Characteristics of SH waves in multilayered piezoelectric semiconductor plates considering interfacial imperfection
Abstract
The dispersion and attenuation characteristics of SH waves in piezoelectric semiconductor multilayered plates with imperfect interfaces are investigated using the improved Legendre orthogonal polynomial method. The field quantities of each layer are expanded into individual Legendre polynomials. By incorporating the interface conditions, the imperfect interface model is integrated into the Legendre polynomials associated with the imperfect interface layer. This method ultimately converts the complex wave partial differential equations into a generalized eigenvalue problem, thereby eliminating the redundant integration operations typical of traditional polynomial methods and allowing for the derivation of complete solutions throughout the entire wave frequency domain. The solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of modes. The study encompasses cases ranging from a single-layer ZnO plate, which serves to validate the method, to bilayered and sandwiched piezoelectric semi-conductor plates with imperfect interfaces. The effects of steady-state carrier concentration, imperfect interface coefficients, and stacking sequences on the phase velocity, dispersion, and attenuation curves of SH waves are illustrated. The findings can offer a theoretical foundation for controlling the wave characteristics of piezoelectric semiconductors and for the design of acoustic devices.Keywords:
piezoelectric semiconductor, multilayered plate, SH wave, imperfect interface, Legendre orthogonal polynomial method, dispersion and attenuationReferences
- G. Wang, J. Liu, X. Liu, W. Feng, J. Yang, Extensional vibration characteristics and screening of polarization charges in a ZnO piezoelectric semiconductor nanofiber, Journal of Applied Physics, 124, 9, 094502, 2018.
- J. Guo, G. Nie, J. Liu, L. Zhang, Free vibration of a bi-layered composite plate of a piezoelectric semiconductor and a piezoelectric dielectric, AIP Advances, 13, 9, 095317, 2023.
- A. Singhal, S.A. Sahu, S. Chaudhary, Liouville-Green approximation: An analytical approach to study the elastic waves vibrations in composite structure of piezo material, Composite Structures, 184, 714–727, 2018.
- A. Seema, A. Singhal, Study of surface wave velocity in distinct rheological models with flexoelectric effect in piezoelectric aluminium nitride structure, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 47, 1, 29, 2025.
- D.L. Xiao, Q. Han, T. Jiang, Guided wave propagation in a multilayered magneto-electro-elastic curved panel by Chebyshev spectral elements method, Composite Structures, 207, 701–710, 2019.
- Q. Gao, Y. Zhang, An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures, Acta Mechanica, 231, 5, 1783–1804, 2020.
- J. Chen, E. Pan, H. Chen, Wave propagation in magneto-electro-elastic multilayered plates, International Journal of Solids and Structures, 44, 34, 1073–1085, 2007.
- H. Ezzin, M. Ben Amor, M.H. Ben Ghozlen, Lamb waves propagation in layered piezoelectric/piezomagnetic plates, Ultrasonics, 76, 63–69, 2017.
- J.S. Yang, X.M. Yang, J.A. Turner, Amplification of acoustic waves in laminated piezoelectric semiconductor plates, Archive of Applied Mechanics, 74, 34, 288–298, 2004.
- S. Gupta, N. Bhengra, Implementation of finite difference approximation on the SH-wave propagation in a multilayered magnetoelastic orthotropic composite medium, Acta Mechanica, 228, 10, 3421–3444, 2017.
- O. Matar, N. Gasmi, H. Zhou, M. Goueygou, A. Talbi, Legendre and Laguerre polynomial approach for modeling of wave propagation in layered magneto-electro-elastic media, Journal of the Acoustical Society of America, 133, 3, 1415–1424, 2013.
- C. Othmani, F. Takali, A. Njeh, Modeling of phase velocity and frequency spectrum of guided Lamb waves in piezoelectric-semiconductor multilayered structures made of AlAs and GaAs, Superlattices and Microstructures, 111, 396–404, 2017.
- C. Othmani, F. Takali, A. Njeh, Theoretical study on the dispersion curves of Lamb waves in piezoelectric-semiconductor sandwich plates GaAs-FGPM-AlAs: Legendre polynomial series expansion, Superlattices and Microstructures, 106, 86–101, 2017.
- M.X. Deng, Analysis of second-harmonic generation of Lamb waves propagating in layered planar structures with imperfect interfaces, Applied Physics Letters, 88, 22, 221902, 2006.
- X. Guo, P.J. Wei, Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces, International Journal of Solids and Structures, 51, 21, 3735–3751, 2014.
