Applied Mathematics and Mechanics >
Vibration characteristic analysis of a cracked piezoelectric semiconductor curved beam
Received date: 2025-05-23
Revised date: 2025-08-11
Online published: 2025-09-30
Supported by
Project supported by the National Natural Science Foundation of China (No. 12272353), the Postdoctoral Research Grant in Henan Province of China (No. 202003091), and the Key Scientific Research Projects in Colleges and Universities of Henan Province of China (No. 22A130008)
Copyright
The fracture mechanics theory posits that cracks induce strain energy concentration near their tips in structural components, generating localized flexibility that impedes crack propagation. Theoretically, cracks are represented as dimensionless, massless spring models, effectively capturing crack characteristics and cross-sectional properties at the crack location. Leveraging this spring-based representation, this study establishes an open-crack model for a one-dimensional (1D) piezoelectric semiconductor (PSC) curved beam under dynamic loading. This model enables the investigation of vibration characteristics in cracked structures. The analytical solutions for the electromechanical fields of the beam are derived using the differential operator method, and the natural frequencies together with the corresponding generalized mode shapes of the beam are determined analytically. Furthermore, the effects of the crack parameters on the natural vibration characteristics of the PSC curved beam are analyzed.
Qiaoyun ZHANG , Xiaoyan ZHANG , Jiahao XU , Zhicai SONG , Minghao ZHAO . Vibration characteristic analysis of a cracked piezoelectric semiconductor curved beam[J]. Applied Mathematics and Mechanics, 2025 , 46(10) : 1967 -1982 . DOI: 10.1007/s10483-025-3307-6
| [1] | WANG, X. D., ZHOU, J., SONG, J. H., JIN, L., XU, N. S., and WANG, Z. L. Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Letters, 6(12), 2768–2772 (2006) |
| [2] | SHIM, Y. S., ZHANG, L., KIM, D. H., YOU, R. C., NAHM, S. H., KANG, C. Y., LEE, W., and JANG, H. W. Highly sensitive and selective H2 and NO2 gas sensors based on surface-decorated WO3 nanoigloos. Sensors and Actuators B-Chemical, 198(2), 294–301 (2014) |
| [3] | PU, X. G., SONG, J., JIN, L., and WANG, Z. L. Nanowire piezoelectric nanogenerators on plastic substrates as flexible power sources for nanodevices. Advanced Materials, 19(1), 67–72 (2006) |
| [4] | PURUSOTHAMAN, Y., ALLURI, N. R., CHANDRASEKHAR, A., and KIM, S. J. Photoactive piezoelectric energy harvester driven by antimony sulfoiodide (SbSI): a AV BVI CVII class ferroelectric-semiconductor compound. Nano Energy, 50, 256–265 (2018) |
| [5] | DIETZ, D. R. and BUSSE, L. J. Acoustoelectric detection of ultrasound power with composite piezoelectric and semiconductor devices. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 35(2), 146–151 (1988) |
| [6] | KINO, G. S. Acoustoelectric interactions in acoustic-surface-wave devices. Proceedings of the IEEE, 64(5), 724–748 (1976) |
| [7] | YANG, Q., WANG, W. H., XU, S., and WANG, Z. L. Enhancing light emission of ZnO microwire-based diodes by piezo-phototronic effect. Nano Letters, 11(9), 4012–4017 (2011) |
| [8] | WANG, Z. L. Nanopiezotronics. Advanced Materials, 19(6), 889–892 (2007) |
| [9] | WANG, Z. L. Piezopotential gated nanowire devices: piezotronics and piezo-phototronics. Nano Today, 5(6), 540–552 (2010) |
