Dispersion of Elastic Waves in an Asymmetric Three-Layered Structure in the Presence of Magnetic and Rotational Effects

Abstract

The present paper investigates the propagation and dispersion of elastic surface waves in an asymmetric inhomogeneous isotropic three-layered plate in the presence of magnetic field and rotational effects. The skin layers are exposed to an external magnetic field force while the core layer is assumed to be in a rotational frame of reference, which are perfectly bounded together with free-ends conditions. The resultant displacements and shear stresses in the respective layers are derived analytically together with the general dispersion relation. Further, the general dispersion relation is analyzed for some physical cases of interest. Finally, the effects of the magnetic field, rotation, and electric field on the propagation and dispersion of the present model are presented graphically.

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

“…This section gives the numerical simulation and results of the formulated problem by considering some physical data of interest in both the coating and half-space. Moreover, copper material is considered for the coating layer, while aluminum is chosen for the half-plane, which respectively admit the following physical data [23,28,29]:…”

“…The celebrated equation of motion in an elastic isotropic homogeneous medium with body forces F i and gravity G i is given via Einstein summation by [28][29][30][31][32][33][34]…”

“…Moreover, the gravitational field force G i is considered based on Biot's definition [40,41]. Finally, when the media are assumed to be in moving frame with only centripetal acceleration, the acceleration in Equation ( 1) becomes [29,32,34]…”

“…The techniques are computational, analytical, and asymptotic to appropriately analyze the governing model. We mention here certain methods in [27][28][29][30][31][32][33][34][35][36][37][38][39], where such methodologies were utilized, including the integral transform approach, normal mode analysis approach, harmonic solution approach, eigenvalues approach, and some numerical schemes, among others.…”

Asymptotic approach to anti‐plane dynamic problem of asymmetric three‐layered composite plate

“…For instance, the investigation of elec-tromechanical propagation in pre-stressed layered piezoelectric materials, 17 the dispersion of shear waves in piezoelectric layered cylinders with initial stresses, 18 and the influence of magnetic and rotational effects on the wave propagation in elastic three-layered laminates. 19 We have equally got other relevance including the SH waves propagation in nonlinear heterogeneous plates, 20 the effect of viscous damping on the propagation of waves in three-layered composites, 21 and the diffraction of electromagnetic waves in bi-isotropic homogeneous media, 22 to mention a few. Moreover, the literature on multilayered media is indeed very rich and accommodates various features counting the stability and vibrational analysis aspects of multilayered canonical, cylindrical, and rectangular shells [23][24][25][26] as well as examining different wave forms in a variety of structures.…”