Two-step computational scheme for modeling the excitation of elastic waves by an ultrasonic piezoelectric transducer

Authors

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-21-1-57-69

Abstract

The problem of excitation of ultrasonic vibrations by a piezoactuator in an isotropic elastic layer is considered. Its dynamic behavior is described using a semi-analytical integral approach, in which the effect of a piezoelectric transducer on a waveguide is taken into account through an unknown vector function of contact stresses. To determine it, a two-stage computational scheme is proposed, in which, at the first stage, the dynamic spatial contact problem is solved using the finite element method (FEM), and displacements in an area coinciding in shape with the contact area, but taken on the opposite side of the waveguide, are taken from the resulting FEM solution. At the second stage, the required contact voltages are found from the solution of a system of boundary integral equations in which the displacements found using FEM are included in the right part. To verify the proposed approach, the results obtained on its basis are compared with FEM solutions, as well as with experimental data.

Keywords:

piezoactuator, isotropic elastic layer, finite element method, integral approach, elastic guided waves

Acknowledgement

The work has been supported by the state assignment of the Ministry of Science and Higher Education of the Russian Federation (Project No. FZEN-2020-0017).

Author Info

Mikhail V. Vareldzhan

младший научный сотрудник Института математики, механики и информатики Кубанского государственного университета