| [10] | ZHANG, C. L., WANG, X. Y., CHEN, W. Q., and YANG, J. S. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force. Smart Materials and Structures, 26(2), 025030 (2017) |
| [11] | YANG, G. Y., DU, J. K., WANG, J., and YANG, J. S. Extension of a piezoelectric semiconductor fiber with consideration of electrical nonlinearity. Acta Mechanica, 229(11), 4663–4676 (2018) |
| [12] | CHENG, R. R., ZHANG, C., CHEN, W. Q., and YANG, J. S. Piezotronic effects in the extension of a composite fiber of piezoelectric dielectrics and nonpiezoelectric semiconductors. Journal of Applied Physics, 124(6), 064506 (2018) |
| [13] | LI, P., JIN, F., and MA, J. X. One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis. Applied Mathematics and Mechanics (English Edition), 39(5), 685–702 (2018) https://doi.org/10.1007/s10483-018-2325-6 |
| [14] | HAN, C. F., LU, C. S., ZHAO, M. H., and ZHANG, Q. Y. Nonlinear finite element analysis of electromechanical behaviors in a piezoelectric semiconductor beam. International Journal of Non-linear Mechanics, 49, 104311 (2023) |
| [15] | LIU, Z. W., BIAN, P. L., QU, Y. L., HUANG, W. C., CHEN, L. L., CHEN, J. B., SAXENA, P., and YU, T. T. A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams. European Journal of Mechanics-A/Solids, 103, 105145 (2024) |
| [16] | WANG, G. L., LIU, J. X., LIU, X. L., FENG, W. J., and YANG, J. S. Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber. Journal of Applied Physics, 124(9), 094502 (2018) |
| [17] | DAI, X. Y., ZHU, F., QIAN, Z. H., and YANG, J. S. Electric potential and carrier distribution in a piezoelectric semiconductor nanowire in time-harmonic bending vibration. Nano Energy, 43, 22–28 (2018) |
| [18] | YAN, Y. X., ZHU, C. S., and FANG, X. Q. Free vibration of three-layered piezoelectric semiconductor rectangular beam. Materials Today Communications, 38, 107859 (2024) |
| [19] | QU, Y. L., JIN, F., and YANG, J. S. Stress-induced electric potential barriers in thickness-stretch deformations of a piezoelectric semiconductor plate. Acta Mechanica, 232(11), 4533–4543 (2021) |
| [20] | LI, M. E., ZHANG, Q. Y., WANG, B. B., and ZHAO, M. H. Analysis of flexural vibrations of a piezoelectric semiconductor nanoplate driven by a time-harmonic force. Materials, 14(14), 3926 (2021) |
| [21] | REN, C., WANG, K. F., and WANG, B. L. Adjusting the electromechanical coupling behaviors of piezoelectric semiconductor nanowires via strain gradient and flexoelectric effects. Journal of Applied Physics, 128(21), 215701 (2020) |
| [22] | CHU, L. L., DUI, G., MEI, H., LIU, L. S., and LI, Y. B. An analysis of flexoelectric coupling associated electroelastic fields in functionally graded semiconductor nanobeams. Journal of Applied Physics, 130(11), 115701 (2021) |
| [23] | SLADEK, J., SLADEK, V., REPKA, M., and PAN, E. Size effect in piezoelectric semiconductor nanostructures. Journal of Intelligent Material Systems and Structures, 33(11), 1351–1363 (2022) |
| [24] | YANG, J. S. An anti-plane crack in a piezoelectric semiconductor. International Journal of Fracture, 136, L27–L32 (2005) |
| [25] | HU, Y. T., ZENG, Y., and YANG, J. S. A mode III crack in a piezoelectric semiconductor of crystals with 6mm symmetry. International Journal of Solids and Structures, 44(11-12), 3928–3938 (2007) |
| [26] | SLADEK, J., SLADEK, V., PAN, E., and WüNSCHE, M. Fracture analysis in piezoelectric semiconductors under a thermal load. Engineering Fracture Mechanics, 126, 27–39 (2014) |
