Propagation of generalised Rayleigh wave at the surface of piezoelectric medium with arbitrary anisotropy

Abstract

Mathematical model for mechanical and electrical dynamics is solved for threedimensional propagation of harmonic plane waves in a piezoelectric medium with arbitrary anisotropy. A system of modified Christoffel equations is derived to explain the existence and propagation of bulk waves or decaying phases in the considered medium. At the free plane boundary, a superposition of decaying phases form a generalised Rayleigh wave, which is governed by a linear system of four homogeneous equations. A complex determinantal secular equation ensures a solution to this system. True surface wave at the boundary of the considered medium demands a real solution of this complex secular equation. The linear system of four equations is then transformed to replace the complex secular equation with a real one, which can be solved by standard numerical methods. A real solution of this real secular equation provides the phase velocity for generalised Rayleigh wave at the boundary of piezoelectric medium with arbitrary anisotropy. This phase velocity defines a complex slowness vector, which is used to calculate the motion of material particles and the wave-induced electric field. A numerical example is considered to compute the phase velocity as well as group velocity for given (arbitrary) propagation directions of Rayleigh wave at the boundary. Variations in particle motion and electric field, induced by Rayleigh wave, are analysed at different depths for different propagation directions at the boundary.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

“…When we neglect the effects of temperature, voids, memory and nonlocality, the current model agrees with a particular case studied by Sharma (2023).…”

“…The presented plots reveal captivating phenomena in which particles exhibit a spiral elliptical trajectory over time, including both horizontal and vertical motion, across all examined depth ( z ) values. The intriguing behavior seen may be due to the intricate characteristics of Rayleigh waves, which are well-known for their ability to induce simultaneous horizontal and vertical vibrations (Sharma, 2023; Kumar et al , 2023c). One notable observation is that, while the general spiral ellipse pattern stays consistent, there are subtle variations in the amplitude of horizontal and vertical particle motion.…”

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

“…Each plot showcases a mesmerizing phenomenon: particles trace an elliptical path that spirals over time, encompassing both vertical and horizontal motion. This behavior aligns with the well-established property of Rayleigh waves to induce simultaneous horizontal and vertical vibrations [68,69]. Intriguingly, the spiraling elliptical motion remains consistent overall, but a closer look reveals subtle variations in the intensity of U 1 and U 3 .…”