Dispersion of elastic waves in a layer interacting with a Winkler foundation

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

This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

Surface Wave Propagation in a Rotating Doubly Coated Nonhomogeneous Half Space with Application

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

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

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.

A new Rayleigh-like wave in guided propagation of antiplane waves in couple stress materials

Motivated by the unexpected appearance of shear horizontal Rayleigh surface waves, we investigate the mechanics of antiplane wave reflection and propagation in couple stress (CS) elastic materials. Surface waves arise by mode conversion at a free surface, whereby bulk travelling waves trigger inhomogeneous modes. Indeed, Rayleigh waves are perturbations of the travelling mode and stem from its reflection at grazing incidence. As is well known, they correspond to the real zeros of the Rayleigh function. Interestingly, we show that the same generating mechanism sustains a new inhomogeneous wave, corresponding to a purely imaginary zero of the Rayleigh function. This wave emerges from 'reflection' of a bulk standing mode: This produces a new type of Rayleigh-like wave that travels away from, as opposed to along, the free surface, with a speed lower than that of bulk shear waves. Besides, a third complex zero of the Rayleigh function may exist, which represents waves attenuating/exploding both along and away from the surface. Since none of these zeros correspond to leaky waves, a new classification of the Rayleigh zeros is proposed. Furthermore, we extend to CS elasticity Mindlin's boundary conditions, by which partial waves are identified, whose interference lends Rayleigh-Lamb guided waves. Finally, asymptotic analysis in the thin-plate limit provides equivalent one-dimensional models.