Analytical Derivation of the Secular Equation for Surface Waves in an Imperfectly Bonded Complex Structure Employing the GN-III Model

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.