Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

Abstract

The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis procedure is adopted as the methodology of interest for its high level of efficiency in the literature. The analytically obtained frequency equation is analyzed for certain scenarios of curiosity, in addition to the determination of the resulting displacements and stresses. Moreover, certain physical data of relevance with the viscoelasticity index of unity are considered for the numerical simulations. As for the findings, the presented graphical illustrations showed that both the magnetic field and rotation positively accelerated the dispersion of surface waves in the coated half-space, while the obtained approximate fields in the half-space are found to be oscillatory as they steadily move towards the limiting point.

Surface Waves on a Coated Homogeneous Half-Space under the Effects of External Forces

“…Let us begin by considering the governing equations of motion under the influence of magnetic field force F as follows [12,15,16]…”

“…The displacements u q j , (j = 1, 2) can be expressed further through the following potential functions φ q and ψ q as follows [12]…”

“…We also recall their significance in material science, glazing and flooring, and above all, its applicability in the design and construction of the multi-layered media [3][4][5][6][7]. Moreover, the propagation of surface waves in coated elastic solids have inspired many research questions in recent times, having frequently arisen, for instance, in modeling seismic protection, improving highways and rail transportation quality to mention a few, see, for example, [8][9][10][11][12][13][14] and the references provided therein for more readings. The Rayleigh wave propagation, being a form of a surface wave on a homogeneous elastic half-space, is widely known to occur only for stress-free surfaces [15,16].…”

“…However, in this regard, the idea for the construction of the associated effective boundary conditions, which is also analogous to the interfacial conditions for hyperbolic-elliptic formulation to study the Rayleigh-type waves which firstly appeared in the works of Kaplunov and Kossovich [37], with further advances in [33]. The same method was also used for various propagation problems in elastic media, including coated half-spaces [8][9][10][11][12][13][14], where a pseudo-differential operator is realized, and the crack propagation scenario related to the mixed boundary value problems [22]. More so, the method provides the asymptotic formulas for the corrections to the Rayleigh wave speed in favor of the thin light coating that follows from the pseudo-differential equation along the half-space surface.…”

“…In brief, the present research is aimed at modeling and analyzing the propagation of plane surface wave scenarios with regard to a half-space coated by a light-coating layer under the influence of certain external forces. However, since there are a number of external forces in the literature, we will be considering the structure under deliberation to be exposed to the magnetic field force [12] and the normal mechanical load due to Winkler's elastic foundation [30,38,39] only, respectively, owing to their practical thoughts and natural occurrence. A methodology kit, comprising analytical and asymptotic tools, will be deployed, such that the influence of the coating layer is to be asymptotically tackled through the acquisition of apposite effective boundary conditions [10,13]-depending on the long-wave approximation condition [40].…”