Analytical Derivation of the Secular Equation for Surface Waves in an Imperfectly Bonded Complex Structure Employing the GN-III Model
Publication: International Journal of Geomechanics
Volume 24, Issue 12
Abstract
In this thorough study, the examination explores the Rayleigh-type surface wave propagation in an imperfectly bonded layered structure. The present study adopts the conceptual framework of the Green–Naghdi model type III of hyperbolic thermoelasticity. This approach allows for an in-depth exploration of the interactions and properties of the system, offering valuable insights into how these arrangements behave within the scope of thermoelastic phenomena. The process of deriving the secular equations for Rayleigh-type surface waves are accomplished in this study. Four distinct secular equations are derived corresponding to different boundary conditions. In this article, plane harmonic wave solutions are used to determine the mechanical displacement, electrical potential for the layer, and the mechanical displacement, electrical potential, and temperature change for the half-space. The effects on various wave properties, including phase velocity, attenuation coefficient, and specific loss, are shown graphically within the framework of the GN-III type model with cadmium selenide (CdSe) and PZT-5H material. This mathematical framework may be useful for a variety of scientific and engineering disciplines that involve the implementation of sensors, actuators, capacitors, electrostatic transducers, and applications for surface acoustic wave devices and Rayleigh-type wave sensors.
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
The authors convey their sincere thanks to the editors and reviewers for their valuable and insightful comments which helped to improve the quality of the manuscript. The authors also express their sincere thanks to the Science and Engineering Research Board (SERB), DST, India, for their financial support that facilitated the execution of this research endeavor under Project No. SRG/2020/001141.
Notation
The following symbols are used in this paper:
- Specific heat;
- Symmetric elastic tensor;
- Phase velocity;
- Electric Displacements;
- Electric field;
- Piezoelectric moduli tensor;
- Coefficient of heat conduction;
- Heat conductivity rate;
- Heat flux;
- Mechanical displacements;
- Amplitude ratio;
- Elastic energy;
- Speed of propagation;
- Thermoelastic coupling coefficient;
- Electric permittivity;
- Strain components;
- Entropy;
- Temperature change;
- Wave number;
- Electric potential;
- Density;
- Stress components;
- Phase lag;
- Coefficient of surface heat transfer; and
- Angular frequency.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 17, 2023
Accepted: Jun 12, 2024
Published online: Sep 30, 2024
Published in print: Dec 1, 2024
Discussion open until: Mar 1, 2025
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