Hybrid computational scheme for modeling the excitation of elastic waves in an isotropic layer by a piezoceramic actuator of various configurations
DOI:
https://doi.org/10.7242/1999-6691/2026.19.2.17Keywords:
hybrid computing scheme, elastic guided waves, finite element method, piezoceramic actuatorAbstract
Modeling of elastic guided wave excitation by surface-mounted or embedded ultrasonic transducers is one of the key problems in the development and verification of nondestructive testing and structural health monitoring methods. To address this challenge, the dynamics of three-dimensional waveguides is analyzed by applying a hybrid numerical-analytical scheme. The problem reduces to studying the dynamic behavior of an isotropic elastic layer subjected to a localized vibration source positioned at an arbitrary distance from the layer boundaries. Within the proposed scheme, the construction of a solution involves two stages. In the first stage, a set of auxiliary numerical solutions is constructed in the vicinity of the transducer. In the second stage, these solutions are coupled with the wave field in the remaining homogeneous part of the waveguide, which is represented as a sum of cylindrical guided waves. Each wave is expressed as the product of the modal waveform along the vertical coordinate by the function, characterizing the intensity of radiation in a given direction. The latter can be represented as a Fourier series expansion in a polar angle, whose coefficients are determined from the condition of continuity of the displacement and stress vectors at the interface between the region containing the vibration source and the remaining part of the waveguide. The proposed scheme is capable of modeling the interaction between the elastic layer and arbitrarily shaped transducer with consideration for physical fields coupling and does not require an independent software implementation of finite element calculations. Moreover, it can be used to evaluate the excitation efficiency of normal modes in a selected frequency range as a function of the propagation direction. Verification of the scheme is performed by comparing its results with the numerical solutions obtained by use of other approaches. The specific features of elastic guided wave excitation by piezoceramic transducers of various geometries, either surface-mounted or embedded in an elastic layer, are analyzed to demonstrate the applicability of the developed scheme to ultrasonic monitoring of thin-walled structures.
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Raghavan A., Cesnik C.E.S. Review of Guided-wave Structural Health Monitoring. The Shock and Vibration Digest. 2007. Vol. 39. P. 91–114. DOI: 10.1177/0583102406075428
Giurgiutiu V. Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition. Elsevier, 2014. 1032 p. . DOI: 10.1016/c2013-0-00155-7
Shardakov I.N., Shestakov A.P., Glot I.O., Gusev G.N., Epin V.V., Tsvetkov R.V. Comparison of the dynamic characteristics of piezoceramic actuators used in vibration diagnostics of large-scale structures. Computational Continuum Mechanics. 2024. Vol. 17, no. 3. P. 376–386. DOI: 10.7242/1999-6691/2024.17.3.31
Feng T., Aliabadi M.H.F. Influence of placing positions of PZT transducers in thick composites on ultrasonic guided waves. Procedia Structural Integrity. 2024. Vol. 52. P. 785–794. DOI: 10.1016/j.prostr.2023.12.077
Qi R., Wang L., Jin J., Yuan L., Shen Z., Ge Y. An embedded piezoelectric actuator for active vibration control: Concept, modeling, simulation, and investigation. Chinese Journal of Aeronautics. 2025. Vol. 38, no. 4. 103345. DOI: 10.1016/j.cja.2024.103345
Glushkov E.V., Glushkova N.V., Kvasha O.V., Lammering R. Selective Lamb mode excitation by piezoelectric coaxial ring actuators. Smart Materials and Structures. 2010. Vol. 19, no. 3. 035018. DOI: 10.1088/0964-1726/19/3/035018
Schmidt D., Sinapius M., Wierach P. Design of mode selective actuators for Lamb wave excitation in composite plates. CEAS Aeronautical Journal. 2013. Vol. 4. P. 105–112. DOI: 10.1007/s13272-012-0059-3
Mohammadgholiha M., Moll J., Tschöke K., Kruska C., Gebhardt S., De Marchi L. Unidirectional Frequency-Steerable Acoustic Transducer for guided ultrasonic wave damage imaging. Mechanical Systems and Signal Processing. 2025. Vol. 229. 112505. DOI: 10.1016/j.ymssp.2025.112505
Soman R., Kudela P., Balasubramaniam K., Singh S.K., Malinowski P. A Study of Sensor Placement Optimization Problem for Guided Wave-Based Damage Detection. Sensors. 2019. Vol. 19, no. 8. 1856. DOI: 10.3390/s19081856
Skelton E., Adams S., Craster R. Guided elastic waves and perfectly matched layers. Wave Motion. 2007. Vol. 44. P. 573–592. DOI: 10.1016/j.wavemoti.2007.03.001
Berenger J.- P. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics. 1994. Vol. 114, no. 2. P. 185–200. DOI: 10.1006/jcph.1994.1159
Moreau L., Castaings M., Hosten B., Predoi M.V. An orthogonality relation-based technique for post-processing finite element predictions of waves scattering in solid waveguides. The Journal of the Acoustical Society of America. 2006. Vol. 120, no. 2. P. 611–620. DOI: 10.1121/1.2216563
Moreau L., Castaings M. The use of an orthogonality relation for reducing the size of finite element models for 3D guided waves scattering problems. Ultrasonics. 2008. Vol. 48, no. 5. P. 357–366. DOI: 10.1016/j.ultras.2008.01.005
