Torsional Wave Propagation in a Pre-Stressed Structure with Corrugated and Loosely Bonded Surfaces

Abstract

An analytical model is presented to study the behaviour of propagation of torsional surface waves in initially stressed porous layer, sandwiched between an orthotropic half-space with initial stress and pre-stressed inhomogeneous anisotropic half-space. The boundary surfaces of the layer and halfspaces are taken as corrugated, as well as loosely bonded. The heterogeneity of the lower half-space is due to trigonometric variation in elastic parameters of the pre-stressed inhomogeneous anisotropic medium. Expression for dispersion relation has been obtained in closed form for the present analytical model to observe the effect of undulation parameter, flatness parameter and porosity on the propagation of torsional surface waves. The obtained dispersion relation is found to be in well agreement with classical Love wave equation for a particular case. The cases of ideally smooth interface and welded interface have also been analysed. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, wave number, heterogeneity parameter and initial stress on the phase velocity of torsional surface waves.KEY WORDS: Corrugation, loose bonding, dispersion, orthotropic, heterogeneity LIST OF SYMBOLSK is the effective bonding parameter; k is the wave number; ς is the pure real number; g 1 (r) is the corrugated boundary surfaces of the porous layer; g 2 (r) is the corrugated boundary surfaces of lower the half-space;H is the thickness of the layer; z are the components of displacement for the upper half-space; D, F are the rigidity of upper half-space along radial and axial direction; P is the initial stress for the upper half-space; β 1 is the shear wave velocity for the upper half-space; J 1 (kr) is the Bessel's function of first order; ij are the components of stress for the porous layer; wz are the components of solid phase displacements for the porous layer; W r , W θ , W z are the components of fluid phase displacements for the porous layer; P 1 is the initial stress for the porous layer; u r , u θ , u z are the rotational components for the porous layer; α ij are the strain components for the porous layer; p f is the pressure in the fluid of porous layer; π is the porosity of the poroelastic layer; ρ rr , ρ rθ , ρ θθ are the mass coefficients;is the density the solid-liquid for the porous layer; p s , p f are the mass densities of the solid and liquid for the porous layer;N , L are the rigidities of the porous layer, along radial and axial direction;Q is the porosity parameter for the porous layer; β 2 is the shear wave velocity of porous layer; τ ij are stress components for the lower inhomogeneous anisotropic half-space; α is the heterogeneity parameter for the lower half-space; P is the initial stress for the lower half-space; ρ 3 is the density of the lower medium; β 3 is the shear wave velocity for the lower half-space; L , A are the rigidity of the lower half-space along radial and axial direction;Ω 1 is bonding parameter of common interface of upper half-space and ...

Analysis of integrated effect of irregularity and corrugated interfaces of doubly layered half space on torsional surface wave propagation

“…So, it is important to study the influence of these imperfect interfaces on the torsional phase velocity. Propagation characteristics of surface wave on different type of interfaces were studied by Zang and Shinozuka [6], Singh and Lakshman [7], Tomar and Kaur [8], Sahu et al [9], Singh and Sahu [10], Saha et al [11], Singh et al [12], and Pal et al [13].…”

Propagation of the torsional wave in an irregular self-reinforced composite material bounded between two half-spaces

“…The Earth's surface may not only be considered as a plane surface but a surface having irregular boundaries. Elastic wave propagation in irregular layered media has been substantially encapsulated in many research works such as Kaur and Tomar (2005), Kaur et al (2005), Chattopadhyay et al (2009), Singh and Sahu (2017), etc.…”