 49, 512–518 (2013)
[13]	BIAN, X. L., JIN, H., WANG, X. Z., DONG, S. R., CHEN, G. H., LUO, J. K., DEEN, M. J., and QI, B. S. UV sensing using film bulk acoustic resonators based on Au/n-ZnO/piezoelectric-ZnO/Al structure. Scientific Reports, 5, 9123 (2015)
[14]	ZHANG, C., WANG, X., CHEN, W., and YANG, J. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force. Smart Materials and Structures, 26, 025030 (2017)
[15]	FAN, S., LIANG, Y., XIE, J., and HU, Y. Exact solutions to the electromechanical quantities inside a statically-bent circular ZnO nanowire by taking into account both the piezoelectric property and the semiconducting performance: part I — linearized analysis. Nano Energy, 40, 82–87 (2017)
[16]	LUO, Y., ZHANG, C., CHEN, W., and YANG, J. Piezopotential in a bended composite fiber made of a semiconductive core and of two piezoelectric layers with opposite polarities. Nano Energy, 54, 341–348 (2018)
[17]	XIAO, Z. G., LI, S. P., and ZHANG, C. L. Analysis of piezoelectric semiconductor structures considering both physical and geometric nonlinearities. Acta Mechanics Solida Sinica, 37, 72–81 (2024)
[18]	HU, Y., ZENG, Y., and YANG, J. A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry. International Journal of Solids and Structures, 44, 3928–3938 (2007)
[19]	SLADEK, J., SLADEK, V., BISHAY, P., and GARCIA-SANCHEZ, F. Influence of electric conductivity on intensity factors for cracks in functionally graded piezoelectric semiconductors. International Journal of Solids and Structures, 59, 79–89 (2015)
[20]	ZHAO, M., PAN, Y., FAN, C., and XU, G. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. International Journal of Solids and Structures, 94, 50–59 (2016)
[21]	YANG, C. H., ZHAO, M. H., LU, C. S., and ZHANG, Q. Y. Analysis of a penny-shaped crack with semi-permeable boundary conditions across crack face in a 3D thermal piezoelectric semiconductor. Engineering Analysis with Boundary Elements, 131, 76–85 (2021)
[22]	LI, Y., YAN, S. J., ZHAO, M. H., and REN, J. L. Fracture analysis of planar cracks in 3D thermal piezoelectric semiconductors. International Journal of Mechanical Sciences, 273, 109212 (2024)
[23]	GU, C. L. and JIN, F. Shear-horizontal surface waves in a half-space of piezoelectric semiconductors. Philosophical Magazine Letters, 95(2), 92–100 (2015)
[24]	JIAO, F. Y., WEI, P. J., ZHOU, Y. H., and ZHOU, X. L. Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. European Journal of Mechanics A-Solids, 75, 70–81 (2019)
[25]	TIAN, R., LIU, J. X., PAN, E., WANG, Y., and AI, K. S. Some characteristics of elastic waves in a piezoelectric semiconductor plate. Journal of Applied Physics, 126(12), 125701 (2019)
[26]	XU, C. Y., WEI, P. J., WEI, Z. B., and GUO, X. Shear horizontal wave propagation on a piezoelectric semiconductor substrate under slight ridge or thin metal strip gratings. Thin-Walled Structures, 191, 111059 (2023)
[27]	LI, D. Z., LI, S. P., MA, N. N., WANG, H. M., ZHANG, C. L., and CHEN, W. Q. Propagation characteristics of elastic longitudinal wave in a piezoelectric semiconductor metamaterial rod and its tuning. International Journal of Mechanical Sciences, 266, 108977 (2024)
[28]	YANG, L., ZAPPINO, E., CARRERA, E., and DU, J. K. Rotation effects on propagation of shear horizontal surface waves in piezomagnetic-piezoelectric semiconductor layered structures. Applied Mathematical Modelling, 129, 494–508 (2024)
[29]	LI, D. Z., ZHANG, C. L., ZHANG, S. F., WANG, H. M., CHEN, W. Q., and ZHANG, C. Z. Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods. Ultrasonics, 132, 106964 (2023)
[30]	YANG, W. L., GUO, L. Y., ZHANG, S. L., and HU, Y. T. On elastic wave propagation in piezoelectric semiconductors with coupled piezoelectric and semiconductor properties. International Journal of Engineering Science, 205, 104160 (2024)
[31]	LUO, Y. X., CHENG, R. R., and ZHANG, C. L. Analysis of flexural vibrations of laminated piezoelectric semiconductor plates. Chinese Journal of Solid Mechanics, 41(1), 15–29 (2020)
