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

Abstract

In this manuscript, the anti‐plane shear motion of an asymmetric three‐layered inhomogeneous elastic plate is examined. An asymptotic approach is employed for the present investigation. Both thgeneralized and unified dispersion relations within the long‐wave low‐frequency range have been successfully determined. The obtained unified dispersion relation is investigated taking into account the recently analyzed material contrast for layered plates with mixed stiff‐soft layers of different material properties. The asymptotic formulae for the respective fields in addition to the determination of approximate equations of motions have also been presented. A comparative study with the symmetric plate is made; being a special case of the asymmetric plate under consideration. In the end, we provide some deductions and concluding remarks.

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

“…This section deploys the asymptotic approach [7,[9][10][11][12] to analyze the acquired exact PDR. Indeed, it is important to note that classical numerical methods, such as finite difference and finite element methods, may introduce numerical dispersion when high-frequency components of the solution are truncated.…”

“…The analysis of multilayered structures is often more difficult than standard singlelayer structures due to inhomogeneous material characteristics among the layers of the structure. Different researchers have examined many dissimilar problems and analyzed vibrational response inhomogeneous beam composed of alternating stiffsoft components [6], three-layered laminate [7], three-layered plate [8][9][10][11][12][13], five-layered plate [14], multicomponent elastic rod, bar and wave-guides [15][16][17][18][19] due to the extensive uses of layered structures in current innovative and hybrid technology. Furthermore, the authors [20][21][22][23][24][25][26][27] have highlighted the effects of external forces such as damping effects, magneto-electroelastic, thermal stress, hygrothermal response, magnetic fields, and rotation on the propagation of waves in multilayer media.…”

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

“…The waveguides, elastic plates, beams, laminates, panels, rods, as well as cylindrical shells, are some of the structures that may be found in multiply-bond layers, to highlight a few, see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] In terms of layered structure design and structural analysis, which frequently has contrasting material and geometrical parameters, such as size, volume density, and stiffness. Layered structures offer advantages such as high resistance, lightweight, and strength; additionally, they have static and dynamic excitations.…”

“…The application of asymptotic techniques [22][23][24] enhances a better understanding of the relationship between the contrast in parameters of its components and the lowest eigenfrequencies of the structure. The authors 7,[11][12][13][17][18][19][20][21][22][23] used asymptotic analysis to investigate the elastic waves dispersion in highly inhomogeneous multilayered structures having three and five layers, exclusively sandwich structures with contrasting material parameter setups, and analyzed the cut-off frequency properties. In addition, regarding the influence of external forces like a hygro-thermal response, thermal stress, rotation, magnetic fields, and viscoelasticity.…”

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

“…This subject is governed by Hooke's law and the famous Newton's second law of motion, among others, for appropriately modeling different wave propagation problems in diverse elastic media and structures. Furthermore, engineering fields including aerospace, civil, seismic, and marine, to mention a few, are known to enjoy many contributions from the elasticity theory (see [1][2][3][4][5][6]). A more particular concern in this study is the modeling and analysis of coated half-space.…”