The influence of heterogeneity and initial stress on the propagation of Love-type wave in a transversely isotropic layer subjected to rotation

Introduction: In this paper, a mathematical model of Love-type wave propagation in a heterogeneous transversely isotropic elastic layer subjected to initial stress and rotation of the resting on a rigid foundation. Frequency equation of Love-type wave is obtained in closed form. The material constants and initial stress have been taken as space dependent and arbitrary functions of depth in the respective media. Objectives: The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, rotation, wave number, the phase velocity on the Love-type wave propagation. Methods: The analytical solution has been obtained, we have used the separation of variables, method and the numerical solution using the bisection method implemented in MATLAB. Results: We present a general dispersion relation to describe the impacts as the propagation of Love-type waves in the structures. Numerical results analyzing the dispersion equation are discussed and presented graphically. Moreover, the obtained dispersion relation is found in well agreement with the classical case in isotropic and transversely isotropic layer resting on a rigid foundation. Finally, some graphical presentations have been made to assess the effects of various parameters in the plane wave propagation in elastic media of different nature.

Study of Axi-Symmetric Vibrations in a Micropolar Transversely Isotropic Layer

The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.

Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source

Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool to calculate the interior deformations of the model; consequently, we obtain a closed-form dispersion relation for the wave. Six numerical examples for the transversely isotropic layer, namely, beryl, magnesium, cadmium, zinc, cobalt, and simply isotropic, have been considered. The role of magneto-elastic coupling parameter, hydrostatic stress, inhomogeneity, the order of the depth variation in inhomogeneity function, and different examples of the layer on the propagation of Love-type wave has been observed by numerical examples and graphical demonstrations.