[32]	GUO, J. Y., NIE, G. Q., LIU, J. X., and ZHANG, L. L. Free vibration of a piezoelectric semiconductor plate. European Journal of Mechanics A-Solids, 95, 104647 (2022)
[33]	WANG, W. J., JIN, F., HE, T. H., and MA, Y. B. Size-dependent and nonlinear magneto-mechanical coupling characteristics analysis for extensional vibration of composite multiferroic piezoelectric semiconductor nanoharvester with surface effect. European Journal of Mechanics A-Solids, 96, 104708 (2022)
[34]	ZHANG, Z. C., LIANG, C., KONG, D. J., XIAO, Z. G., ZHANG, C. L., and CHEN, W. Q. Dynamic buckling and free bending vibration of axially compressed piezoelectric semiconductor rod with surface effect. International Journal of Mechanical Sciences, 238, 107823 (2023)
[35]	FANG, X. Q., DUAN, J. Q., ZHU, C. S., and LIU, J. X. Vibration analysis of piezoelectric semiconductor beams with size-dependent damping characteristic. Materials Today Communications, 36, 106929 (2023)
[36]	YAN, Y. X., ZHU, C. S., FANG, X. Q., and SHI, L. Free vibration of functionally-graded piezoelectric semiconductor rectangular beam under thermal load. Physica B, 690, 416265 (2024)
[37]	CAO, Y., GUO, Z. W., and QU, Y. L. Static bending and forced vibration analyses of a piezoelectric semiconductor cylindrical shell within first-order shear deformation theory. Applied Mathematical Modelling, 126, 625–645 (2024)
[38]	LUO, Y. X., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Piezotronic effect of a thin film with elastic and piezoelectric semiconductor layers under a static flexural loading. Journal of Applied Mechanics, 86(5), 051003 (2019)
[39]	JI, M., KANG, C., SEKIGUCHI, Y., NAITO, M., and SATO, C. Spectral collocation method for free vibration of sandwich plates containing a viscoelastic core. Composite Structures, 337, 118024 (2024)
[40]	BILASSE, M. and OGUAMANAM, D. C. D. Forced harmonic response of sandwich plates with viscoelastic core using reduced-order model. Composite Structures, 105, 311–318 (2013)
[41]	D'OTTAVIO, M., KRASNOBRIZHA, A., VALOT, E., POLIT, O., VESCOVINI, R., and DOZIO, L. Dynamic response of viscoelastic multiple-core sandwich structures. Journal of Sound and Vibration, 491, 115753 (2021)
[42]	MARYNOWSKI, K. Free vibration analysis of the axially moving Levy-type viscoelastic plate. European Journal of Mechanics A-Solids, 29, 879–886 (2010)
[43]	HOSSEINI-HASHEMI, S., ABAEI, A. R., and ILKHANI, M. R. Free vibrations of functionally graded viscoelastic cylindrical panel under various boundary conditions. Composite Structures, 126, 1–15 (2015)
[44]	MOKHTARI, M., PERMOON, M. R., and HADDADPOUR, H. Aeroelastic analysis of sandwich cylinder with fractional viscoelastic core described by Zener model. Journal of Fluids and Structures, 85, 1–16 (2019)
[45]	ALAIMO, A., ORLANDO, C., and VALVANO, S. Analytical frequency response solution for composite plates embedding viscoelastic layers. Aerospace Science and Technology, 92, 429–445 (2019)
[46]	PERMOON, M. R., SHAKOURI, M., and HADDADPOUR, H. Free vibration analysis of sandwich conical shells with fractional viscoelastic core. Composite Structures, 214, 62–72 (2019)
[47]	PERMOON, M. R. and FARSADI, T. Free vibration of three-layer sandwich plate with viscoelastic core modelled with fractional theory. Mechanics Research Communication, 116, 103766 (2021)
[48]	WANG, Q. On buckling of column structures with a pair of piezoelectric layers. Engineering Structures, 24, 199–205 (2002)
[49]	LI, Y. S. and PAN, E. Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory. International Journal of Engineering Science, 97, 40–59 (2015)
[50]	WANG, T. Q., ZHU, F., LI, P., XU, Z. L., MA, T. F., KUZNETSOVA, I., and QIAN, Z. H. Analysis and modeling of two-dimensional piezoelectric semiconductor shell theory. European Journal of Mechanics A-Solids, 106, 105331 (2024)