Investigating the viscous damping effects on the propagation of Rayleigh waves in a three-layered inhomogeneous plate

Abstract

The present paper investigates the propagation of anti-plane Rayleigh waves in an elastic three-layered inhomogeneous plate in the presence of viscous damping. The core layer is sandwiched between skin layers with appropriate perfect interfacial boundary conditions, while traction-free conditions are prescribed on the outer faces. The eigenfunctions expansion method is employed for the study. Various cases of damped and undamped situations have been examined in connection to the obtained displacements and shear stresses. Finally, the effects of viscous damping on the propagation of Rayleigh waves are reported graphically using some physical available data.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations

“…In addition, regarding the influence of external forces like a hygro-thermal response, thermal stress, rotation, magnetic fields, and viscoelasticity. [26][27][28][29][30][31] Likewise, for the significance of cracks and void pores on the propagation of waves in layered mediums, see Refs. 32,33 and the references therein.…”

Studies on Love Waves. Part 1. Nonlinear Modulation of Love Waves on a Heterogeneous Half-Space covered by a Homogeneous Layer

“…Under the condition that the shear wave velocity of the layer must be slower than the shear wave velocity of the half-space, the existence of a horizontally shear wave, having an amplitude that decayed rapidly with the thickness in the half-space, was shown. Later, elastic waves in different contexts such as exact solutions [7], a comparative study [8], large-amplitude [9], heterogeneity [10][11][12][13], layered structures [14][15][16][17][18] were considered.…”

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.…”

“…The material contrast setup considered in 10 for a three-layered plate with stiff skin layers and soft core layer will be investigated here for the long-wave low-frequency dispersion. Moreover, the choice of a three-layered structure in this study is connected to its various needs and emergence in many engineering applications in addition to its different forms comprising of plates 1,[9][10][11]19,21 as well as canonical and cylindrical shells 23 and, 24 respectively. The manuscript is arranged as follows: Section 2 gives the problem formulation, the determination of the dispersion relation and cut-off frequency is presented in Section 3 for the generalized case and in Section 4 for the unified case.…”