- T. Kepceler, Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface, Applied Mathematical Modelling, 34, 12, 4058–4073, 2010.
- G. Nie, J. Liu, X. Fang, Z. An, Shear horizontal (SH) waves propagating in piezoelectricpiezomagnetic bilayer system with an imperfect interface, Acta Mechanica, 223, 9, 1999–2009, 2012.
- G. Nie, J. Liu, X. Liu, Lamb wave propagation in a piezoelectric/piezomagnetic bi-material plate with an imperfect interface, Acta Acustica United with Acustica, 102, 5, 893–901, 2016.
- S. Chaudhary, S.A. Sahu, A. Singhal, S. Nirwal, Interfacial imperfection study in pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach, Materials Research Express, 6, 10, 105704, 2019.
- I. Kurt, S. Akbarov, S. Sezer, Lamb wave dispersion in a PZT/metal/PZT sandwich plate with imperfect interface, Waves in Random and Complex Media, 26, 3, 301–327, 2016.
- A. Seema, A. Singhal, Theoretical investigation of SH wave transmission in magneto-electro-elastic structure having imperfect interface using approximating method, Applied Physics A, 130, 8, 597, 2024.
- H. Kuo, S. Yu, Effect of the imperfect interface on the scattering of SH wave in a piezoelectric cylinder in a piezomagnetic matrix, International Journal of Engineering Science, 85, 186–202, 2014.
- S. Kumari, S. Sahu, K. Pankaj, Analysis of SH wave in hollow piezo-composite cylinder with coupled imperfect interface condition, Mechanics Based Design of Structures and Machines, 51, 4, 2080–2100, 2023.
- P. Kumar, M. Mahanty, A. Chattopadhyay, A. Singh, Effect of interfacial imperfection on shear wave propagation in a piezoelectric composite structure: Wentzel–Kramers–Brillouin asymptotic approach, Journal of Intelligent Material Systems and Structures, 30, 1819, 2789–2807, 2019.
- J.N. Sharma, K.K. Sharma, A. Kumar, Surface waves in a piezoelectric-semiconductor composite structure, International Journal of Solids and Structures, 47, 6, 816–826, 2010.
- C.L. Gu, F. Jin, Shear-horizontal surface waves in a half-space of piezoelectric semiconductors, Philosophical Magazine Letters, 95, 2, 92–100, 2015.
- X.S. Cao, S.M. Hu, J.J. Liu, J.P. Shi, Generalized Rayleigh surface waves in a piezoelectric semiconductor half space, Meccanica, 54, 12, 271–281, 2019.
- F.Y. Jiao, P.J. Wei, X.L. Zhou, Y.H. Zhou, The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor, Ultrasonics, 92, 68–78, 2018.
- V.J. Gokhale, M. Rais-Zodeh, Phonon-electron interactions in piezoelectric semiconductor bulk acoustic wave resonators, Scientific Reports, 4, 5617, 2014.
- I. Ben Salah, F. Takali, C. Othmani, A. Njeh, SH wave in a stressed piezoelectric semiconductor plates: Electron and hole drift phenomenon, International Journal of Mechanical Sciences, 223, 107281, 2022.
- R. Tian, J.X. Liu, E.N. Pan, Y.S. Wang, A.K. Soh, Some characteristics of elastic waves in a piezoelectric semiconductor plate, Journal of Applied Physics, 126, 12, 125701, 2019.
- D.Z. Li, S.P. Li, C.L. Zhang, W.Q. Chen, Propagation characteristics of shear horizontal waves in piezoelectric semiconductor nanoplates incorporating surface effect, International Journal of Mechanical Sciences, 247, 108201, 2023.
- Z.B. Wei, P.J. Wei, C.Y. Xu, X. Guo, Equivalent imperfect interface model of PN junction of piezoelectric semiconductor for the multi-field coupled waves propagation, Acta Mechanica, 235, 1, 73–92, 2024.
- L. Elmaimouni, J.E. Lefebvre, V. Zhang, T. Gryba, A polynomial approach to the analysis of guided waves in anisotropic cylinders of infinite length, Wave Motion, 42, 2, 177–189, 2005
- A. Boström, M. Golub, Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions, Quarterly Journal of Mechanics and Applied Mathematics, 62, 1, 39–52, 2008.
- X.M. Zhang, J.G. Yu, Effects of initial stresses on guided waves in unidirectional plates, Archives of Mechanics, 65, 1, 3–26, 2013.
- P. Ernian, W.Q. Chen, Static Green’s Functions In Anisotropic Media, Cambridge University Press, New York, USA, 2015.