Propagation of generalised Rayleigh wave at the surface of piezoelectric medium with arbitrary anisotropy. Issue 3 (20th November 2022)

• Record Type: Journal Article
• Authors: Sharma, M. D.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 103:Issue 3(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-11-20
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202000160
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: Mathematical model for mechanical and electrical dynamics is solved for three‐dimensional 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. Abstract : Mathematical model for mechanical and electrical dynamics is solved for three‐dimensional 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.…