Dynamic stress analysis of semi-elliptical notches in PZT media under SH wave interaction using Mathieu functions
- Title
- Dynamic stress analysis of semi-elliptical notches in PZT media under SH wave interaction using Mathieu functions
- Creator
- Mofarreh, Fatemah; Panwar, Sarika; Saeed, Abdulkafi Mohammed; Radhakrishnan, Ganesh V.; Date, Saroj; Alharthi, N.S.; Ganie, Abdul Hamid; Singhal, Abhinav
- Description
- This work develops a rigorous analytical framework to examine the scattering behavior and dynamic stress response of semi-elliptical notches in piezoelectric half-planes subjected to anti-plane shear (SH) waves. The framework unifies the treatment of cracks, circular holes, and notches within a consistent wavedefect interaction model, while explicitly incorporating piezoelectric coupling and nanoscale surface/interface effects. The analysis employs the complex function method in combination with the Helmholtz equation and wavefield superposition theory, resulting in an infinite system of equations that rigorously enforces continuity and boundary conditions. A systematic truncation scheme is then applied to ensure stable and convergent solutions. The results reveal that surface/interface effects play a crucial role in suppressing the dynamic stress concentration factor (DSCF), particularly under vertical SH-wave excitation, while sharper resonance peaks emerge at low modulus ratios and higher piezoelectric constants, such as PZT-5H and BaTiO?. In the absence of piezoelectric coupling, the formulation seamlessly reduces to classical elasticity, ensuring strong theoretical consistency. Validation is achieved through recovery of benchmark solutions (semicircular notch and edge crack), graphical comparisons with prior results, and the rapid convergence of the truncated system, confirming the models accuracy and robustness. The findings hold significant implications for structural health monitoring, non-destructive evaluation, and the design of advanced piezoelectric composites, where accurate prediction of stress amplification and defect evolution is essential. Although the present study focuses on semi-elliptical notches in half-plane geometries under SH-wave loading, the approach can be readily extended to more general defect shapes and mixed-mode disturbances. The novelty of this work lies in capturing piezoelectric surface/interface effects within an exact analytical framework, thereby enhancing predictive capability for defect-induced stress concentrations and providing a reliable basis for the design and durability assessment of high-performance piezoelectric materials. The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.
- Source
- Acta Mechanica;Volume;237;Issue;1;pp.89-115
- Date
- 01-01-2026
- Publisher
- Springer
- Coverage
- Mofarreh F., Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, 11546, Saudi Arabia; Panwar S., Department of Electronics and Telecommunication Engineering, AISSMSs Institute of Information Technology, Pune, 411001, India; Saeed A.M., Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia; Radhakrishnan G.V., Department of Economics and Finance, KIIT School of Management (KSOM), KIIT University, Bhubaneswar, India; Date S., Artificial Intelligence and Data Science Department, Chh. Shahu College of Engineering, Kanchanwadi, Paithan Road,Chhatrapati Sambhajinagar (Aurangabad) MS, 431002, India; Alharthi N.S., Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University, Rabigh, 21911, Saudi Arabia; Ganie A.H., Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Saudi Arabia; Singhal A., Christ University, Bengaluru, 560029, India
- Rights
- Restricted Access; Hardcopy may be available in the library
- Relation
- ISSN: 15970; CODEN: AMHCA
- Format
- online
- Language
- English
- Type
- Article
Collection
Citation
Mofarreh, Fatemah; Panwar, Sarika; Saeed, Abdulkafi Mohammed; Radhakrishnan, Ganesh V.; Date, Saroj; Alharthi, N.S.; Ganie, Abdul Hamid; Singhal, Abhinav, “Dynamic stress analysis of semi-elliptical notches in PZT media under SH wave interaction using Mathieu functions,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 17, 2026, https://archives.christuniversity.in/items/show/21855.