e-mail: michael.vareldzhan.777@mail.ru

References

  1. Farrar, C.R., Worden, K., An introduction to structural health monitoring. Phil. Trans. R. Soc. A., 2006, vol. 365, pp. 303–315. DOI: 10.1098/rsta.2006.1928
  2. Giurgiutiu, V., Structural Health Monitoring with Piezoelectric Wafer Active Sensors. Columbia, Elsevier Inc., 2014.
  3. Raghavan, A., Cesnik, E.S., Finite-dimensional piezoelectric transducer modeling for guided wave based structural health monitoring. Smart Materials and Structures, 2005, vol. 14, pp. 1448–1461. DOI: 10.1088/0964-1726/14/6/037
  4. Еремин, А.А., Глушков, Е.В., Глушкова, Н.В., Применение пленочных пьезопреобразователей для возбуждения и регистрации бегущих упругих волн в системах активного мониторинга протяженных конструкций. Дефектоскопия, 2020, № 10, с. 24–38. [Eremin, A.A., Glushkov, E.V., Glushkova, N.V., Application of piezoelectric wafer active sensors for elastic guided wave excitation and detection in structural health monitoring systems for elongated constructions. Defektoskopiya = Russian Journal of Nondestructive Testing, 2020, no. 10, pp. 24–38. (in Russian)] DOI: 10.31857/S0130308220100036
  5. Benmeddour, F., Treyssède, F., Laguerre, L., Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders. International Journal of Solids and Structures, 2011, vol. 48, iss. 5, pp. 764-–774. DOI: 10.1016/j.ijsolstr.2010.11.013
  6. Глушков, Е.В., Глушкова, Н.В., Евдокимов, А.А., Гибридная численно-аналитическая схема для расчета дифракции упругих волн в локально неоднородных волноводах. Акустический журнал, 2018, № 1, с. 3–12. [Glushkov, E.V., Glushkova, N.V., Evdokimov, A.A., Hybrid numerical-analytical scheme for calculating elastic wave diffraction in locally inhomogeneous waveguides. Akusticheskiy zhurnal = Acoustical Physics, 2018, no. 1, pp. 3–12. (in Russian)] DOI: 10.7868/S0320791918010082
  7. Golub, M.V., Shpak, A.N., Semi-analytical hybrid approach for the simulation of layered waveguide with a partially debonded piezoelectric structure. Applied Mathematical Modelling, 2019, vol. 65, pp. 234–255. DOI: 10.1016/j.apm.2018.08.019
  8. Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических тел. Москва, Наука, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh tel = Dynamic mixed problems of the theory of elasticity for non-classical bodies. Moscow, Nauka, 1979. (in Russian)]
  9. Glushkov, E., Glushkova, N., Kvasha, O., Seemann, W. Integral equation based modeling of the interaction between piezoelectric patch actuators and an elastic substrate. Smart Materials and Structures, 2007, vol. 16, pp. 650–664. DOI: 10.1088/0964-1726/16/3/012
  10. Sinclair, G.B., Cormier, N.G., Griffin, J.H., Meda, G., Contact stresses in dovetail attachments: finite element modeling. The Journal of Engineering for Gas Turbines and Power, 2002, vol. 124, iss. 1, pp. 182–189. DOI: 10.1115/1.1391429
  11. Партон, В.З., Кудрявцев, Б.А., Электромагнитоупругость пьезоэлектрических и электропроводных тел. Москва, Наука, 1998. [Parton, V.Z., Kudryavcev, B.A., Electromagnitouprugost piezoelectricheskih i electroprovodnyh tel = Electromagnetoelasticity of piezoelectric and electrically conductive media, Moscow, Nauka, 1998 (in Russian)]
  12. Свешников, А.Г., Принцип предельного поглощения для волновода. ДАН, 1951, т. 80, № 3, с. 341–344. [Sveshnikov, A.G., The principle of limiting absorption for a waveguide. Doklady Akademii nauk = Report of the Academy of Sciences, 1951, vol. 80, no. 3, pp. 341–344. (in Russian)]
  13. Бабешко, В.А., Глушков, Е.В., Глушкова, Н.В., Анализ волновых полей, возбуждаемых в упругом стратифицированном полупространстве, поверхностными источниками. Акустический журнал, 1986, т. 32, вып. 3, с. 366–371. [Babeshko, V.A., Glushkov, E.V., Glushkova, N.V., Analysis of wave fields generated in a stratified elastic half-space by surface sources. Sov. Phys. Acoust. (USA), 1986, no. 32(3), pp. 223–226.]
  14. Глушкова, Н.В., Определение и учет сингулярных составляющих в задачах теории упругости. Диссертация на соискание ученой степени доктора наук, 2000, Ростовский федеральный университет, Ростов-на-Дону, Россия. [Glushkova, N.V., Determination and accounting singular terms in Elasticity. Diss. \ldots Doctor of Sciences, 2000, Rostov State University, Rostov-on-Don, Russia. (in Russian)]
  15. Глушков, Е.В., Глушкова, Н.В., Варелджан, М.В., Сравнительный анализ эффективности программной реализации полуаналитических методов расчета волновых полей в многослойных анизотропных композитах. Вестник Южно-Уральского государственного университета. Cерия: Математическое моделирование и программирование, 2022, т. 15, вып. 2, с. 56–69. [Glushkov, E.V., Glushkova, N.V., Vareldzhan, M.V., Comparative analysis of software implementation efficiency of the semi-analytical methods for calculating wave fields in multilayer anisotropic composites. Bull. of the South Ural State University. Ser. Mathematical Modelling, Programming and Computer Software, 2022, vol. 15, no. 2, pp. 56–69. (in Russian)]
  16. Moulin, E., Assaad, J., Delebarre, C., Osmont, D., Modeling of Lamb waves generated by integrated transducers in composite plates using a coupled finite element–normal modes expansion method. Acoustical Society of America, 2000, vol. 107, iss. 1, pp. 87–94. DOI: 10.1121/1.428294
  17. Quaegebeur, N., Ostiguy, P-C, Masson, P., Hybrid empirical/analytical modeling of guided wave generation by circular piezoceramics. Smart Materials and Structures, 2015, vol. 24, no. 3. DOI: 10.1088/0964-1726/24/3/035003
  18. Liu, Y., Fan, H., Yang. J., Analysis of the shear stress transferred from a partially electroded piezoelectric actuator to an elastic substrate. Smart Materials and Structures, 2000, vol. 9, no. 2, pp. 248–254. DOI: 10.1088/0964-1726/9/2/406
  19. Huang. J., Heng-I, Y., Dynamic electromechanical response of piezoelectric plates as sensors or actuators. Materials Letters, 2000, vol. 46, iss. 2–3, pp. 70–80. DOI: 10.1016/S0167-577X(00)00145-2
  20. Бабешко, В.А., Глушков, Е.В., Глушкова, Н.В., К проблеме динамических контактных задач в произвольных областях. Известия АН СССР. МТТ, 1978, № 3, с. 61–67. [Babeshko, V.A., Glushkov, E.V., Glushkova, N.V., Dynamic contact problems with arbitrary areas. Izvestiya Akademii Nauk SSSR. Mekhanika tverdogo tela = Bull. of the USSR Academy of Sciences. Solid Mechanics, 1978, no. 3, pp. 61–67. (in Russian)]
  21. Lowe, M.J.S., Cawley, P., Kao, J-Y., Diligent, O., The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave from a rectangular notch in a plate. The Journal of the Acoustical Society of America, 2010, vol. 112, iss. 6, pp. 2612–2622. DOI: 10.1121/1.1512702
  22. Ha, S., Lonkar, K., Mittal, A., Chang, F., Adhesive Layer Effects on PZT-induced Lamb Waves at Elevated Temperatures. Structural Health Monitoring, 2010, vol. 9, iss. 3, pp. 247–256. DOI: 10.1177/1475921710365267
  23. Glushkov, E.V., Glushkova, N.V., Fomenko, S.I., Wave energy transfer in elastic half-spaces with soft interlayers. The Journal of the Acoustical Society of America, 2010, vol. 137, iss. 4, pp. 1802–1812. DOI: 10.1121/1.4916607
  24. Wilde, M.V., Golub, M.V., Eremin, A.A., Elastodynamic behaviour of laminate structures with soft thin interlayers: theory and experiment. Materials, 2022, vol. 15, iss. 4, no. 1307, pp. 1–32. DOI: 10.3390/ma15041307

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Issue

2024. Vol. 21. No. 1

Section

Physics

Pages

57-69

Submitted

2023-12-26

Published

2024-03-27

How to Cite

Vareldzhan M.V. Two-step computational scheme for modeling the excitation of elastic waves by an ultrasonic piezoelectric transducer. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2024, vol. 21, no. 1, pp. 57-69. DOI: https://doi.org/10.31429/vestnik-21-1-57-69 (In Russian)

Copyright (c) 2024 Vareldzhan M.V.

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