| [27] | FAN, C. Y., YAN, Y., XU, G. T., and ZHAO, M. H. Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method. Engineering Fracture Mechanics, 165, 183–196 (2016) |
| [28] | ZHANG, Q. Y., FAN, C. Y., XU, G. T., and ZHAO, M. H. Iterative boundary element method for crack analysis of two-dimensional piezoelectric semiconductor. Engineering Analysis with Boundary Elements, 83, 87–95 (2017) |
| [29] | ZHAO, M. H., PAN, Y. B., FAN, C. Y., and XU, G. T. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. International Journal of Solids and Structures, 94-95, 50–59 (2016) |
| [30] | ZHAO, Y. F., ZHOU, C. G., ZHAO, M. H., PAN, E., and FAN, C. Y. Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green’s functions of extended displacement discontinuity. Journal of Intelligent Material Systems and Structures, 28(13), 1775–1788 (2017) |
| [31] | QIN, G. S., MA, S. J., LU, C., WANG, G., and ZHAO, M. H. Influence of electric field and current on the strength of depoled GaN piezoelectric semiconductive ceramics. Ceramics International, 44, 4169–4175 (2018) |
| [32] | PAPADOPOULOS, C. A. and DIMAROGONAS, A. D. Coupled longitudinal and bending vibration of a rotating shaft with an open crack. Journal of Sound and Vibration, 117(1), 81–93 (1987) |
| [33] | GOUNARIS, G. and DIMAROGONAS, A. A finite element of a cracked prismatic beam for structural analysis. Computers & Structures, 28(3), 309–313 (1988) |
| [34] | ARIA, A. I., FRISWELL, M. I., and RABCZUK, T. Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis. Composite Structures, 212, 118–128 (2019) |
| [35] | ZHU, X., LI, T. Y., ZHAO, Y., and LIU, J. X. Structural power flow analysis of Timoshenko beam with an open crack. Journal of Sound and Vibration, 297, 215–226 (2006) |
| [36] | MAO, J. J., WANG, Y. J., ZHANG, W., WU, M. Q., LIU, Y. Z., and LIU, X. H. Vibration and wave propagation in functionally graded beams with inclined cracks. Applied Mathematical Modelling, 118, 166–184 (2023) |
| [37] | KUANG, Y. D., LI, G. Q., and CHEN, C. Y. Admittance function of active piezoelectric elements bonded on a curved cracked beam. Journal of Intelligent Material Systems and Structures, 19(2), 181–191 (2008) |
| [38] | KUANG, Y. D., LI, G. Q., and CHEN, C. Y. An admittance function of active piezoelectric elements bonded on a cracked beam. Journal of Sound and Vibration, 298, 393–403 (2006) |
| [39] | ZHANG, Q. Y., XU, J. H., WANG, B. B., ZHAO, M. H., and LU, C. S. Bending characteristics of a one-dimensional piezoelectric semiconductor curved beam. Archive of Applied Mechanics, 94(10), 2807–2818 (2024) |
| [40] | LI, S. R., CAO, D. F., and WAN, Z. Q. Bending solutions of FGM Timoshenko beams from those of the homogenous Euler-Bernoulli beams. Applied Mathematical Modelling, 37(10-11), 7077–7085 (2013) |
| [41] | XIONG, Y. P., XING, J. T., and PRICE, W. G. Interactive power flow characteristics of an integrated equipment-nonlinear isolator-travelling flexible ship excited by sea waves. Journal of Sound and Vibration, 287(1), 245–276 (2005) |
| [42] | LI, D. Z., ZHANG, C. L., ZHANG, S., WANG, H. M., CHEN, W. Q., and ZHANG, C. Z. Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods. Ultrasonics, 132, 106964 (2023) |
| [43] | RYU, C. H., HWAN, W., CHO, J. Y., KIM, S. B., KIM, K. B., SONG, Y., and SUNG, T. H. Optimization of the energy conversion efficiency by bending deflection of piezoelectric cantilever beams. Journal of the Korea Physical Society, 76(10), 948–953 (2020) |
/
| 〈 |
|
〉 |
Email Alert
RSS