Predoi M., Castaings M., Moreau L. Influence of material viscoelasticity on the scattering of guided waves by defects. The Journal of the Acoustical Society of America. 2008. Vol. 124, no. 5. P. 2883–2894. DOI: 10.1121/1.2977604
Raghavan A., Cesnik E.S. Finite-dimensional piezoelectric transducer modeling for guided wave based structural health monitoring. Smart Materials and Structures. 2005. Vol. 14, no. 6. P. 1448–1461. DOI: 10.1088/0964-1726/14/6/037
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. Russian Journal of Nondestructive Testing. 2020. Vol. 56. P. 795–809. DOI: 10.1134/s1061830920100034
Lin X., Yuan F.G. Diagnostic Lamb waves in an integrated piezoelectric sensor/actuator plate: analytical and experimental studies. Smart Materials and Structures. 2001. Vol. 10, no. 5. P. 907–913. DOI: 10.1088/0964-1726/10/5/307
Glushkov E.V., Glushkova N.V., Kvasha O.V., Seemann W. Integral equation based modeling of the interaction between piezoelectric patch actuators and an elastic substrate. Smart Materials and Structures. 2007. Vol. 16, no. 3. P. 650–664. DOI: 10.1088/0964-1726/16/3/012
Glushkov E.V., Glushkova N.V., Evdokimov A.A. Distribution of the energy of a piezoelectric actuator between traveling waves excited in an elastic layer. Journal of Applied Mechanics and Technical Physics. 2015. Vol. 56. P. 1007–1014. DOI: 10.1134/s0021894415060103
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. The Journal of the Acoustical Society of America. 2000. Vol. 107, no. 1. P. 87–94. DOI: 10.1121/1.428294
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. 035003. DOI: 10.1088/0964-1726/24/3/035003
Golub M., Fomenko S., Shpak A., Gu Y., Wang Y., Zhang C. Semi-analytical hybrid approach for modelling smart structures and guided wave-based SHM systems for a laminate with multiple delaminations and surface-mounted inhomogeneities. Applied Mathematical Modelling. 2023. Vol. 120. P. 812–832. DOI: 10.1016/j.apm.2023.04.017
Yang C., Nakaoka J., Hirose S. Semi-analytical FEM for modelling 3D guided waves scattering in an infinite plate. Applied Mathematical Modelling. 2025. Vol. 148. 116236. DOI: 10.1016/j.apm.2025.116236
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, no. 5. P. 764–774. DOI: 10.1016/j.ijsolstr.2010.11.013
Khanazaryan A.D., Golub M.V. Hybrid method for modelling anti-plane vibrations of layered waveguides with bonded composite joints. Computational Continuum Mechanics. 2023. Vol. 16, no. 1. P. 101–114. DOI: 10.7242/1999-6691/2023.16.1.8
Vivar-Perez J.M., Duczek S., Gabbert U. Analytical and higher order finite element hybrid approach for an efficient simulation of ultrasonic guided waves I: 2D-analysis. Smart Structures and Systems. 2014. Vol. 13, no. 4. P. 587–614. DOI: https://doi.org/10.12989/SSS.2014.13.4.587
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. P. 234–255. DOI: 10.1016/j.apm.2018.08.019
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. P. 57–69. DOI: 10.31429/vestnik-21-1-57-69
Raorane S., Stepinski T., Packo P. A semi-analytical framework for predicting far-field responses of complex elastic waves emitters. Ultrasonics. 2025. Vol. 145. 107483. DOI: 10.1016/j.ultras.2024.107483
Glushkov E.V., Glushkova N.V., Evdokimov A.A. Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides. Acoustical Physics. 2018. Vol. 64. P. 1–9. DOI: 10.1134/s1063771018010086
Evdokimov A.A., Glushkov E.V., Glushkova N.V. Hybrid numerical-analytical scheme for 3D scattering problems. 2021 Days on Diffraction (DD). 2021. P. 42–47. DOI: 10.1109/dd52349.2021.9598757
Evdokimov A.A., Nets P.A., Lesin B.M., Eremin A.A. A hybrid numerical-analytical approach for the simulation of antiplane vibrations of multilayered elastic waveguides with multiple inhomogeneities. Computational Continuum Mechanics. 2025. Vol. 18, no. 2. P. 140–154. DOI: 10.7242/1999-6691/2025.18.2.11
Babeshko V.A., Glushkov E.V., Zinchenko Z.F. Dinamika neodnorodnykh lineyno-uprugikh sred. Moscow: Nauka, 1989. 344 p.
Glushkov E.V., Glushkova N.V. Integral’nyye preobrazovaniya i volnovyye protsessy. Krasnodar: Kuban State University, 2017. 201 p.
Glushkova N.V. Definition and Accounting of Singular Components in Elasticity Theory Problems: dissertation for the degree of Doctor of Physical and Mathematical Sciences / Glushkova N. V. Krasnodar: Kuban State University, 2000. 220 p.
Parton V.Z., Kudryavtsev B.A. Elektromagnitouprugost’ p’yezoelektricheskikh i elektroprovodnykh tel. Moscow: Nauka, 1988. 472 p.
Tiersten H.F. Electromechanical coupling factors and fundamental material constants of thickness vibrating piezoelectric plates. Ultrasonics. 1970. Vol. 8, no. 1. P. 19–23. DOI: 10.1016/0041-624x(70)90793-6
Sveshnikov A.G. Printsip predel’nogo pogloshcheniya dlya volnovoda. Doklady Akademii nauk SSSR. 1951. Vol. 80, no. 3. P. 345–347.
Umov N.A. Izbrannyye sochineniya. Moscow: Gostekhteoretizdat, 1950. 575 p.
Sheeraz M.A., Butt Z., Khan A.M., Mehmood S., Ali A., Azeem M., Nasir A., Imtiaz T. Design and Optimization of Piezoelectric Transducer (PZT-5H Stack). Journal of Electronic Materials. 2019. Vol. 48. P. 6487–6502. DOI: 10.1007/s11664-019-07453-7
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